Machine Learning  Machine learning, a branch of artificial intelligence, concerns the construction and study of systems that can learn from data. For example, a machine learning system could be trained on email messages to learn to distinguish between spam and nonspam messages. After learning, it can then be used to classify new email messages into spam and nonspam folders. The core of machine learning deals with representation and generalization. Representation of data instances and functions evaluated on these instances are part of all machine learning systems. Generalization is the property that the system will perform well on unseen data instances; the conditions under which this can be guaranteed are a key object of study in the subfield of computational learning theory. 
Machine Learning Algorithms alphabetically  A list of machine learning algorithms 
Machine Learning Algorithms by Category  A list of machine learning algorithms 
Machine Learning Canvas  A framework to connect the dots between data collection, machine learning, and value creation 
Machine Listening Intelligence  This manifesto paper will introduce machine listening intelligence, an integrated research framework for acoustic and musical signals modelling, based on signal processing, deep learning and computational musicology. 
Machine Teaching  In this paper, we consider the problem of machine teaching, the inverse problem of machine learning. Different from traditional machine teaching which views the learners as batch algorithms, we study a new paradigm where the learner uses an iterative algorithm and a teacher can feed examples sequentially and intelligently based on the current performance of the learner. We show that the teaching complexity in the iterative case is very different from that in the batch case. Instead of constructing a minimal training set for learners, our iterative machine teaching focuses on achieving fast convergence in the learner model. Depending on the level of information the teacher has from the learner model, we design teaching algorithms which can provably reduce the number of teaching examples and achieve faster convergence than learning without teachers. We also validate our theoretical findings with extensive experiments on different data distribution and real image datasets. 
Machine Vision (MV) 
Machine vision (MV) is the technology and methods used to provide imagingbased automatic inspection and analysis for such applications as automatic inspection, process control, and robot guidance in industry. The scope of MV is broad. MV is related to, though distinct from, computer vision. 
Machines Talking To Machines (M2M) 
We propose Machines Talking To Machines (M2M), a framework combining automation and crowdsourcing to rapidly bootstrap endtoend dialogue agents for goaloriented dialogues in arbitrary domains. M2M scales to new tasks with just a task schema and an API client from the dialogue system developer, but it is also customizable to cater to taskspecific interactions. Compared to the WizardofOz approach for data collection, M2M achieves greater diversity and coverage of salient dialogue flows while maintaining the naturalness of individual utterances. In the first phase, a simulated user bot and a domainagnostic system bot converse to exhaustively generate dialogue ‘outlines’, i.e. sequences of template utterances and their semantic parses. In the second phase, crowd workers provide contextual rewrites of the dialogues to make the utterances more natural while preserving their meaning. The entire process can finish within a few hours. We propose a new corpus of 3,000 dialogues spanning 2 domains collected with M2M, and present comparisons with popular dialogue datasets on the quality and diversity of the surface forms and dialogue flows. 
MAgent  We introduce MAgent, a platform to support research and development of manyagent reinforcement learning. Unlike previous research platforms on single or multiagent reinforcement learning, MAgent focuses on supporting the tasks and the applications that require hundreds to millions of agents. Within the interactions among a population of agents, it enables not only the study of learning algorithms for agents’ optimal polices, but more importantly, the observation and understanding of individual agent’s behaviors and social phenomena emerging from the AI society, including communication languages, leaderships, altruism. MAgent is highly scalable and can host up to one million agents on a single GPU server. MAgent also provides flexible configurations for AI researchers to design their customized environments and agents. In this demo, we present three environments designed on MAgent and show emerged collective intelligence by learning from scratch. 
Magnetic Laplacian Matrix  MagneticMap 
MagnitudeShape Plot  This article proposes a new graphical tool, the magnitudeshape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MSplot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. A dividing curve or surface is provided to separate nonoutlying data from the outliers. Both the simulated data and the practical examples confirm that the MSplot is superior to existing tools for visualizing centrality and detecting outliers for functional data. 
Mahalanobis Distance  The Mahalanobis distance is a descriptive statistic that provides a relative measure of a data point’s distance (residual) from a common point. It is a unitless measure introduced by P. C. Mahalanobis in 1936. The Mahalanobis distance is used to identify and gauge similarity of an unknown sample set to a known one. It differs from Euclidean distance in that it takes into account the correlations of the data set and is scaleinvariant. In other words, it has a multivariate effect size. 
Malware Analysis and Attributed using Genetic Information (MAAGI) 
Artificial intelligence methods have often been applied to perform specific functions or tasks in the cyberdefense realm. However, as adversary methods become more complex and difficult to divine, piecemeal efforts to understand cyberattacks, and malwarebased attacks in particular, are not providing sufficient means for malware analysts to understand the past, present and future characteristics of malware. In this paper, we present the Malware Analysis and Attributed using Genetic Information (MAAGI) system. The underlying idea behind the MAAGI system is that there are strong similarities between malware behavior and biological organism behavior, and applying biologically inspired methods to corpora of malware can help analysts better understand the ecosystem of malware attacks. Due to the sophistication of the malware and the analysis, the MAAGI system relies heavily on artificial intelligence techniques to provide this capability. It has already yielded promising results over its development life, and will hopefully inspire more integration between the artificial intelligence and cyber–defense communities. 
Managed Memory Computing (MMC) 
Aggregated data cubes are the most effective form of storage of aggregated or summarized data for quick analysis. This technology is driven by Online Analytical Processing technology. Utilizing these data cubes involves intense disk I/O operations. This at times lowers the speed for users of data. Conventional, inmemory processing does not rely on stored and summarized or aggregated data but brings all the relevant data to the memory. This technology then utilizes intense processing and large amounts of memory to perform all calculations and aggregations while in memory. Managed Memory Computing blends the best of both methods, allowing users to define data cubes with perstructured and aggregated data, providing a logical business layer to users, and offering inmemory computation. These features make the response time for user interactions far superior and enable the most balanced approach between disk I/O and inmemory processing. The hybrid approach of Managed Memory Computing provides analysis, dashboards, graphical interaction, ad hoc querying, presentation, and discussion driven analytic at blazing speeds, making the Business Intelligence Tool ready for everything from an interactive session in the boardroom to a production planning meeting on the factory floor. 
Managed R Archive Network (MRAN) 
Revolution Analytics’ Managed R Archive Network 
Mandolin  Markov Logic Networks join probabilistic modeling with firstorder logic and have been shown to integrate well with the Semantic Web foundations. While several approaches have been devised to tackle the subproblems of rule mining, grounding, and inference, no comprehensive workflow has been proposed so far. In this paper, we fill this gap by introducing a framework called Mandolin, which implements a workflow for knowledge discovery specifically on RDF datasets. Our framework imports knowledge from referenced graphs, creates similarity relationships among similar literals, and relies on stateoftheart techniques for rule mining, grounding, and inference computation. We show that our best configuration scales well and achieves at least comparable results with respect to other statisticalrelationallearning algorithms on link prediction. 
Manhattan Distance  Taxicab geometry, considered by Hermann Minkowski in 19th century Germany, is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates. The taxicab metric is also known as rectilinear distance, L1 distance or norm, city block distance, Manhattan distance, or Manhattan length, with corresponding variations in the name of the geometry. The latter names allude to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two intersections in the borough to have length equal to the intersections’ distance in taxicab geometry. 
Manhattan Plot  A Manhattan plot is a type of scatter plot, usually used to display data with a large number of datapoints – many of nonzero amplitude, and with a distribution of highermagnitude values, for instance in genomewide association studies (GWAS). It gains its name from the similarity of such a plot to the Manhattan skyline: a profile of skyscrapers towering above the lower level “buildings” which vary around a lower height. 
Manifold Learning  Manifold Learning (often also referred to as nonlinear dimensionality reduction) pursuits the goal to embed data that originally lies in a high dimensional space in a lower dimensional space, while preserving characteristic properties. This is possible because for any high dimensional data to be interesting, it must be intrinsically low dimensional. For example, images of faces might be represented as points in a high dimensional space (let’s say your camera has 5MP – so your images, considering each pixel consists of three values , lie in a 15M dimensional space), but not every 5MP image is a face. Faces lie on a submanifold in this high dimensional space. A submanifold is locally Euclidean, i.e. if you take two very similar points, for example two images of identical twins, you can interpolate between them and still obtain an image on the manifold, but globally not Euclidean – if you take two images that are very different – for example Arnold Schwarzenegger and Hillary Clinton – you cannot interpolate between them. I develop algorithms that map these high dimensional data points into a low dimensional space, while preserving local neighborhoods. This can be interpreted as a nonlinear generalization of PCA. 
ManiFool  Deep convolutional neural networks have been shown to be vulnerable to arbitrary geometric transformations. However, there is no systematic method to measure the invariance properties of deep networks to such transformations. We propose ManiFool as a simple yet scalable algorithm to measure the invariance of deep networks. In particular, our algorithm measures the robustness of deep networks to geometric transformations in a worstcase regime as they can be problematic for sensitive applications. Our extensive experimental results show that ManiFool can be used to measure the invariance of fairly complex networks on high dimensional datasets and these values can be used for analyzing the reasons for it. Furthermore, we build on Manifool to propose a new adversarial training scheme and we show its effectiveness on improving the invariance properties of deep neural networks. 
MannKendall Trend Test (MK Test) 
Given n consecutive observations of a time series zt; t = 1;…; n, Mann (1945) suggested using the Kendall rank correlation of zt with t; t = 1;…; n to test for monotonic trend. ➚ “Kendall Rank Correlation Coefficient” 
MapBased MultiPolicy Reinforcement Learning (MMPRL) 
In order for robots to perform missioncritical tasks, it is essential that they are able to quickly adapt to changes in their environment as well as to injuries and or other bodily changes. Deep reinforcement learning has been shown to be successful in training robot control policies for operation in complex environments. However, existing methods typically employ only a single policy. This can limit the adaptability since a large environmental modification might require a completely different behavior compared to the learning environment. To solve this problem, we propose Mapbased MultiPolicy Reinforcement Learning (MMPRL), which aims to search and store multiple policies that encode different behavioral features while maximizing the expected reward in advance of the environment change. Thanks to these policies, which are stored into a multidimensional discrete map according to its behavioral feature, adaptation can be performed within reasonable time without retraining the robot. An appropriate pretrained policy from the map can be recalled using Bayesian optimization. Our experiments show that MMPRL enables robots to quickly adapt to large changes without requiring any prior knowledge on the type of injuries that could occur. A highlight of the learned behaviors can be found here: https://youtu.be/qcCepAKL32U . 
Maple  Maple combines the world’s most powerful math engine with an interface that makes it extremely easy to analyze, explore, visualize, and solve mathematical problems. 
mapnik  Mapnik is a highpowered rendering library that can take GIS data from a number of sources (ESRI shapefiles, PostGIS databases, etc.) and use them to render beautiful 2dimensional maps. It’s used as the underlying rendering solution for a lot of online mapping services, most notably including MapQuest and the OpenStreetMap project, so it’s a truly productionquality framework. And, despite being written in C++, it comes with bindings for Python and Node, so you can leverage it in the language of your choice. Render Google Maps Tiles with Mapnik and Python 
MapReduce for C (MR4C) 
MR4C is an implementation framework that allows you to run native code within the Hadoop execution framework. Pairing the performance and flexibility of natively developed algorithms with the unfettered scalability and throughput inherent in Hadoop, MR4C enables largescale deployment of advanced data processing applications. 
Marimekko Chart  The Marimekko name has been adopted within business and the management consultancy industry to refer to a bar chart where all the bars are of equal height, there are no spaces between the bars, and the bars are in turn each divided into segments of different width. The design of the ‘marimekko’ chart is said to resemble a Marimekko print. The chart’s design encodes two variables (such as percentage of sales and market share), but it is criticised for making the data hard to perceive and to compare visually. 
Marked Point Process (MPP) 
A simple temporal point process (SPP) is an important class of time series, where the sample realization of the process is solely composed of the times at which events occur. Particular examples of point process data are neuronal spike patterns or spike trains, and a large number of distance and similarity metrics for those data have been proposed. A marked point process (MPP) is an extension of a simple temporal point process, in which a certain vector valued mark is associated with each of the temporal points in the SPP. Analyses of MPPs are of practical importance because instances of MPPs include recordings of natural disasters such as earthquakes and tornadoes. In this paper, we introduce an R package mmpp, which implements a number of distance and similarity metrics for SPP, and also extends those metrics for dealing with MPP. mmpp 
Marker Passing  
MarkerAssisted MiniPooling (mMPA) 
mMPA 
Market Basket Analysis (MBA) 
Market Basket Analysis is a modelling technique based upon the theory that if you buy a certain group of items, you are more (or less) likely to buy another group of items. For example, if you are in an English pub and you buy a pint of beer and don’t buy a bar meal, you are more likely to buy crisps (US. chips) at the same time than somebody who didn’t buy beer. The set of items a customer buys is referred to as an itemset, and market basket analysis seeks to find relationships between purchases. Typically the relationship will be in the form of a rule: IF {beer, no bar meal} THEN {crisps}. The probability that a customer will buy beer without a bar meal (i.e. that the antecedent is true) is referred to as the support for the rule. The conditional probability that a customer will purchase crisps is referred to as the confidence. The algorithms for performing market basket analysis are fairly straightforward (Berry and Linhoff is a reasonable introductory resource for this). The complexities mainly arise in exploiting taxonomies, avoiding combinatorial explosions (a supermarket may stock 10,000 or more line items), and dealing with the large amounts of transaction data that may be available. A major difficulty is that a large number of the rules found may be trivial for anyone familiar with the business. Although the volume of data has been reduced, we are still asking the user to find a needle in a haystack. Requiring rules to have a high minimum support level and a high confidence level risks missing any exploitable result we might have found. One partial solution to this problem is differential market basket analysis, as described below. 
Marketing Attribution  Attribution is the process of identifying a set of user actions (‘events’) that contribute in some manner to a desired outcome, and then assigning a value to each of these events. Marketing attribution provides a level of understanding of what combination of events influence individuals to engage in a desired behavior, typically referred to as a conversion. Attribution is the process of assigning credit to various marketing efforts when a sale is generated. In the modern world, this is no easy task. There are myriad ways to touch a customer today and the goal of attribution is to tease out the impact that each touch had in convincing you to make a purchase. Was it the email you were sent? Or the Google link you clicked? Or the banner ad you clicked when visiting a different site? Or the ad you saw with your video on YouTube? Or one of many other potential touch points? Or is it a mix? It is quite common today for a customer to have been exposed to multiple influences in the lead up to a purchase. How do you attribute the relationship? The question is not simply academic because it has real world consequences. Budgets are set based on performance. So, the person in charge of Google advertising has a huge motivation to ensure that they get all the credit they deserve. Also, accurate attribution will allow resources to be properly focused on the approaches that truly work best. https://…/1029 
Markov Blanket  In machine learning, the Markov blanket for a node A in a Bayesian network is the set of nodes dA composed of A’s parents, its children, and its children’s other parents. In a Markov network, the Markov blanket of a node is its set of neighboring nodes. A Markov blanket may also be denoted by MB(A). The Markov blanket of a node contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node. The term was coined by Pearl in 1988. In a Bayesian network, the values of the parents and children of a node evidently give information about that node; however, its children’s parents also have to be included, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent nodes. 
Markov Brains  Markov Brains are a class of evolvable artificial neural networks (ANN). They differ from conventional ANNs in many aspects, but the key difference is that instead of a layered architecture, with each node performing the same function, Markov Brains are networks built from individual computational components. These computational components interact with each other, receive inputs from sensors, and control motor outputs. The function of the computational components, their connections to each other, as well as connections to sensors and motors are all subject to evolutionary optimization. Here we describe in detail how a Markov Brain works, what techniques can be used to study them, and how they can be evolved. 
Markov Chain  A Markov chain (discretetime Markov chain or DTMC), named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another on a state space. It is a random process usually characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of ‘memorylessness’ is called the Markov property. Markov chains have many applications as statistical models of realworld processes. http://…/9789814451505 
Markov Chain Las Vegas (MCLV) 
We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum number of Markov chain steps K (referred as MCLVK). We present a MCLVK gradient estimator (LVSK) for RBMs and explore the correspondence and differences between LVSK and Contrastive Divergence (CDK), with LVSK significantly outperforming CDK training RBMs over the MNIST dataset, indicating MCLV to be a promising direction in learning generative models. 
Markov Chain Monte Carlo (MCMC) 
In statistics, Markov chain Monte Carlo (MCMC) methods (which include random walk Monte Carlo methods) are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample of the desired distribution. The quality of the sample improves as a function of the number of steps. Usually it is not hard to construct a Markov chain with the desired properties. The more difficult problem is to determine how many steps are needed to converge to the stationary distribution within an acceptable error. A good chain will have rapid mixingthe stationary distribution is reached quickly starting from an arbitrary positiondescribed further under Markov chain mixing time 
Markov Cluster Algorithm (MCL) 
The MCL algorithm is short for the Markov Cluster Algorithm, a fast and scalable unsupervised cluster algorithm for graphs (also known as networks) based on simulation of (stochastic) flow in graphs. MCL 
Markov Decision Process (MDP) 
Markov decision processes (MDPs), named after Andrey Markov, provide a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying a wide range of optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s (cf. Bellman 1957). A core body of research on Markov decision processes resulted from Ronald A. Howard’s book published in 1960, Dynamic Programming and Markov Processes. They are used in a wide area of disciplines, including robotics, automated control, economics, and manufacturing. 
Markov Logic Networks (MLN) 
A Markov logic network (or MLN) is a probabilistic logic which applies the ideas of a Markov network to firstorder logic, enabling uncertain inference. Markov logic networks generalize firstorder logic, in the sense that, in a certain limit, all unsatisfiable statements have a probability of zero, and all tautologies have probability one. Markov Logic Networks 
Markov Random Field (MRF) 
In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. A Markov random field is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can’t represent certain dependencies that a Bayesian network can (such as induced dependencies). 
Mashboard  Also called realtime dashboard, a mashboard is a Web 2.0 buzzword that is used to describe analytic mashups that allow businesses to create or add components that may analyze and present data, look up inventory, accept orders, and other tasks without ever having to access the system that carries out the transaction. 
Masked Autoencoder for Distribution Estimation (MADE) 
There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our method masks the autoencoder’s parameters to respect autoregressive constraints: each input is reconstructed only from previous inputs in a given ordering. Constrained this way, the autoencoder outputs can be interpreted as a set of conditional probabilities, and their product, the full joint probability. We can also train a single network that can decompose the joint probability in multiple different orderings. Our simple framework can be applied to multiple architectures, including deep ones. Vectorized implementations, such as on GPUs, are simple and fast. Experiments demonstrate that this approach is competitive with stateof theart tractable distribution estimators. At test time, the method is significantly faster and scales better than other autoregressive estimators. GitXiv 
Mass Displacement Network (MDN) 
Despite the large improvements in performance attained by using deep learning in computer vision, one can often further improve results with some additional postprocessing that exploits the geometric nature of the underlying task. This commonly involves displacing the posterior distribution of a CNN in a way that makes it more appropriate for the task at hand, e.g. better aligned with local image features, or more compact. In this work we integrate this geometric postprocessing within a deep architecture, introducing a differentiable and probabilistically sound counterpart to the common geometric voting technique used for evidence accumulation in vision. We refer to the resulting neural models as Mass Displacement Networks (MDNs), and apply them to human pose estimation in two distinct setups: (a) landmark localization, where we collapse a distribution to a point, allowing for precise localization of body keypoints and (b) communication across body parts, where we transfer evidence from one part to the other, allowing for a globally consistent pose estimate. We evaluate on largescale pose estimation benchmarks, such as MPII Human Pose and COCO datasets, and report systematic improvements when compared to strong baselines. 
Mass Personalization  Mass personalization is defined as custom tailoring by a company in accordance with its end users tastes and preferences. From collaborative engineering perspective, mass customization can be viewed as collaborative efforts between customers and manufacturers, who have different sets of priorities and need to jointly search for solutions that best match customers’ individual specific needs with manufacturers’ customization capabilities. The main difference between mass customization and mass personalization is that customization is the ability for a company to give its customers an opportunity to create and choose product to certain specifications, but does have limits. Clothing industry has also adopted the mass customization paradigm and some footwear retailers are producing mass customized shoes. The gaming market is seeing personalization in the new custom controller industry. A new, and notable, company called “Experience Custom” gives customers the opportunity to order personalized gaming controllers. A website knowing a user’s location, and buying habits, will present offers and suggestions tailored to the user’s demographics; this is an example of mass personalization. The personalization is not individual but rather the user is first classified and then the personalization is based on the group they belong to. Behavioral targeting represents a concept that is similar to mass personalization. 
Massive Online Analysis (MOA) 
MOA (Massive Online Analysis) is a free opensource software specific for Data stream mining with Concept drift. It’s written in Java and developed at the University of Waikato, New Zealand. MOA is an opensource framework software that allows to build and run experiments of machine learning or data mining on evolving data streams. It includes a set of learners and stream generators that can be used from the Graphical User Interface (GUI), the commandline, and the Java API. MOA contains several collections of machine learning algorithms for classification, regression, clustering, outlier detection and recommendation engines. http://moa.cms.waikato.ac.nz 
Massive Open Online Course (MOOC) 
A Massive Open Online Course (MOOC) is an online course aimed at unlimited participation and open access via the web. In addition to traditional course materials such as videos, readings, and problem sets, MOOCs provide interactive user forums that help build a community for students, professors, and teaching assistants (TAs). MOOCs are a recent development in distance education which began to emerge in 2012. 
Matchbox  We present a probabilistic model for generating personalised recommendations of items to users of a web service. The Matchbox system makes use of content information in the form of user and item meta data in combination with collaborative filtering information from previous user behavior in order to predict the value of an item for a user. Users and items are represented by feature vectors which are mapped into a lowdimensional ‘trait space’ in which similarity is measured in terms of inner products. The model can be trained from different types of feedback in order to learn useritem preferences. Here we present three alternatives: direct observation of an absolute rating each user gives to some items, observation of a binary preference (like/ don’t like) and observation of a set of ordinal ratings on a userspecific scale. Efficient inference is achieved by approximate message passing involving a combination of Expectation Propagation (EP) and Variational Message Passing. We also include a dynamics model which allows an item’s popularity, a user’s taste or a user’s personal rating scale to drift over time. By using AssumedDensity Filtering (ADF) for training, the model requires only a single pass through the training data. This is an online learning algorithm capable of incrementally taking account of new data so the system can immediately reflect the latest user preferences. We evaluate the performance of the algorithm on the MovieLens and Netflix data sets consisting of approximately 1,000,000 and 100,000,000 ratings respectively. This demonstrates that training the model using the online ADF approach yields stateoftheart performance with the option of improving performance further if computational resources are available by performing multiple EP passes over the training data. 
MatchZoo  In recent years, deep neural models have been widely adopted for text matching tasks, such as question answering and information retrieval, showing improved performance as compared with previous methods. In this paper, we introduce the MatchZoo toolkit that aims to facilitate the designing, comparing and sharing of deep text matching models. Specifically, the toolkit provides a unified data preparation module for different text matching problems, a flexible layerbased model construction process, and a variety of training objectives and evaluation metrics. In addition, the toolkit has implemented two schools of representative deep text matching models, namely representationfocused models and interactionfocused models. Finally, users can easily modify existing models, create and share their own models for text matching in MatchZoo. 
Math Kernel Library (MKL) 
Intel Math Kernel Library (Intel MKL) is a library of optimized math routines for science, engineering, and financial applications. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms, and vector math. The routines in MKL are hand optimized by exploiting Intel’s multicore and manycore processors. The library supports Intel and compatible processors and is available for Windows, Linux and OS X operating systems. MKL functions are optimized with each new processor releases from Intel. 
Mathematica  Mathematica is a computational software program used in many scientific, engineering, mathematical and computing fields, based on symbolic mathematics. It was conceived by Stephen Wolfram and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica. 
Mathematical Statistics  Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state – the collection and analysis of facts about a country: its economy, land, military, population, and so forth. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measuretheoretic probability theory. 
Mathematics  Mathematics (from Greek μάθημα máthēma, ‘knowledge, study, learning’), often shortened to maths or math, is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. 
MathJax  A JavaScript display engine for mathematics that works in all browsers. 
MATLAB  MATLAB is the highlevel language and interactive environment used by millions of engineers and scientists worldwide. It lets you explore and visualize ideas and collaborate across disciplines including signal and image processing, communications, control systems, and computational finance. You can use MATLAB in projects such as modeling energy consumption to build smart power grids, developing control algorithms for hypersonic vehicles, analyzing weather data to visualize the track and intensity of hurricanes, and running millions of simulations to pinpoint optimal dosing for antibiotics. 
MatricizedTensor Times KhatriRao Product (MTTKRP) 
The matricizedtensor times KhatriRao product (MTTKRP) is the computational bottleneck for algorithms computing CP decompositions of tensors. In this paper, we develop sharedmemory parallel algorithms for MTTKRP involving dense tensors. The algorithms cast nearly all of the computation as matrix operations in order to use optimized BLAS subroutines, and they avoid reordering tensor entries in memory. We benchmark sequential and parallel performance of our implementations, demonstrating high sequential performance and efficient parallel scaling. We use our parallel implementation to compute a CP decomposition of a neuroimaging data set and achieve a speedup of up to $7.4\times$ over existing parallel software. 
Matrix Calculus  In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices (rather than row vectors). A single convention can be somewhat standard throughout a single field that commonly use matrix calculus (e.g. econometrics, statistics, estimation theory and machine learning). However, even within a given field different authors can be found using competing conventions. Authors of both groups often write as though their specific convention is standard. Serious mistakes can result when combining results from different authors without carefully verifying that compatible notations are used. Therefore great care should be taken to ensure notational consistency. Definitions of these two conventions and comparisons between them are collected in the layout conventions section. 
Matrix Decomposition  In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. 
Matrixcentric Neural Networks  We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as central to the architecture and they compose the input, hidden and output layers. The model representation is more compact and elegant – the number of parameters grows only with the largest dimension of the incoming layer rather than the number of hidden units. We derive feedforward nets that map an input matrix into an output matrix, and recurrent nets which map a sequence of input matrices into a sequence of output matrices. Experiments on handwritten digits recognition, face reconstruction, sequence to sequence learning and EEG classification demonstrate the efficacy and compactness of the matrixcentric architectures. 
MatrixVariate Gaussian (MVG) 
Differential privacy mechanism design has traditionally been tailored for a scalarvalued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrixvalued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the MatrixVariate Gaussian (MVG) mechanism, which adds a matrixvalued noise drawn from a matrixvariate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves $(\epsilon,\delta)$differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrixvalued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrixvalued queries on three privacysensitive datasets. We find that the MVG mechanism notably outperforms four previous stateoftheart approaches, and provides comparable utility to the nonprivate baseline. Our work thus presents a promising prospect for both future research and implementation of differential privacy for matrixvalued query functions. 
Matroid  In combinatorics, a branch of mathematics, a matroid is a structure that captures and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions. Matroid theory borrows extensively from the terminology of linear algebra and graph theory, largely because it is the abstraction of various notions of central importance in these fields. Matroids have found applications in geometry, topology, combinatorial optimization, network theory and coding theory. 
Matthews Correlation Coefficient (MCC) 
The Matthews Correlation Coefficient (MCC) has a range of 1 to 1 where 1 indicates a completely wrong binary classifier while 1 indicates a completely correct binary classifier. Using the MCC allows one to gauge how well their classification model/function is performing. Another method for evaluating classifiers is known as the ROC curve. Wikipedia mccr 
Maucha Diagrams  This diagram was proposed by Rezso Maucha in 1932 as a way to vizualise the relative ionic composition of water samples. oviz 
Maxima Units Search (MUS) 
An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture models. Here we introduce it on its own and explore possible applications in different contexts. 
Maximal Information Coefficient (MIC) 
In statistics, the maximal information coefficient (MIC) is a measure of the strength of the linear or nonlinear association between two variables X and Y. The MIC belongs to the maximal informationbased nonparametric exploration (MINE) class of statistics. In a simulation study, MIC outperformed some selected low power tests, however concerns have been raised regarding reduced statistical power in detecting some associations in settings with low sample size when compared to powerful methods such as distance correlation and HHG. Comparisons with these methods, in which MIC was outperformed, were made in and. It is claimed that MIC approximately satisfies a property called equitability which is illustrated by selected simulation studies. It was later proved that no nontrivial coefficient can exactly satisfy the equitability property as defined by Reshef et al. Some criticisms of MIC are addressed by Reshef et al. in further studies published on arXiv. 
Maximal Label Search (MLS) 
Many graph search algorithms use a vertex labeling to compute an ordering of the vertices. We examine such algorithms which compute a peo (perfect elimination ordering) of a chordal graph and corresponding algorithms which compute an meo (minimal elimination ordering) of a nonchordal graph, an ordering used to compute a minimal triangulation of the input graph. We express all known peocomputing search algorithms as instances of a generic algorithm called MLS (maximal label search) and generalize Algorithm MLS into CompMLS, which can compute any peo. We then extend these algorithms to versions which compute an meo and likewise generalize all known meocomputing search algorithms. We show that not all minimal triangulations can be computed by such a graph search, and, more surprisingly, that all these search algorithms compute the same set of minimal triangulations, even though the computed meos are different. Finally, we present a complexity analysis of these algorithms. An extended abstract of part of this paper was published in WG 2005. Computing a clique tree with algorithm MLS (Maximal Label Search) 
Maximum a posteriori (MAP) 
In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is a mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to Fisher’s method of maximum likelihood (ML), but employs an augmented optimization objective which incorporates a prior distribution over the quantity one wants to estimate. MAP estimation can therefore be seen as a regularization of ML estimation. 
Maximum Complex Correntropy Criterion (MCCC) 
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higherorder statistical moments in nonGaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued to elucidate its properties, nor how to best use it for optimization. This paper presents a probabilistic interpretation for correntropy using complexvalued data called complex correntropy. A recursive solution for the maximum complex correntropy criterion (MCCC) is introduced based on a fixed point solution. This technique is applied to a simple system identification case study, and the results demonstrate prominent advantages when compared to the complex recursive least squares (RLS) algorithm. By using such probabilistic interpretation, correntropy can be applied to solve several problems involving complex data in a more straightforward way. Keywords: complexvalued data correntropy, maximum complex correntropy criterion, fixedpoint algorithm. 
Maximum Entropy Flow Networks  Maximum Entropy Flow Networks 
Maximum Entropy Spectral Analysis (MESA) 

Maximum Inner Product Search (MIPS) 

Maximum Likelihood (ML) 
In statistics, maximumlikelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximumlikelihood estimation provides estimates for the model’s parameters. The method of maximum likelihood corresponds to many wellknown estimation methods in statistics. For example, one may be interested in the heights of adult female penguins, but be unable to measure the height of every single penguin in a population due to cost or time constraints. Assuming that the heights are normally (Gaussian) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish this by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable (given the model). In general, for a fixed set of data and underlying statistical model, the method of maximum likelihood selects the set of values of the model parameters that maximizes the likelihood function. Intuitively, this maximizes the ‘agreement’ of the selected model with the observed data, and for discrete random variables it indeed maximizes the probability of the observed data under the resulting distribution. Maximumlikelihood estimation gives a unified approach to estimation, which is welldefined in the case of the normal distribution and many other problems. However, in some complicated problems, difficulties do occur: in such problems, maximumlikelihood estimators are unsuitable or do not exist. 
Maximum Likelihood Estimates (MLE) 
In statistics, maximumlikelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximumlikelihood estimation provides estimates for the model’s parameters. 
Maximum Margin Interval Trees  Learning a regression function using censored or intervalvalued output data is an important problem in fields such as genomics and medicine. The goal is to learn a realvalued prediction function, and the training output labels indicate an interval of possible values. Whereas most existing algorithms for this task are linear models, in this paper we investigate learning nonlinear tree models. We propose to learn a tree by minimizing a marginbased discriminative objective function, and we provide a dynamic programming algorithm for computing the optimal solution in loglinear time. We show empirically that this algorithm achieves stateoftheart speed and prediction accuracy in a benchmark of several data sets. 
Maximum Margin Principal Components  Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first $K$ principal components minimizes the sum of squared errors between the original data and the projected data over all possible rank $K$ projections. Thus, PCA provides optimal lowrank representations of data for leastsquares linear regression under standard modeling assumptions. On the other hand, when the loss function for a prediction problem is not the leastsquares error, PCA is typically a heuristic choice of dimensionality reduction — in particular for classification problems under the zeroone loss. In this paper we target classification problems by proposing a straightforward alternative to PCA that aims to minimize the difference in margin distribution between the original and the projected data. Extensive experiments show that our simple approach typically outperforms PCA on any particular dataset, in terms of classification error, though this difference is not always statistically significant, and despite being a filter method is frequently competitive with Partial Least Squares (PLS) and Lasso on a wide range of datasets. 
Maximum Mean Discrepancy (MMD) 
The core idea in maximum mean discrepancy (MMD) in a reproducing kernel Hilbert space (RKHS) is to match two distributions based on the mean of features in the Hilbert space induced by a kernel K. This is justified because when K is universal there is an injection between the space of distributions and the space of mean feature vectors lying in its RKHS. From a practical perspective too, the MMD approach is appealing because unlike other parametric density estimation methods, it can be applied to arbitrary domains and to highdimensional data, and is computationally tractable. This approach was earlier used in the covariance shift problem (Gretton et al., 2009), the twosample problem (Gretton et al., 2012a), and recently in (Zhang et al., 2013) for estimating class ratios. 
Maximum Variance Total Variation Denoising (MVTV) 
We consider the problem of estimating a regression function in the common situation where the number of features is small, where interpretability of the model is a high priority, and where simple linear or additive models fail to provide adequate performance. To address this problem, we present Maximum Variance Total Variation denoising (MVTV), an approach that is conceptually related both to CART and to the more recent CRISP algorithm, a stateoftheart alternative method for interpretable nonlinear regression. MVTV divides the feature space into blocks of constant value and fits the value of all blocks jointly via a convex optimization routine. Our method is fully dataadaptive, in that it incorporates highly robust routines for tuning all hyperparameters automatically. We compare our approach against CART and CRISP via both a complexityaccuracy tradeoff metric and a human study, demonstrating that that MVTV is a more powerful and interpretable method. 
MaximumMargin Markov Network (M3N) 
In typical classification tasks, we seek a function which assigns a label to a single object. Kernelbased approaches, such as support vector machines (SVMs), which maximize the margin of confidence of the classifier, are the method of choice for many such tasks. Their popularity stems both from the ability to use highdimensional feature spaces, and from their strong theoretical guarantees. However, many realworld tasks involve sequential, spatial, or structured data, where multiple labels must be assigned. Existing kernelbased methods ignore structure in the problem, assigning labels independently to each object, losing much useful information. Conversely, probabilistic graphical models, such as Markov networks, can represent correlations between labels, by exploiting problem structure, but cannot handle highdimensional feature spaces, and lack strong theoretical generalization guarantees. In this paper, we present a new framework that combines the advantages of both approaches: Maximum margin Markov (M3) networks incorporate both kernels, which efficiently deal with highdimensional features, and the ability to capture correlations in structured data. We present an efficient algorithm for learning M3 networks based on a compact quadratic program formulation. We provide a new theoretical bound for generalization in structured domains. Experiments on the task of handwritten character recognition and collective hypertext classification demonstrate very significant gains over previous approaches. 
MaxMargin Deep Generative Models (mmDGMs) 
Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, it is relatively insufficient to empower the discriminative ability of DGMs on making accurate predictions. This paper presents maxmargin deep generative models (mmDGMs) and a classconditional variant (mmDCGMs), which explore the strongly discriminative principle of maxmargin learning to improve the predictive performance of DGMs in both supervised and semisupervised learning, while retaining the generative capability. In semisupervised learning, we use the predictions of a maxmargin classifier as the missing labels instead of performing full posterior inference for efficiency; we also introduce additional maxmargin and labelbalance regularization terms of unlabeled data for effectiveness. We develop an efficient doubly stochastic subgradient algorithm for the piecewise linear objectives in different settings. Empirical results on various datasets demonstrate that: (1) maxmargin learning can significantly improve the prediction performance of DGMs and meanwhile retain the generative ability; (2) in supervised learning, mmDGMs are competitive to the best fully discriminative networks when employing convolutional neural networks as the generative and recognition models; and (3) in semisupervised learning, mmDCGMs can perform efficient inference and achieve stateoftheart classification results on several benchmarks. 
Maxout Network  We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and because it is a natural companion to dropout) designed to both facilitate optimization by dropout and improve the accuracy of dropout’s fast approximate model averaging technique. We empirically verify that the model successfully accomplishes both of these tasks. We use maxout and dropout to demonstrate state of the art classification performance. Maxout Networks GitXiv 
McDiarmid Drift Detection Method (MDDM) 
Increasingly, Internet of Things (IoT) domains, such as sensor networks, smart cities, and social networks, generate vast amounts of data. Such data are not only unbounded and rapidly evolving. Rather, the content thereof dynamically evolves over time, often in unforeseen ways. These variations are due to socalled concept drifts, caused by changes in the underlying data generation mechanisms. In a classification setting, concept drift causes the previously learned models to become inaccurate, unsafe and even unusable. Accordingly, concept drifts need to be detected, and handled, as soon as possible. In medical applications and military zones, for example, change in behaviors should be detected in near realtime, to avoid potential loss of life. To this end, we introduce the McDiarmid Drift Detection Method (MDDM), which utilizes McDiarmid’s inequality in order to detect concept drift. The MDDM approach proceeds by sliding a window over prediction results, and associate window entries with weights. Higher weights are assigned to the most recent entries, in order to emphasize their importance. As instances are processed, the detection algorithm compares a weighted mean of elements inside the sliding window with the maximum weighted mean observed so far. A significant difference between the two weighted means, upperbounded by the McDiarmid inequality, implies a concept drift. Our extensive experimentation against synthetic and realworld data streams show that our novel method outperforms the stateoftheart. Specifically, MDDM yields shorter detection delays as well as lower false negative rates, while maintaining high classification accuracies. 
McNemar Test  In statistics, McNemar’s test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal (that is, whether there is “marginal homogeneity”). It is named after Quinn McNemar, who introduced it in 1947. An application of the test in genetics is the transmission disequilibrium test for detecting linkage disequilibrium. 
Mean Absolute Deviation (MAD) 
The mean absolute deviation (MAD), also referred to as the mean deviation (or sometimes average absolute deviation, though see above for a distinction), is the mean of the absolute deviations of a set of data about the data’s mean. In other words, it is the average distance of the data set from its mean. MAD has been proposed to be used in place of standard deviation since it corresponds better to real life. Because the MAD is a simpler measure of variability than the standard deviation, it can be used as pedagogical tool to help motivate the standard deviation. 
Mean Absolute Percentage Deviation (MAPD) 
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of accuracy of a method for constructing fitted time series values in statistics, specifically in trend estimation. It usually expresses accuracy as a percentage, 
Mean Average Percentage Error (MAPE) 
The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of accuracy of a method for constructing fitted time series values in statistics, specifically in trend estimation. It usually expresses accuracy as a percentage, 
Mean Directional Accuracy (MDA) 
Mean Directional Accuracy (MDA), also known as Mean Direction Accuracy, is a measure of prediction accuracy of a forecasting method in statistics. It compares the forecast direction (upward or downward) to the actual realized direction. In simple words, MDA provides the probability that the under study forecasting method can detect the correct direction of the time series. MDA is a popular metric for forecasting performance in economics and finance. MDA is used in economics applications where the economists is often interested only in directional movement of variable of interest. As an example in macroeconomics, a monetary authority who likes to know the direction of the inflation, to raises interest rates or decrease the rates if inflation is predicted to rise or drop respectively. Another example can be found in financial planning where the user wants to know if the demand has increasing direction or decreasing trend. 
Mean Field Residual Network  We study randomly initialized residual networks using mean field theory and the theory of difference equations. Classical feedforward neural networks, such as those with tanh activations, exhibit exponential behavior on the average when propagating inputs forward or gradients backward. The exponential forward dynamics causes rapid collapsing of the input space geometry, while the exponential backward dynamics causes drastic vanishing or exploding gradients. We show, in contrast, that by adding skip connections, the network will, depending on the nonlinearity, adopt subexponential forward and backward dynamics, and in many cases in fact polynomial. The exponents of these polynomials are obtained through analytic methods and proved and verified empirically to be correct. In terms of the ‘edge of chaos’ hypothesis, these subexponential and polynomial laws allow residual networks to ‘hover over the boundary between stability and chaos,’ thus preserving the geometry of the input space and the gradient information flow. In our experiments, for each activation function we study here, we initialize residual networks with different hyperparameters and train them on MNIST. Remarkably, our initialization time theory can accurately predict test time performance of these networks, by tracking either the expected amount of gradient explosion or the expected squared distance between the images of two input vectors. Importantly, we show, theoretically as well as empirically, that common initializations such as the Xavier or the He schemes are not optimal for residual networks, because the optimal initialization variances depend on the depth. Finally, we have made mathematical contributions by deriving several new identities for the kernels of powers of ReLU functions by relating them to the zeroth Bessel function of the second kind. 
Mean Shift  Mean shift is a nonparametric featurespace analysis technique for locating the maxima of a density function, a socalled modeseeking algorithm. Application domains include cluster analysis in computer vision and image processing. http://…/MeanShiftTheory.pdf 
Mean Shift Clustering  The mean shift algorithm is a nonparametric clustering technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the clusters. http://…/mean_shift.pdf http://…/meanshift 
Mean Squared Error (MSE) 
In statistics, the mean squared error (MSE) of an estimator measures the average of the squares of the “errors”, that is, the difference between the estimator and what is estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss. The difference occurs because of randomness or because the estimator doesn’t account for information that could produce a more accurate estimate. 
Meaningful Purposive Interaction Analysis (MPIA) 
This book introduces Meaningful Purposive Interaction Analysis (MPIA) theory, which combines social network analysis (SNA) with latent semantic analysis (LSA) to help create and analyse a meaningful learning landscape from the digital traces left by a learning community in the coconstruction of knowledge. The hybrid algorithm is implemented in the statistical programming language and environment R, introducing packages which capture – through matrix algebra – elements of learners’ work with more knowledgeable others and resourceful content artefacts. The book provides comprehensive packagebypackage application examples, and code samples that guide the reader through the MPIA model to show how the MPIA landscape can be constructed and the learner’s journey mapped and analysed. This building block application will allow the reader to progress to using and building analytics to guide students and support decisionmaking in learning. 
Measure Differential Equations (MDE) 
A new type of differential equations for probability measures on Euclidean spaces, called Measure Differential Equations (briefly MDEs), is introduced. MDEs correspond to Probability Vector Fields, which map measures on an Euclidean space to measures on its tangent bundle. Solutions are intended in weak sense and existence, uniqueness and continuous dependence results are proved under suitable conditions. The latter are expressed in terms of the Wasserstein metric on the base and fiber of the tangent bundle. MDEs represent a natural measuretheoretic generalization of Ordinary Differential Equations via a monoid morphism mapping sums of vector fields to fiber convolution of the corresponding Probability Vector Fields. Various examples, including finitespeed diffusion and concentration, are shown, together with relationships to Partial Differential Equations. Finally, MDEs are also natural meanfield limits of multiparticle systems, with convergence results extending the classical Dubroshin approach. 
Measure Forecast Accuracy  
MEBoost  Class imbalance problem has been a challenging research problem in the fields of machine learning and data mining as most real life datasets are imbalanced. Several existing machine learning algorithms try to maximize the accuracy classification by correctly identifying majority class samples while ignoring the minority class. However, the concept of the minority class instances usually represents a higher interest than the majority class. Recently, several cost sensitive methods, ensemble models and sampling techniques have been used in literature in order to classify imbalance datasets. In this paper, we propose MEBoost, a new boosting algorithm for imbalanced datasets. MEBoost mixes two different weak learners with boosting to improve the performance on imbalanced datasets. MEBoost is an alternative to the existing techniques such as SMOTEBoost, RUSBoost, Adaboost, etc. The performance of MEBoost has been evaluated on 12 benchmark imbalanced datasets with state of the art ensemble methods like SMOTEBoost, RUSBoost, Easy Ensemble, EUSBoost, DataBoost. Experimental results show significant improvement over the other methods and it can be concluded that MEBoost is an effective and promising algorithm to deal with imbalance datasets. 
Mechanical Turk (MTurk) 
Amazon Mechanical Turk (MTurk) is a crowdsourcing Internet marketplace that enables individuals and businesses (known as Requesters) to coordinate the use of human intelligence to perform tasks that computers are currently unable to do. It is one of the sites of Amazon Web Services. Employers are able to post jobs known as HITs (Human Intelligence Tasks), such as choosing the best among several photographs of a storefront, writing product descriptions, or identifying performers on music CDs. Workers (called Providers in Mechanical Turk’s Terms of Service, or, more colloquially, Turkers) can then browse among existing jobs and complete them for a monetary payment set by the employer. To place jobs, the requesting programs use an open application programming interface (API), or the more limited MTurk Requester site. Employers are restricted to USbased entities. 
Median Absolute Deviation (MAD) 
In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample. Consider the data (1, 1, 2, 2, 4, 6, 9). It has a median value of 2. The absolute deviations about 2 are (1, 1, 0, 0, 2, 4, 7) which in turn have a median value of 1 (because the sorted absolute deviations are (0, 0, 1, 1, 2, 4, 7)). So the median absolute deviation for this data is 1. 
Median Polish  The median polish is an exploratory data analysis procedure proposed by the statistician John Tukey. It finds an additivelyfit model for data in a twoway layout table (usually, results from a factorial experiment) of the form row effect + column effect + overall median. STMedianPolish 
Mediation  In statistics, a mediation model is one that seeks to identify and explicate the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third explanatory variable, known as a mediator variable. Rather than hypothesizing a direct causal relationship between the independent variable and the dependent variable, a mediational model hypothesizes that the independent variable influences the mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables. In other words, mediating relationships occur when a third variable plays an important role in governing the relationship between the other two variables. mediation,mma,mlma 
Medoid  Medoids are representative objects of a data set or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined such as 3D trajectories or in the gene expression context. The term is used in computer science in data clustering algorithms. 
Medusa  Applications such as web search and social networking have been moving from centralized to decentralized cloud architectures to improve their scalability. MapReduce, a programming framework for processing large amounts of data using thousands of machines in a single cloud, also needs to be scaled out to multiple clouds to adapt to this evolution. The challenge of building a multicloud distributed architecture is substantial. Notwithstanding, the ability to deal with the new types of faults introduced by such setting, such as the outage of a whole datacenter or an arbitrary fault caused by a malicious cloud insider, increases the endeavor considerably. In this paper we propose Medusa, a platform that allows MapReduce computations to scale out to multiple clouds and tolerate several types of faults. Our solution fulfills four objectives. First, it is transparent to the user, who writes her typical MapReduce application without modification. Second, it does not require any modification to the widely used Hadoop framework. Third, the proposed system goes well beyond the faulttolerance offered by MapReduce to tolerate arbitrary faults, cloud outages, and even malicious faults caused by corrupt cloud insiders. Fourth, it achieves this increased level of fault tolerance at reasonable cost. We performed an extensive experimental evaluation in the ExoGENI testbed, demonstrating that our solution significantly reduces execution time when compared to traditional methods that achieve the same level of resilience. 
Memetic Algorithms (MA) 
Memetic algorithms (MA) represent one of the recent growing areas of research in evolutionary computation. The term MA is now widely used as a synergy of evolutionary or any populationbased approach with separate individual learning or local improvement procedures for problem search. Quite often, MA are also referred to in the literature as Baldwinian evolutionary algorithms (EA), Lamarckian EAs, cultural algorithms, or genetic local search. A Gentle Introduction to Memetic Algorithms 
Memory Augmented Control Network (MACN) 
Planning problems in partially observable environments cannot be solved directly with convolutional networks and require some form of memory. But, even memory networks with sophisticated addressing schemes are unable to learn intelligent reasoning satisfactorily due to the complexity of simultaneously learning to access memory and plan. To mitigate these challenges we introduce the Memory Augmented Control Network (MACN). The proposed network architecture consists of three main parts. The first part uses convolutions to extract features and the second part uses a neural networkbased planning module to preplan in the environment. The third part uses a network controller that learns to store those specific instances of past information that are necessary for planning. The performance of the network is evaluated in discrete grid world environments for path planning in the presence of simple and complex obstacles. We show that our network learns to plan and can generalize to new environments. 
Memory Augmented Neural Network (MANN) 
Deep learning typically requires training a very capable architecture using large datasets. However, many important learning problems demand an ability to draw valid inferences from small size datasets, and such problems pose a particular challenge for deep learning. In this regard, various researches on ‘metalearning’ are being actively conducted. Recent work has suggested a Memory Augmented Neural Network (MANN) for metalearning. MANN is an implementation of a Neural Turing Machine (NTM) with the ability to rapidly assimilate new data in its memory, and use this data to make accurate predictions. In models such as MANN, the input data samples and their appropriate labels from previous step are bound together in the same memory locations. This often leads to memory interference when performing a task as these models have to retrieve a feature of an input from a certain memory location and read only the label information bound to that location. In this paper, we tried to address this issue by presenting a more robust MANN. We revisited the idea of metalearning and proposed a new memory augmented neural network by explicitly splitting the external memory into feature and label memories. The feature memory is used to store the features of input data samples and the label memory stores their labels. Hence, when predicting the label of a given input, our model uses its feature memory unit as a reference to extract the stored feature of the input, and based on that feature, it retrieves the label information of the input from the label memory unit. In order for the network to function in this framework, a new memorywritingmodule to encode label information into the label memory in accordance with the metalearning task structure is designed. Here, we demonstrate that our model outperforms MANN by a large margin in supervised oneshot classification tasks using Omniglot and MNIST datasets. 
Memory Networks  We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a longterm memory component; they learn how to use these jointly. The longterm memory can be read and written to, with the goal of using it for prediction. We investigate these models in the context of question answering (QA) where the longterm memory effectively acts as a (dynamic) knowledge base, and the output is a textual response. We evaluate them on a largescale QA task, and a smaller, but more complex, toy task generated from a simulated world. In the latter, we show the reasoning power of such models by chaining multiple supporting sentences to answer questions that require understanding the intension of verbs. 
MemoryEfficient Convolution (MEC) 
Convolution is a critical component in modern deep neural networks, thus several algorithms for convolution have been developed. Direct convolution is simple but suffers from poor performance. As an alternative, multiple indirect methods have been proposed including im2colbased convolution, FFTbased convolution, or Winogradbased algorithm. However, all these indirect methods have high memoryoverhead, which creates performance degradation and offers a poor tradeoff between performance and memory consumption. In this work, we propose a memoryefficient convolution or MEC with compact lowering, which reduces memoryoverhead substantially and accelerates convolution process. MEC lowers the input matrix in a simple yet efficient/compact way (i.e., much less memoryoverhead), and then executes multiple small matrix multiplications in parallel to get convolution completed. Additionally, the reduced memory footprint improves memory subsystem efficiency, improving performance. Our experimental results show that MEC reduces memory consumption significantly with good speedup on both mobile and server platforms, compared with other indirect convolution algorithms. 
Mendelian Randomization  The basic idea behind Mendelian Randomization is the following. In a simple, randomly mating population Mendel’s laws tell us that at any genomic locus (a measured spot in the genome) the allele (genetic material you got) you get is assigned at random. At the chromosome level this is very close to true due to properties of meiosis (here is an example of how this looks in very cartoonish form in yeast). http://…/018150.full.pdf 
MentorNet  Recent studies have discovered that deep networks are capable of memorizing the entire data even when the labels are completely random. Since deep models are trained on big data where labels are often noisy, the ability to overfit noise can lead to poor performance. To overcome the overfitting on corrupted training data, we propose a novel technique to regularize deep networks in the data dimension. This is achieved by learning a neural network called MentorNet to supervise the training of the base network, namely, StudentNet. Our work is inspired by curriculum learning and advances the theory by learning a curriculum from data by neural networks. We demonstrate the efficacy of MentorNet on several benchmarks. Comprehensive experiments show that it is able to significantly improve the generalization performance of the stateoftheart deep networks on corrupted training data. 
Merge and Select  In this article we introduce Merge and Select – a methodology – and factorMerger – an R package – for exploration and visualization of kgroup comparisons. Comparison of kgroups is one of the most important issues in exploratory analyses and it has zillions of applications. The classical solution is to test a null hypothesis that observations from all groups come from the same distribution. If the global null hypothesis is rejected a more detailed analysis of differences among pairs of groups is performed. The traditional approach is to use pairwise post hoc tests in order to verify which groups differ significantly. However, this approach fails with large number of groups in both interpretation and visualization layer. The Merge and Select methodology solves this problem by using easy to understand description of LRT based similarity among groups. 
MergeShuffle  This article introduces an algorithm, MergeShuffle, which is an extremely efficient algorithm to generate random permutations (or to randomly permute an existing array). It is easy to implement, runs in $n\log_2 n + O(1)$ time, is inplace, uses $n\log_2 n + \Theta(n)$ random bits, and can be parallelized accross any number of processes, in a sharedmemory PRAM model. Finally, our preliminary simulations using OpenMP suggest it is more efficient than the RaoSandelius algorithm, one of the fastest existing random permutation algorithms. We also show how it is possible to further reduce the number of random bits consumed, by introducing a second algorithm BalancedShuffle, a variant of the RaoSandelius algorithm which is more conservative in the way it recursively partitions arrays to be shuffled. While this algorithm is of lesser practical interest, we believe it may be of theoretical value. Our full code is available at: https://…/mergeshuffle 
mermaid  Generation of diagrams and flowcharts from text in a similar manner as markdown. Ever wanted to simplify documentation and avoid heavy tools like Visio when explaining your code? This is why mermaid was born, a simple markdownlike script language for generating charts from text via javascript. 
Mesa  Mesa is a highly scalable analytic data warehousing system that stores critical measurement data related to Google’s Internet advertising business. Mesa is designed to satisfy a complex and challenging set of user and systems requirements, including near realtime data ingestion and queryability, as well as high availability, reliability, fault tolerance, and scalability for large data and query volumes. Specifically, Mesa handles petabytes of data, processes millions of row updates per second, and serves billions of queries that fetch trillions of rows per day. Mesa is georeplicated across multiple datacenters and provides consistent and repeatable query answers at low latency, even when an entire datacenter fails. 
Message Importance Divergence (MID) 
Information transfer which reveals the state variation of variables can play a vital role in big data analytics and processing. In fact, the measure for information transfer can reflect the system change from the statistics by using the variable distributions, similar to KL divergence and Renyi divergence. Furthermore, in terms of the information transfer in big data, small probability events dominate the importance of the total message to some degree. Therefore, it is significant to design an information transfer measure based on the message importance which emphasizes the small probability events. In this paper, we propose the message importance divergence (MID) and investigate its characteristics and applications on three aspects. First, the message importance transfer capacity based on MID is presented to offer an upper bound for the information transfer with disturbance. Then, we utilize the MID to guide the queue length selection, which is the fundamental problem considered to have higher social or academic value in the caching operation of mobile edge computing. Finally, we extend the MID to the continuous case and discuss the robustness by using it to measuring information distance. 
Message Passing Algorithms  Constraint Satisfaction Problems (CSPs) are defined over a set of variables whose state must satisfy a number of constraints. We study a class of algorithms called Message Passing Algorithms, which aim at finding the probability distribution of the variables over the space of satisfying assignments. These algorithms involve passing local messages (according to some message update rules) over the edges of a factor graph constructed corresponding to the CSP. 
Message Passing Interface (MPI) 
Message Passing Interface (MPI) is a standardized and portable messagepassing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers. The standard defines the syntax and semantics of a core of library routines useful to a wide range of users writing portable messagepassing programs in Fortran or the C programming language. There are several welltested and efficient implementations of MPI, including some that are free or in the public domain. These fostered the development of a parallel software industry, and there encouraged development of portable and scalable largescale parallel applications. http://…/randmetaanalysis.html metaplus,MAVIS 
Message Understanding Conference (MUC) 
The Message Understanding Conferences (MUC) were initiated and financed by DARPA (Defense Advanced Research Projects Agency) to encourage the development of new and better methods of information extraction. The character of this competition—many concurrent research teams competing against one another—required the development of standards for evaluation, e.g. the adoption of metrics like precision and recall. 
MEstimation  In statistics, Mestimators are a broad class of estimators, which are obtained as the minima of sums of functions of the data. Leastsquares estimators are a special case of Mestimators. The definition of Mestimators was motivated by robust statistics, which contributed new types of Mestimators. The statistical procedure of evaluating an Mestimator on a data set is called Mestimation. More generally, an Mestimator may be defined to be a zero of an estimating function. This estimating function is often the derivative of another statistical function. For example, a maximumlikelihood estimate is often defined to be a zero of the derivative of the likelihood function with respect to the parameter; thus, a maximumlikelihood estimator is often a critical point of the score function. In many applications, such Mestimators can be thought of as estimating characteristics of the population. geex 
Meta Bag Algorithm  
Meta Networks  Deep neural networks have been successfully applied in applications with a large amount of labeled data. However, there are major drawbacks of the neural networks that are related to rapid generalization with small data and continual learning of new concepts without forgetting. We present a novel meta learning method, Meta Networks (MetaNet), that acquires a metalevel knowledge across tasks and shifts its inductive bias via fast parameterization for the rapid generalization. When tested on the standard oneshot learning benchmarks, our MetaNet models achieved near humanlevel accuracy. We demonstrated several appealing properties of MetaNet relating to generalization and continual learning. 
MetaAnalysis for Pathway Enrichment (MAPE) 
Motivation: Many pathway analysis (or gene set enrichment analysis) methods have been developed to identify enriched pathways under different biological states within a genomic study. As more and more microarray datasets accumulate, metaanalysis methods have also been developed to integrate information among multiple studies. Currently, most metaanalysis methods for combining genomic studies focus on biomarker detection and metaanalysis for pathway analysis has not been systematically pursued. Results: We investigated two approaches of metaanalysis for pathway enrichment (MAPE) by combining statistical significance across studies at the gene level (MAPE_G) or at the pathway level (MAPE_P). Simulation results showed increased statistical power of metaanalysis approaches compared to a single study analysis and showed complementary advantages of MAPE_G and MAPE_P under different scenarios. We also developed an integrated method (MAPE_I) that incorporates advantages of both approaches. Comprehensive simulations and applications to real data on drug response of breast cancer cell lines and lung cancer tissues were evaluated to compare the performance of three MAPE variations. MAPE_P has the advantage of not requiring gene matching across studies. When MAPE_G and MAPE_P show complementary advantages, the hybrid version of MAPE_I is generally recommended. MetaPath 
MetaCognitive Machine Learning  Machine learning is usually defined in behaviourist terms, where external validation is the primary mechanism of learning. In this paper, I argue for a more holistic interpretation in which finding more probable, efficient and abstract representations is as central to learning as performance. In other words, machine learning should be extended with strategies to reason over its own learning process, leading to socalled metacognitive machine learning. As such, the de facto definition of machine learning should be reformulated in these intrinsically multiobjective terms, taking into account not only the task performance but also internal learning objectives. To this end, we suggest a ‘model entropy function’ to be defined that quantifies the efficiency of the internal learning processes. It is conjured that the minimization of this model entropy leads to concept formation. Besides philosophical aspects, some initial illustrations are included to support the claims. 
MetaForest  A requirement of classic metaanalysis is that the studies being aggregated are conceptually similar, and ideally, close replications. However, in many fields, there is substantial heterogeneity between studies on the same topic. Similar research questions are studied in different laboratories, using different methods, instruments, and samples. Classic metaanalysis lacks the power to assess more than a handful of univariate moderators, or to investigate interactions between moderators, and nonlinear effects. MetaForest, by contrast, has substantial power to explore heterogeneity in metaanalysis. It can identify important moderators from a larger set of potential candidates, even with as little as 20 studies (Van Lissa, in preparation). This is an appealing quality, because many metaanalyses have small sample sizes. Moreover, MetaForest yields a measure of variable importance which can be used to identify important moderators, and offers partial prediction plots to explore the shape of the marginal relationship between moderators and effect size. metaforest 
MetaUnsupervisedLearning  We introduce a new paradigm to investigate unsupervised learning, reducing unsupervised learning to supervised learning. Specifically, we mitigate the subjectivity in unsupervised decisionmaking by leveraging knowledge acquired from prior, possibly heterogeneous, supervised learning tasks. We demonstrate the versatility of our framework via comprehensive expositions and detailed experiments on several unsupervised problems such as (a) clustering, (b) outlier detection, and (c) similarity prediction under a common umbrella of metaunsupervisedlearning. We also provide rigorous PACagnostic bounds to establish the theoretical foundations of our framework, and show that our framing of metaclustering circumvents Kleinberg’s impossibility theorem for clustering. 
Metcalfe’s Law  Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (n^2). First formulated in this form by George Gilder in 1993, and attributed to Robert Metcalfe in regard to Ethernet, Metcalfe’s law was originally presented, circa 1980, not in terms of users, but rather of ‘compatible communicating devices’ (for example, fax machines, telephones, etc.). Only more recently with the launch of the Internet did this law carry over to users and networks as its original intent was to describe Ethernet purchases and connections. The law is also very much related to economics and business management, especially with competitive companies looking to merge with one another. In the real world, requirements of Pareto efficiency imply that the law will not hold. 
Method of Moments (MM) 
In statistics, the method of moments is a method of estimation of population parameters. One starts with deriving equations that relate the population moments (i.e., the expected values of powers of the random variable under consideration) to the parameters of interest. Then a sample is drawn and the population moments are estimated from the sample. The equations are then solved for the parameters of interest, using the sample moments in place of the (unknown) population moments. This results in estimates of those parameters. The method of moments was introduced by Karl Pearson in 1894. momentchi2 
Method of Simulated Moments (MSM) 
In econometrics, the method of simulated moments (MSM) (also called simulated method of moments) is a structural estimation technique introduced by Daniel McFadden. It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve highdimensional integrals. MSM’s earliest and principal applications have been to research in industrial organization, after its development by Ariel Pakes, David Pollard, and others, though applications in consumption are emerging. 
Metric  In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable. 
Metric Optimization Engine (MOE) 
MOE (Metric Optimization Engine) is an efficient way to optimize a system’s parameters, when evaluating parameters is timeconsuming or expensive. It is an open source, machine learning tool for solving these global, black box optimization problems in an optimal way. Here are some examples of when you could use MOE: 1. Optimizing a system’s clickthrough rate (CTR). 2. Optimizing tunable parameters of a machinelearning prediction method. 3. Optimizing the design of an engineering system 4. Optimizing the parameters of a realworld experiment 
MetricConstrained Kernel UnionofSubspaces (MCKUoS) 
Modern information processing relies on the axiom that highdimensional data lie near lowdimensional geometric structures. This paper revisits the problem of datadriven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing ‘related’ objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the unionofsubspaces model, and is termed the metricconstrained unionofsubspaces (MCUoS) model. The second one of these models—suited for data drawn from a mixture of nonlinear manifolds—generalizes the kernel subspace model, and is termed the metricconstrained kernel unionofsubspaces (MCKUoS) model. The main contributions of this paper in this regard include the following. First, it motivates and formalizes the problems of MCUoS and MCKUoS learning. Second, it presents algorithms that efficiently learn an MCUoS or an MCKUoS underlying data of interest. Third, it extends these algorithms to the case when parts of the data are missing. Last, but not least, it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed geometric models and learning algorithms over existing approaches in the literature. These experiments also help clarify the connections between this work and the literature on (subspace and kernel kmeans) clustering. GitXiv 
MetricConstrained UnionofSubspaces (MCUoS) 
Modern information processing relies on the axiom that highdimensional data lie near lowdimensional geometric structures. This paper revisits the problem of datadriven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing ‘related’ objects/phenomena. The first one of these models straddles the two extremes of the subspace model and the unionofsubspaces model, and is termed the metricconstrained unionofsubspaces (MCUoS) model. The second one of these models—suited for data drawn from a mixture of nonlinear manifolds—generalizes the kernel subspace model, and is termed the metricconstrained kernel unionofsubspaces (MCKUoS) model. The main contributions of this paper in this regard include the following. First, it motivates and formalizes the problems of MCUoS and MCKUoS learning. Second, it presents algorithms that efficiently learn an MCUoS or an MCKUoS underlying data of interest. Third, it extends these algorithms to the case when parts of the data are missing. Last, but not least, it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed geometric models and learning algorithms over existing approaches in the literature. These experiments also help clarify the connections between this work and the literature on (subspace and kernel kmeans) clustering. GitXiv 
MetricsGraphics.js  MetricsGraphics.js is a library built on top of D3 that is optimized for visualizing and laying out timeseries data. It provides a simple way to produce common types of graphics in a principled, consistent and responsive way. The library currently supports line charts, scatterplots and histograms as well as features like rug plots and basic linear regression. metricsgraphics 
Metropolis Adjusted Langevin Algorithm (MALA) 
The MetropolisAdjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo method which creates a Markov chain reversible with respect to a given target distribution, ?N, with Lebesgue density on R^N; it can hence be used to approximately sample the target distribution. When the dimension N is large a key question is to determine the computational cost of the algorithm as a function of N. One approach to this question, which we adopt here, is to derive diffusion limits for the algorithm. The family of target measures that we consider in this paper are, in general, in nonproduct form and are of interest in applied problems as they arise in Bayesian nonparametric statistics and in the study of conditioned diffusions. Furthermore, we study the situation, which arises in practice, where the algorithm is started out of stationarity. We thereby significantly extend previous works which consider either only measures of product form, when the Markov chain is started out of stationarity, or measures defined via a density with respect to a Gaussian, when the Markov chain is started in stationarity. We prove that, in the nonstationary regime, the computational cost of the algorithm is of the order N^(1/2) with dimension, as opposed to what is known to happen in the stationary regime, where the cost is of the order N^(1/3). 
MetropolisHastings Algorithm  In statistics and in statistical physics, the MetropolisHastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult. This sequence can be used to approximate the distribution (i.e., to generate a histogram), or to compute an integral (such as an expected value). MetropolisHastings and other MCMC algorithms are generally used for sampling from multidimensional distributions, especially when the number of dimensions is high. For singledimensional distributions, other methods are usually available (e.g. adaptive rejection sampling) that can directly return independent samples from the distribution, and are free from the problem of autocorrelated samples that is inherent in MCMC methods. http://…/1504.01896 
Metzler Matrix  In mathematics, a Metzler matrix is a matrix in which all the offdiagonal components are nonnegative (equal to or greater than zero). It is named after the American economist Lloyd Metzler. Metzler matrices appear in stability analysis of time delayed differential equations and positive linear dynamical systems. Their properties can be derived by applying the properties of nonnegative matrices to matrices of the form M + aI where M is a Metzler matrix. 
MicroMacro Multilevel Modeling  MicroMacroMultilevel 
Microsoft Project Oxford  Set of technologies dubbed Project Oxford that allows developers to create smarter apps, which can do things like recognize faces and interpret natural language even if the app developers are not experts in those fields. “If you are an app developer, you could just take the API capabilities and not worry about the machine learning aspect,” said Vijay Vokkaarne, a principal group program manager with Bing, whose team is working on the speech aspect of Project Oxford. 
MillerHagberg Algorithm  We present an efficient algorithm to generate random graphs with a given sequence of expected degrees. Existing algorithms run in O(N 2 ) O(N2) time where N is the number of nodes. We prove that our algorithm runs in O(N+M) O(N+M) expected time where M is the expected number of edges. If the expected degrees are chosen from a distribution with finite mean, this is O(N) O(N) as N>Inf. 
Mined Semantic Analysis (MSA) 
Mined Semantic Analysis (MSA) is a novel distributional semantics approach which employs data mining techniques. MSA embraces knowledgedriven analysis of natural languages. It uncovers implicit relations between concepts by mining for their associations in target encyclopedic corpora. MSA exploits not only target corpus content but also its knowledge graph (e.g., ‘See also’ link graph of Wikipedia). Empirical results show competitive performance of MSA compared to prior stateoftheart methods for measuring semantic relatedness on benchmark data sets. Additionally, we introduce the first analytical study to examine statistical significance of results reported by different semantic relatedness methods. Our study shows that, top performing results could be statistically equivalent though mathematically different. The study positions MSA as one of stateoftheart methods for measuring semantic relatedness. 
Minibatch Tempered MCMC (MINTMCMC) 
In this paper we propose a general framework of performing MCMC with only a minibatch of data. We show by estimating the MetropolisHasting ratio with only a minibatch of data, one is essentially sampling from the true posterior raised to a known temperature. We show by experiments that our method, Minibatch Tempered MCMC (MINTMCMC), can efficiently explore multiple modes of a posterior distribution. As an application, we demonstrate one application of MINTMCMC as an inference tool for Bayesian neural networks. We also show an cyclic version of our algorithm can be applied to build an ensemble of neural networks with little additional training cost. 
Minimally Sufficient Statistic  In using a statistic to estimate a parameter in a probability distribution, it is important to remember that there can be multiple sufficient statistics for the same parameter. Indeed, the entire data set,X1 … Xn , can be a sufficient statistic – it certainly contains all of the information that is needed to estimate the parameter. However, using all n variables is not very satisfying as a sufficient statistic, because it doesn’t reduce the information in any meaningful way – and a more compact, concise statistic is better than a complicated, multidimensional statistic. If we can use a lowerdimensional statistic that still contains all necessary information for estimating the parameter, then we have truly reduced our data set without stripping any value from it. 
Minimax Concave Penalty (MCP) 
regnet 
Minimizing Approximated Information Criteria (MIC) 
coxphMIC 
Minimum Description Length (MDL) 
The minimum description length (MDL) principle is a formalization of Occam’s razor in which the best hypothesis for a given set of data is the one that leads to the best compression of the data. MDL was introduced by Jorma Rissanen in 1978. It is an important concept in information theory and computational learning theory. 
Minimum Description Length Principle (MDL) 
The minimum description length (MDL) principle is a formalization of Occam’s razor in which the best hypothesis for a given set of data is the one that leads to the best compression of the data. MDL was introduced by Jorma Rissanen in 1978. It is an important concept in information theory and computational learning theory. 
Minimum Incremental Coding Length (MICL) 
We present a simple new criterion for classification, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum number of additional bits to code the test sample, subject to an allowable distortion. We demonstrate the asymptotic optimality of this criterion for Gaussian distributions and analyze its relationships to classical classifiers. The theoretical results clarify the connections between our approach and popular classifiers such as maximum a posteriori (MAP), regularized discriminant analysis (RDA), $k$nearest neighbor ($k$NN), and support vector machine (SVM), as well as unsupervised methods based on lossy coding. Our formulation induces several good effects on the resulting classifier. First, minimizing the lossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small sample setting. Second, compression provides a uniform means of handling classes of varying dimension. The new criterion and its kernel and local versions perform competitively on synthetic examples, as well as on real imagery data such as handwritten digits and face images. On these problems, the performance of our simple classifier approaches the best reported results, without using domainspecific information. 
Minimum Spanning Tree (MST) 
Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components. http://…/43mst http://…/t0000021.pdf 
Mining High Utility Itemset using PUNLists (MIP) 
In this paper, we propose a novel data structure called PUNlist, which maintains both the utility information about an itemset and utility upper bound for facilitating the processing of mining high utility itemsets. Based on PUNlists, we present a method, called MIP (Mining high utility Itemset using PUNLists), for fast mining high utility itemsets. The efficiency of MIP is achieved with three techniques. First, itemsets are represented by a highly condensed data structure, PUNlist, which avoids costly, repeatedly utility computation. Second, the utility of an itemset can be efficiently calculated by scanning the PUNlist of the itemset and the PUNlists of long itemsets can be fast constructed by the PUNlists of short itemsets. Third, by employing the utility upper bound lying in the PUNlists as the pruning strategy, MIP directly discovers high utility itemsets from the search space, called setenumeration tree, without generating numerous candidates. Extensive experiments on various synthetic and real datasets show that PUNlist is very effective since MIP is at least an order of magnitude faster than recently reported algorithms on average. 
Minka’s Expectation Propagation  
Minkowski Distance  The Minkowski distance is a metric on Euclidean space which can be considered as a generalization of both the Euclidean distance and the Manhattan distance. 
Minkowski Weighted KMeans (MWKMeans) 
This paper represents another step in overcoming a drawback of KMeans, its lack of defense against noisy features, using feature weights in the criterion. The Weighted KMeans method by Huang et al. (2008, 2004, 2005) is extended to the corresponding Minkowski metric for measuring distances. Under Minkowski metric the feature weights become intuitively appealing feature rescaling factors in a conventional KMeans criterion. To see how this can be used in addressing another issue of KMeans, the initial setting, a method to initialize KMeans with anomalous clusters is adapted. The Minkowski metric based method is experimentally validated on datasets from the UCI Machine Learning Repository and generated sets of Gaussian clusters, both as they are and with additional uniform random noise features, and appears to be competitive in comparison with other KMeans based feature weighting algorithms. The problem we are tracking here relates to the fact that KMeans treats all features in a dataset as if they had the same degree of relevance. However, we do know that in most datasets different features will have different degrees of relevance. It is not just a matter of feature selection (in which we say: features a and b are relevant but c isn’t), but of feature weighting. 
MinMax Scaling  An alternative approach to Zscore normalization (or standardization) is the socalled MinMax scaling (often also simply called “normalization” – a common cause for ambiguities). In this approach, the data is scaled to a fixed range – usually 0 to 1. 
MINT  We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recentlydeveloped efficient entropy estimators derived from nearest neighbour distances. The proposed critical values, which may be obtained from simulation (in the case where one marginal is known) or resampling, guarantee that the test has nominal size, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide a new goodnessoffit tests of normal linear models based on assessing the independence of our vector of covariates and an appropriatelydefined notion of an error vector. The theory is supported by numerical studies on both simulated and real data. 
MinWise Independent Permutations Locality Sensitive Hashing Scheme (MinHash) 
In computer science, MinHash (or the minwise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The scheme was invented by Andrei Broder (1997), and initially used in the AltaVista search engine to detect duplicate web pages and eliminate them from search results. It has also been applied in largescale clustering problems, such as clustering documents by the similarity of their sets of words. 
Missing View Imputation with Generative Adversarial Networks (VIGAN) 
In an era where big data is becoming the norm, we are becoming less concerned with the quantity of the data for our models, but rather the quality. With such large amounts of data collected from multiple heterogeneous sources comes the associated problems, often missing views. As most models could not handle whole view missing problem, it brings up a significant challenge when conducting any multiview analysis, especially when used in the context of very large and heterogeneous datasets. However if dealt with properly, joint learning from these complementary sources can be advantageous. In this work, we present a method for imputing missing views based on generative adversarial networks called VIGAN which combines crossdomain relations given unpaired data with multiview relations given paired data. In our model, VIGAN first learns bidirectional mapping between view X and view Y using a cycleconsistent adversarial network. Moreover, we incorporate a denoising multimodal autoencoder to refine the initial approximation by making use of the joint representation. Empirical results give evidence indicating VIGAN offers competitive results compared to other methods on both numeric and image data. 
MIXed data Multilevel Anomaly Detection (MIXMAD) 
Anomalies are those deviating from the norm. Unsupervised anomaly detection often translates to identifying low density regions. Major problems arise when data is highdimensional and mixed of discrete and continuous attributes. We propose MIXMAD, which stands for MIXed data Multilevel Anomaly Detection, an ensemble method that estimates the sparse regions across multiple levels of abstraction of mixed data. The hypothesis is for domains where multiple data abstractions exist, a data point may be anomalous with respect to the raw representation or more abstract representations. To this end, our method sequentially constructs an ensemble of Deep Belief Nets (DBNs) with varying depths. Each DBN is an energybased detector at a predefined abstraction level. At the bottom level of each DBN, there is a Mixedvariate Restricted Boltzmann Machine that models the density of mixed data. Predictions across the ensemble are finally combined via rank aggregation. The proposed MIXMAD is evaluated on highdimensional realworld datasets of different characteristics. The results demonstrate that for anomaly detection, (a) multilevel abstraction of highdimensional and mixed data is a sensible strategy, and (b) empirically, MIXMAD is superior to popular unsupervised detection methods for both homogeneous and mixed data. 
Mixed Markov Models (MMM) 
Markov random fields can encode complex probabilistic relationships involving multiple variables and admit efficient procedures for probabilistic inference. However, from a knowledge engineering point of view, these models suffer from a serious limitation. The graph of a Markov field must connect all pairs of variables that are conditionally dependent even for a single choice of values of the other variables. This makes it hard to encode interactions that occur only in a certain context and are absent in all others. Furthermore, the requirement that two variables be connected unless always conditionally independent may lead to excessively dense graphs, obscuring the independencies present among the variables and leading to computationally prohibitive inference algorithms. Mumford proposed an alternative modeling framework where the graph need not be rigid and completely determined a priori. Mixed Markov models contain nodevalued random variables that, when instantiated, augment the graph by a set of transient edges. A single joint probability distribution relates the values of regular and nodevalued variables. In this article, we study the analytical and computational properties of mixed Markov models. In particular, we show that positive mixed models have a local Markov property that is equivalent to their global factorization. We also describe a computationally efficient procedure for answering probabilistic queries in mixed Markov models. 
Mixed Membership Models (MMM) 
… We have reviewed and seen mixture models in detail. And we’ve seen hierarchical modelsparticularly those that capture nested structure in the data. 1. We will now combine these ideas to form mixed membership models, which is a powerful modeling methodology. 2. The basic ideas are • Data are grouped. • Each group is modeled with a mixture. • The mixture components are shared across all the groups. • The mixture proportions are vary from group to group. … mixedMem 
Mixed Neighbourhood Selection (MNS) 
MNS 
MixedData Sampling (MIDAS) 
Mixeddata sampling (MIDAS) is an econometric regression or filtering method developed by Ghysels et al. The regression models can be viewed in some cases as substitutes for the Kalman filter when applied in the context of mixed frequency data. Bai, Ghysels and Wright (2010) examine the relationship between MIDAS regressions and Kalman filter state space models applied to mixed frequency data. In general, the latter involve a system of equations, whereas in contrast MIDAS regressions involve a (reduced form) single equation. As a consequence, MIDAS regressions might be less efficient, but also less prone to specification errors. In cases where the MIDAS regression is only an approximation, the approximation errors tend to be small. 
Mixture Density Network  The core idea is to have a Neural Net that predicts an entire (and possibly complex) distribution. In this example we’re predicting a mixture of gaussians distributions via its sufficient statistic. This means that the network knows what it doesn’t know: it will predict diffuse distributions in situations where the target variable is very noisy, and it will predict a much more peaky distribution in nearly deterministic parts. 
Mixture Model (MM) 
In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the subpopulation to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with “mixture distributions” relate to deriving the properties of the overall population from those of the subpopulations, “mixture models” are used to make statistical inferences about the properties of the subpopulations given only observations on the pooled population, without subpopulation identity information. 
MLJAR  MLJAR is a platform for rapid prototyping, development and deploying pattern recognition algorithms. It works with many data types – basically all data are arrays 🙂 mljar 
MNIST Database (MNIST) 
The MNIST database (Mixed National Institute of Standards and Technology database) is a large database of handwritten digits that is commonly used for training various image processing systems. The database is also widely used for training and testing in the field of machine learning. 
mobile Question Answering (mQA) 
In this paper, we present a novel proposal for Question An swering through mobile devices. Thus, an architecture for a mobile Ques tion Answering system based on WAP technologies is deployed. The ar chitecture propose moves the issue of Question Answering to the context of mobility. This paradigm ensures that QA is seen as an activity that provides entertainment and excitement pleasure. This characteristic gives to QA an added value. Furthermore, the method for answering de¯nition questions is very precise. It could answer almost 90% of the questions; moreover, it never replies wrong or unsupported answers. Considering that the mobilephone has had a boom in the last years and that a lot of people already have mobile telephones (approximately 3.5 billions), we propose an architecture for a new mobile system that makes QA some thing natural and e®ective for work in all ¯elds of development. This obeys to that the new mobile technology can help us to achieve our perspectives of growth. This system provides to user with a permanent communication in anytime, anywhere and any device (PDA’s, cellphone, NDS, etc.). 
MobiRNN  In this paper, we explore optimizations to run Recurrent Neural Network (RNN) models locally on mobile devices. RNN models are widely used for Natural Language Processing, Machine Translation, and other tasks. However, existing mobile applications that use RNN models do so on the cloud. To address privacy and efficiency concerns, we show how RNN models can be run locally on mobile devices. Existing work on porting deep learning models to mobile devices focus on Convolution Neural Networks (CNNs) and cannot be applied directly to RNN models. In response, we present MobiRNN, a mobilespecific optimization framework that implements GPU offloading specifically for mobile GPUs. Evaluations using an RNN model for activity recognition shows that MobiRNN does significantly decrease the latency of running RNN models on phones. 
MOCHA  Federated learning poses new statistical and systems challenges in training machine learning models over distributed networks of devices. In this work, we show that multitask learning is naturally suited to handle the statistical challenges of this setting, and propose a novel systemsaware optimization method, MOCHA, that is robust to practical systems issues. Our method and theory for the first time consider issues of high communication cost, stragglers, and fault tolerance for distributed multitask learning. The resulting method achieves significant speedups compared to alternatives in the federated setting, as we demonstrate through simulations on realworld federated datasets. 
Model Average Double Robust (MADR) 
Estimates average treatment effects using model average double robust (MADR) estimation. The MADR estimator is defined as weighted average of double robust estimators, where each double robust estimator corresponds to a specific choice of the outcome model and the propensity score model. The MADR estimator extend the desirable double robustness property by achieving consistency under the much weaker assumption that either the true propensity score model or the true outcome model be within a specified, possibly large, class of models. madr 
Model Averaging  
Model Based Clustering for Mixed Data (clustMD) 
A model based clustering procedure for data of mixed type, clustMD, is developed using a latent variable model. It is proposed that a latent variable, following a mixture of Gaussian distributions, generates the observed data of mixed type. The observed data may be any combination of continuous, binary, ordinal or nominal variables. clustMD employs a parsimonious covariance structure for the latent variables, leading to a suite of six clustering models that vary in complexity and provide an elegant and unified approach to clustering mixed data. An expectation maximisation (EM) algorithm is used to estimate clustMD; in the presence of nominal data a Monte Carlo EM algorithm is required. The clustMD model is illustrated by clustering simulated mixed type data and prostate cancer patients, on whom mixed data have been recorded. 
Model Based Machine Learning (MBML) 
Several decades of research in the field of machine learning have resulted in a multitude of different algorithms for solving a broad range of problems. To tackle a new application, a researcher typically tries to map their problem onto one of these existing methods, often influenced by their familiarity with specific algorithms and by the availability of corresponding software implementations. In this study, we describe an alternative methodology for applying machine learning, in which a bespoke solution is formulated for each new application. The solution is expressed through a compact modelling language, and the corresponding custom machine learning code is then generated automatically. This modelbased approach offers several major advantages, including the opportunity to create highly tailored models for specific scenarios, as well as rapid prototyping and comparison of a range of alternative models. Furthermore, newcomers to the field of machine learning do not have to learn about the huge range of traditional methods, but instead can focus their attention on understanding a single modelling environment. In this study, we show how probabilistic graphical models, coupled with efficient inference algorithms, provide a very flexible foundation formodelbased machine learning, and we outline a largescale commercial application of this framework involving tens of millions of users. 
Model Confidence Set (MCS) 
The Model Confidence Set (MCS) procedure was recently developed by Hansen et al. (2011). The Hansen’s procedure consists on a sequence of tests which permits to construct a set of ‘superior’ models, where the null hypothesis of Equal Predictive Ability (EPA) is not rejected at a certain confidence level. The EPA statistic tests is calculated for an arbitrary loss function, meaning that we could test models on various aspects, for example punctual forecasts. MCS 
Model Explanation System (MES) 
We propose a general model explanation system (MES) for “explaining” the output of black box classifiers. In this introduction we use the motivating example of a classifier trained to detect fraud in a credit card transaction history. The key aspect is that we provide explanations applicable to a single prediction, rather than provide an interpretable set of parameters. The labels in the provided examples are usually negative. Hence, we focus on explaining positive predictions (alerts). In many classification applications, but especially in fraud detection, there is an expectation of false positives. Alerts are given to a human analyst before any further action is taken. Analysts often insist on understanding “why” there was an alert, since an opaque alert makes it difficult for them to proceed. Analogous scenarios occur in computer vision , credit risk , spam detection , etc. Furthermore, the MES framework is useful for model criticism. In the world of generative models, practitioners often generate synthetic data from a trained model to get an idea of “what the model is doing”. Our MES framework augments such tools. As an added benefit, MES is applicable to completely nonprobabilistic black boxes that only provide hard labels. In Section 3 we use MES to visualize the decisions of a face recognition system. 
Model Selection  Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a preexisting set of data is considered. However, the task can also involve the design of experiments such that the data collected is wellsuited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice. Konishi & Kitagawa (2008, p.75) state, ‘The majority of the problems in statistical inference can be considered to be problems related to statistical modeling’. Relatedly, Sir David Cox (2006, p.197) has said, ‘How translation from subjectmatter problem to statistical model is done is often the most critical part of an analysis’. 
Model, MetaModel and Anomaly Detection (M3A) 
Alice’ is submitting one web search per five minutes, for three hours in a row – is it normal? How to detect abnormal search behaviors, among Alice and other users? Is there any distinct pattern in Alice’s (or other users’) search behavior? We studied what is probably the largest, publicly available, query log that contains more than 30 million queries from 0.6 million users. In this paper, we present a novel, userand grouplevel framework, M3A: Model, MetaModel and Anomaly detection. For each user, we discover and explain a surprising, bimodal pattern of the interarrival time (IAT) of landed queries (queries with user clickthrough). Specifically, the model CamelLog is proposed to describe such an IAT distribution; we then notice the correlations among its parameters at the group level. Thus, we further propose the metamodel MetaClick, to capture and explain the twodimensional, heavytail distribution of the parameters. Combining CamelLog and MetaClick, the proposed M3A has the following strong points: (1) the accurate modeling of marginal IAT distribution, (2) quantitative interpretations, and (3) anomaly detection. 
ModelAveraged Confidence Intervals  MuMIn 
ModelAveraged Tail Area Wald Confidence Interval (MATAWald) 
MATA 
Modelaveraged Wald Confidence Intervals  
ModelBased Clustering  Sample observations arise from a distribution that is a mixture of two or more components. Each component is described by a density function and has an associated probability or \weight” in the mixture. In principle, we can adopt any probability model for the components, but typically we will assume that components are pvariate normal distributions. (This does not necessarily mean things are easy: inference in tractable, however.) Thus, the probability model for clustering will often be a mixture of multivariate normal distributions. Each component in the mixture is what we call a cluster. mclust,SelvarMix 
ModelBased Priors for ModelFree Reinforcement Learning (MBMF) 
Reinforcement Learning is divided in two main paradigms: modelfree and modelbased. Each of these two paradigms has strengths and limitations, and has been successfully applied to real world domains that are appropriate to its corresponding strengths. In this paper, we present a new approach aimed at bridging the gap between these two paradigms. We aim to take the best of the two paradigms and combine them in an approach that is at the same time dataefficient and costsavvy. We do so by learning a probabilistic dynamics model and leveraging it as a prior for the intertwined modelfree optimization. As a result, our approach can exploit the generality and structure of the dynamics model, but is also capable of ignoring its inevitable inaccuracies, by directly incorporating the evidence provided by the direct observation of the cost. As a proofofconcept, we demonstrate on simulated tasks that our approach outperforms purely modelbased and modelfree approaches, as well as the approach of simply switching from a modelbased to a modelfree setting. 
ModelImplied Instrumental Variable (MIIV) 
Modelimplied instrumental variables are the observed variables in the model that can serve as instrumental variables in a given equation. 
ModelImplied Instrumental Variable – Generalized Method of Moments (MIIVGMM) 
The common maximum likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes modelimplied instrumental variable – generalized method of moments (MIIVGMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions, the MIIVGMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are ‘distributionfree,’ robust to heteroscedasticity, and have overidentification goodnessoffit Jtests with asymptotic chisquare distributions. In addition, MIIVGMM estimators are ‘scalable’ in that they can estimate and test the full model or any subset of equations, and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIVGMM estimators. Two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes. 
Moderated Regression  ➘ “Moderation” pequod 
Moderation  In statistics and regression analysis, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator. The effect of a moderating variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zeroorder correlation between two other variables, or the value of the slope of the dependent variable on the independent variable. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation. pequod 
ModhaSpangler Clustering  ModhaSpangler clustering, which uses a bruteforce strategy to maximize the cluster separation simultaneously in the continuous and categorical variables. kamila 
ModSpace  Mango Solutions have developed a configurable software application to allow statisticians, programmers and analysts to centralise and manage the oftencomplex statistical knowledge (held in SAS, R, Matlab and other languages, documents, data, images etc). The application was designed to provide a centralised platform for analysts to store, share and reuse complex analytical IP in an approach which helps enforce business and coding standards and promote collaboration and continual improvement within teams. ModSpace has proved especially valuable for teams working in diverse geographic locations as it promotes increased interaction between sites and individuals. The easy to use tool contains intuitive searching capabilities, enabling analysts to reuse their code and reduce the duplication of effort. The system also supports quality assurance with the use of audit trails, version control and an archiving functionality, which allows valuable historic information to be accessed without interfering with day to day activities. The system can be configured for different coding style templates which promote standards and can identify current/legacy and customer specific standards. Managers are also able to take advantage of the powerful reporting environment which allows them to track usage within their teams, spot trends and identify areas of process improvement. http://…/#sthash.ZGls4IJx.dpuf 
Modular, Optimal Learning Testing Environment (MOLTE) 
We address the relative paucity of empirical testing of learning algorithms (of any type) by introducing a new publicdomain, Modular, Optimal Learning Testing Environment (MOLTE) for Bayesian ranking and selection problem, stochastic bandits or sequential experimental design problems. The Matlabbased simulator allows the comparison of a number of learning policies (represented as a series of .m modules) in the context of a wide range of problems (each represented in its own .m module) which makes it easy to add new algorithms and new test problems. Stateoftheart policies and various problem classes are provided in the package. The choice of problems and policies is guided through a spreadsheetbased interface. Different graphical metrics are included. MOLTE is designed to be compatible with parallel computing to scale up from local desktop to clusters and clouds. We offer MOLTE as an easytouse tool for the research community that will make it possible to perform much more comprehensive testing, spanning a broader selection of algorithms and test problems. We demonstrate the capabilities of MOLTE through a series of comparisons of policies on a starter library of test problems. We also address the problem of tuning and constructing priors that have been largely overlooked in optimal learning literature. We envision MOLTE as a modest spur to provide researchers an easy environment to study interesting questions involved in optimal learning. 
Modularity  Modularity is one measure of the structure of networks or graphs. It was designed to measure the strength of division of a network into modules (also called groups, clusters or communities). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks. However, it has been shown that modularity suffers a resolution limit and, therefore, it is unable to detect small communities. Biological networks, including animal brains, exhibit a high degree of modularity. 
Module Graphical Lasso (MGL) 
We propose module graphical lasso (MGL), an aggressive dimensionality reduction and network estimation technique for a highdimensional Gaussian graphical model (GGM). MGL achieves scalability, interpretability and robustness by exploiting the modularity property of many realworld networks. Variables are organized into tightly coupled modules and a graph structure is estimated to determine the conditional independencies among modules. MGL iteratively learns the module assignment of variables, the latent variables, each corresponding to a module, and the parameters of the GGM of the latent variables. In synthetic data experiments, MGL outperforms the standard graphical lasso and three other methods that incorporate latent variables into GGMs. 
Moment Matching Method  The momentmatching methods are also called the Krylov subspace methods, as well as Padé approximation methods. They belong to the Projection based MOR methods. These methods are applicable to nonparametric linear time invariant systems, often descriptor systems … momentchi2 
Monalytics  To effectively manage largescale data centers and utility clouds, operators must understand current system and application behaviors. This requires continuous monitoring along with online analysis of the data captured by the monitoring system. As a result, there is a need to move to systems in which both tasks can be performed in an integrated fashion, thereby better able to drive online system management. Coining the term ‘monalytics’ to refer to the combined monitoring and analysis systems used for managing largescale data center systems, this paper articulates principles for monalytics systems, describes software approaches for implementing them, and provides experimental evaluations justifying principles and implementation approach. Specific technical contributions include consideration of scalability across both ‘space’ and ‘time’, the ability to dynamically deploy and adjust monalytics functionality at multiple levels of abstraction in target systems, and the capability to operate across the range of application to hypervisor layers present in largescale data center or cloud computing systems. Our monalytics implementation targets virtualized systems and cloud infrastructures, via the integration of its functionality into the Xen hypervisor. 
MongoDB  MongoDB (from humongous) is a crossplatform documentoriented database. Classified as a NoSQL database, MongoDB eschews the traditional tablebased relational database structure in favor of JSONlike documents with dynamic schemas (MongoDB calls the format BSON), making the integration of data in certain types of applications easier and faster. Released under a combination of the GNU Affero General Public License and the Apache License, MongoDB is free and opensource software. First developed by the software company 10gen (now MongoDB Inc.) in October 2007 as a component of a planned platform as a service product, the company shifted to an open source development model in 2009, with 10gen offering commercial support and other services. Since then, MongoDB has been adopted as backend software by a number of major websites and services, including Craigslist, eBay, Foursquare, SourceForge, Viacom, and The New York Times among others. As of 2014, MongoDB was the most popular NoSQL database system. 
Monte Carlo Tree Search (MCTS) 
In computer science, Monte Carlo tree search (MCTS) is a heuristic search algorithm of making decisions in some decision processes, most notably employed in game playing. The leading example of its use is in contemporary computer Go programs, but it is also used in other board games, as well as realtime video games and nondeterministic games such as poker. A Survey of Monte Carlo Tree Search Methods 
Morpheo  Morpheo is a transparent and secure machine learning platform collecting and analysing large datasets. It aims at building stateofthe art prediction models in various fields where data are sensitive. Indeed, it offers strong privacy of data and algorithm, by preventing anyone to read the data, apart from the owner and the chosen algorithms. Computations in Morpheo are orchestrated by a blockchain infrastructure, thus offering total traceability of operations. Morpheo aims at building an attractive economic ecosystem around data prediction by channelling cryptomoney from prediction requests to useful data and algorithms providers. Morpheo is designed to handle multiple data sources in a transfer learning approach in order to mutualize knowledge acquired from large datasets for applications with smaller but similar datasets. 
Mountain Plot  A mountain plot (or “folded empirical cumulative distribution plot”) is created by computing a percentile for each ranked difference between a new method and a reference method. To get a folded plot, the following transformation is performed for all percentiles above 50: percentile = 100 – percentile. These percentiles are then plotted against the differences between the two methods (Krouwer & Monti, 1995). The mountain plot is a useful complementary plot to the Bland & Altman plot. In particular, the mountain plot offers the following advantages: • It is easier to find the central 95% of the data, even when the data are not Normally distributed. • Different distributions can be compared more easily. mountainplot 
Moving Average  In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms (described below). seismicRoll 
MRNetProduct2Vec  Ecommerce websites such as Amazon, Alibaba, Flipkart, and Walmart sell billions of products. Machine learning (ML) algorithms involving products are often used to improve the customer experience and increase revenue, e.g., product similarity, recommendation, and price estimation. The products are required to be represented as features before training an ML algorithm. In this paper, we propose an approach called MRNetProduct2Vec for creating generic embeddings of products within an ecommerce ecosystem. We learn a dense and lowdimensional embedding where a diverse set of signals related to a product are explicitly injected into its representation. We train a Discriminative Multitask Bidirectional Recurrent Neural Network (RNN), where the input is a product title fed through a Bidirectional RNN and at the output, product labels corresponding to fifteen different tasks are predicted. The task set includes several intrinsic characteristics about a product such as price, weight, size, color, popularity, and material. We evaluate the proposed embedding quantitatively and qualitatively. We demonstrate that they are almost as good as sparse and extremely highdimensional TFIDF representation in spite of having less than 3% of the TFIDF dimension. We also use a multimodal autoencoder for comparing products from different languageregions and show preliminary yet promising qualitative results. 
MS MARCO  Microsoft Machine Reading Comprehension (MS MARCO) is a new large scale dataset for reading comprehension and question answering. In MS MARCO, all questions are sampled from real anonymized user queries. The context passages, from which answers in the dataset are derived, are extracted from real web documents using the most advanced version of the Bing search engine. The answers to the queries are human generated if they could summarize the answer. 
mTSNE  Multivariate time series (MTS) have become increasingly common in healthcare domains where human vital signs and laboratory results are collected for predictive diagnosis. Recently, there have been increasing efforts to visualize healthcare MTS data based on star charts or parallel coordinates. However, such techniques might not be ideal for visualizing a large MTS dataset, since it is difficult to obtain insights or interpretations due to the inherent high dimensionality of MTS. In this paper, we propose ‘mTSNE’: a simple and novel framework to visualize highdimensional MTS data by projecting them into a lowdimensional (2D or 3D) space while capturing the underlying data properties. Our framework is easy to use and provides interpretable insights for healthcare professionals to understand MTS data. We evaluate our visualization framework on two realworld datasets and demonstrate that the results of our mTSNE show patterns that are easy to understand while the other methods’ visualization may have limitations in interpretability. 
Muller Plot  A Muller plot combines information about the succession of different OTUs (genotypes, phenotypes, species, …) and information about dynamics of their abundances (populations or frequencies) over time. Muller plots may be used to visualize evolutionary dynamics. They may be also employed in the study of diversity and its dynamics; that is, how diversity emerges and how changes over time. An example of a Muller plot (produced by the MullerPlot package in R) showing the evolutionary dynamics of an artificial community They are called Muller plots in honor of Hermann Joseph Muller, who used them to explain his idea of Muller’s ratchet. ggmuller 
Multi Agent System (MAS) 
A multiagent system (M.A.S.) is a computerized system composed of multiple interacting intelligent agents within an environment. Multiagent systems can be used to solve problems that are difficult or impossible for an individual agent or a monolithic system to solve. Intelligence may include some methodic, functional, procedural approach, algorithmic search or reinforcement learning. Although there is considerable overlap, a multiagent system is not always the same as an agentbased model (ABM). The goal of an ABM is to search for explanatory insight into the collective behavior of agents (which don’t necessarily need to be “intelligent”) obeying simple rules, typically in natural systems, rather than in solving specific practical or engineering problems. The terminology of ABM tends to be used more often in the sciences, and MAS in engineering and technology. Topics where multiagent systems research may deliver an appropriate approach include online trading, disaster response, and modelling social structures. 
Multi Attribute Utility Theory (MAUT) 
mau 
Multi Expression Programming (MEP) 
In this paper a new evolutionary paradigm, called MultiExpression Programming (MEP), intended for solving computationally difficult problems is proposed. A new encoding method is designed. MEP individuals are linear entities that encode complex computer programs. In this paper MEP is used for solving some computationally difficult problems like symbolic regression, game strategy discovering, and for generating heuristics. Other exciting applications of MEP are suggested. Some of them are currently under development. MEP is compared with Gene Expression Programming (GEP) by using a wellknown test problem. For the considered problems MEP performs better than GEP. Evolving TSP heuristics using Multi Expression Programming 
MultiAdvisor Reinforcement Learning  This article deals with a novel branch of Separation of Concerns, called MultiAdvisor Reinforcement Learning (MAdRL), where a singleagent RL problem is distributed to $n$ learners, called advisors. Each advisor tries to solve the problem with a different focus. Their advice is then communicated to an aggregator, which is in control of the system. For the local training, three offpolicy bootstrapping methods are proposed and analysed: localmax bootstraps with the local greedy action, randpolicy bootstraps with respect to the random policy, and aggpolicy bootstraps with respect to the aggregator’s greedy policy. MAdRL is positioned as a generalisation of Reinforcement Learning with Ensemble methods. An experiment is held on a simplified version of the Ms. PacMan Atari game. The results confirm the theoretical relative strengths and weaknesses of each method. 
MultiAgent Path Finding  Explanation of the hot topic ‘multiagent path finding’. 
Multiagent Reinforcement Learning (MARL) 
To achieve general intelligence, agents must learn how to interact with others in a shared environment: this is the challenge of multiagent reinforcement learning (MARL). The simplest form is independent reinforcement learning (InRL), where each agent treats its experience as part of its (nonstationary) environment. 
MultiAgent Systems (MAS) 
A multiagent system (M.A.S.) is a computerized system composed of multiple interacting intelligent agents within an environment. Multiagent systems can be used to solve problems that are difficult or impossible for an individual agent or a monolithic system to solve. Intelligence may include some methodic, functional, procedural approach, algorithmic search or reinforcement learning. Although there is considerable overlap, a multiagent system is not always the same as an agentbased model (ABM). The goal of an ABM is to search for explanatory insight into the collective behavior of agents (which don’t necessarily need to be ‘intelligent’) obeying simple rules, typically in natural systems, rather than in solving specific practical or engineering problems. The terminology of ABM tends to be used more often in the sciences, and MAS in engineering and technology. Topics where multiagent systems research may deliver an appropriate approach include online trading, disaster response, and modelling social structures. 
MultiArmed Bandit  In probability theory, the multiarmed bandit problem (sometimes called the K or Narmed bandit problem) is the problem a gambler faces at a row of slot machines, sometimes known as “onearmed bandits”, when deciding which machines to play, how many times to play each machine and in which order to play them. When played, each machine provides a random reward from a distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. 
MultIclass learNing Algorithm for data Streams (MINAS) 
Novelty detection has been presented in the literature as oneclass problem. In this case, new examples are classified as either belonging to the target class or not. The examples not explained by the model are detected as belonging to a class named novelty. However, novelty detection is much more general, especially in data streams scenarios, where the number of classes might be unknown before learning and new classes can appear any time. In this case, the novelty concept is composed by different classes. This work presents a new algorithm to address novelty detection in data streams multiclass problems, the MINAS algorithm. Moreover, we also present a new experimental methodology to evaluate novelty detection methods in multiclass problems. The data used in the experiments include artificial and real data sets. Experimental results show that MINAS is able to discover novelties in multiclass problems. 
Multicollinearity  In statistics, multicollinearity (also collinearity) is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a nontrivial degree of accuracy. In this situation the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others. In case of perfect multicollinearity the predictor matrix is singular and therefore cannot be inverted. Under these circumstances, the ordinary leastsquares estimator \hat{\beta} = (X’X)^{1}X’y does not exist. Note that in statements of the assumptions underlying regression analyses such as ordinary least squares, the phrase ‘no multicollinearity’ is sometimes used to mean the absence of perfect multicollinearity, which is an exact (nonstochastic) linear relation among the regressors. 
MultiDimensional Recurrent Neural Network (MDRNN) 
Some of the properties that make RNNs suitable for one dimensional sequence learning tasks, are also desirable in multidimensional domains. This paper introduces multidimensional recurrent neural networks (MDRNNs), thereby extending the potential applicability of RNNs to vision, video processing, medical imaging and many other areas. 
Multidimensional Scaling (MDS) 
Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. It refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. An MDS algorithm aims to place each object in Ndimensional space such that the betweenobject distances are preserved as well as possible. Each object is then assigned coordinates in each of the N dimensions. The number of dimensions of an MDS plot N can exceed 2 and is specified a priori. Choosing N=2 optimizes the object locations for a twodimensional scatterplot. 
MultiDirectional Recurrent Neural Network (MRNN) 
Missing data is a ubiquitous problem. It is especially challenging in medical settings because many streams of measurements are collected at different – and often irregular – times. Accurate estimation of those missing measurements is critical for many reasons, including diagnosis, prognosis and treatment. Existing methods address this estimation problem by interpolating within data streams or imputing across data streams (both of which ignore important information) or ignoring the temporal aspect of the data and imposing strong assumptions about the nature of the datagenerating process and/or the pattern of missing data (both of which are especially problematic for medical data). We propose a new approach, based on a novel deep learning architecture that we call a Multidirectional Recurrent Neural Network (MRNN) that interpolates within data streams and imputes across data streams. We demonstrate the power of our approach by applying it to five realworld medical datasets. We show that it provides dramatically improved estimation of missing measurements in comparison to 11 stateoftheart benchmarks (including Spline and Cubic Interpolations, MICE, MissForest, matrix completion and several RNN methods); typical improvements in Root Mean Square Error are between 35% – 50%. Additional experiments based on the same five datasets demonstrate that the improvements provided by our method are extremely robust. 
Multifractal Detrended Fluctuation Analysis  ➚ “Detrended Fluctuation Analysis” 
MultiFunction Recurrent Units (MuFuRU) 
Recurrent neural networks such as the GRU and LSTM found wide adoption in natural language processing and achieve stateoftheart results for many tasks. These models are characterized by a memory state that can be written to and read from by applying gated composition operations to the current input and the previous state. However, they only cover a small subset of potentially useful compositions. We propose MultiFunction Recurrent Units (MuFuRUs) that allow for arbitrary differentiable functions as composition operations. Furthermore, MuFuRUs allow for an input and statedependent choice of these composition operations that is learned. Our experiments demonstrate that the additional functionality helps in different sequence modeling tasks, including the evaluation of propositional logic formulae, language modeling and sentiment analysis. 
MultiInstance Learning (MIL) 
In machine learning, multipleinstance learning (MIL) is a variation on supervised learning. Instead of receiving a set of instances which are individually labeled, the learner receives a set of labeled bags, each containing many instances. In the simple case of multipleinstance binary classification, a bag may be labeled negative if all the instances in it are negative. On the other hand, a bag is labeled positive if there is at least one instance in it which is positive. From a collection of labeled bags, the learner tries to either (i) induce a concept that will label individual instances correctly or (ii) learn how to label bags without inducing the concept. Take image classification for example in Amores (2013). Given an image, we want to know its target class based on its visual content. For instance, the target class might be ‘beach’, where the image contains both ‘sand’ and ‘water’. In MIL terms, the image is described as a bag X = , where eachX_i is the feature vector (called instance) extracted from the corresponding ith region in the image and N is the total regions (instances) partitioning the image. The bag is labeled positive (‘beach’) if it contains both ‘sand’ region instances and ‘water’ region instances. Multipleinstance learning was originally proposed under this name by Dietterich, Lathrop & LozanoPérez (1997), but earlier examples of similar research exist, for instance in the work on handwritten digit recognition by Keeler, Rumelhart & Leow (1990). Recent reviews of the MIL literature include Amores (2013), which provides an extensive review and comparative study of the different paradigms, and Foulds & Frank (2010), which provides a thorough review of the different assumptions used by different paradigms in the literature. Examples of where MIL is applied are: • Molecule activity • Predicting binding sites of Calmodulin binding proteins • Predicting function for alternatively spliced isoforms Li, Menon & et al. (2014),Eksi et al. (2013) • Image classification Maron & Ratan (1998) • Text or document categorization Kotzias et al. (2015) • Predicting functional binding sites of MicroRNA targets Bandyopadhyay, Ghosh & et al. (2015) Numerous researchers have worked on adapting classical classification techniques, such as support vector machines or boosting, to work within the context of multipleinstance learning. Multiple Instance Learning: Algorithms and Applications 
MultiItem Gamma Poisson Shrinker (MGPS) 
MGPS is a disproportionality method that utilizes an empirical Bayesian model to detect the magnitude of drugevent associations in drug safety databases. MGPS calculates adjusted reporting ratios for pairs of drug event combinations. The adjusted reporting ratio values are termed the EBGM or the “Empirical Bayes Geometric Mean.” EBGM values indicate the strength of the reporting relationship between a particular drug and event pair. openEBGM 
Multilabel Feature Selection (MLFS) 
Multilabel feature selection: A comprehensive review and guiding experiments 
MultiLayer Convolutional Sparse Coding (MLCSC) 
The recently proposed MultiLayer Convolutional Sparse Coding (MLCSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the computation of the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors — or feature maps — from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the MLCSC is still lacking: there are no pursuit algorithms that can serve this model exactly, nor are there conditions to guarantee a nonempty model. While one can easily obtain signals that approximately satisfy the MLCSC constraints, it remains unclear how to simply sample from the model and, more importantly, how one can train the convolutional filters from real data. In this work, we propose a sound pursuit algorithm for the MLCSC model by adopting a projection approach. We provide new and improved bounds on the stability of the solution of such pursuit and we analyze different practical alternatives to implement this in practice. We show that the training of the filters is essential to allow for nontrivial signals in the model, and we derive an online algorithm to learn the dictionaries from real data, effectively resulting in cascaded sparse convolutional layers. Last, but not least, we demonstrate the applicability of the MLCSC model for several applications in an unsupervised setting, providing competitive results. Our work represents a bridge between matrix factorization, sparse dictionary learning and sparse autoencoders, and we analyze these connections in detail. 
MultiLayer KMeans (MLKM) 
Datatarget association is an important step in multitarget localization for the intelligent operation of un manned systems in numerous applications such as search and rescue, traffic management and surveillance. The objective of this paper is to present an innovative data association learning approach named multilayer Kmeans (MLKM) based on leveraging the advantages of some existing machine learning approaches, including Kmeans, Kmeans++, and deep neural networks. To enable the accurate data association from different sensors for efficient target localization, MLKM relies on the clustering capabilities of Kmeans++ structured in a multilayer framework with the error correction feature that is motivated by the backpropogation that is wellknown in deep learning research. To show the effectiveness of the MLKM method, numerous simulation examples are conducted to compare its performance with Kmeans, Kmeans++, and deep neural networks. 
MultiLayer Vector Approximate Message Passing (MLVAMP) 
Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the networks from the outputs. Inference is also required for sampling during stochastic training on these generative models. This paper considers inference in a deep stochastic neural network where the parameters (e.g., weights, biases and activation functions) are known and the problem is to estimate the values of the input and hidden units from the output. While several approximate algorithms have been proposed for this task, there are few analytic tools that can provide rigorous guarantees in the reconstruction error. This work presents a novel and computationally tractable outputtoinput inference method called MultiLayer Vector Approximate Message Passing (MLVAMP). The proposed algorithm, derived from expectation propagation, extends earlier AMP methods that are known to achieve the replica predictions for optimality in simple linear inverse problems. Our main contribution shows that the meansquared error (MSE) of MLVAMP can be exactly predicted in a certain large system limit (LSL) where the numbers of layers is fixed and weight matrices are random and orthogonallyinvariant with dimensions that grow to infinity. MLVAMP is thus a principled method for outputtoinput inference in deep networks with a rigorous and precise performance achievability result in high dimensions. 
Multilevel Model (MLM) 
Multilevel models (also hierarchical linear models, nested models, mixed models, random coefficient, randomeffects models, random parameter models, or splitplot designs) are statistical models of parameters that vary at more than one level. These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to nonlinear models. These models became much more popular after sufficient computing power and software became available. 
Multilevel Networks Analysis  Described in Lazega et al (2008) <doi:10.1016/j.socnet.2008.02.001> and in Lazega and Snijders (2016, ISBN:9783319245201). multinets 
Multilinear ClassSpecific Discriminant Analysis  There has been a great effort to transfer linear discriminant techniques that operate on vector data to highorder data, generally referred to as Multilinear Discriminant Analysis (MDA) techniques. Many existing works focus on maximizing the interclass variances to intraclass variances defined on tensor data representations. However, there has not been any attempt to employ classspecific discrimination criteria for the tensor data. In this paper, we propose a multilinear subspace learning technique suitable for applications requiring classspecific tensor models. The method maximizes the discrimination of each individual class in the feature space while retains the spatial structure of the input. We evaluate the efficiency of the proposed method on two problems, i.e. facial image analysis and stock price prediction based on limit order book data. 
Multilinear Subspace Learning (MSL) 
Multilinear subspace learning (MSL) aims to learn a specific small part of a large space of multidimensional objects having a particular desired property. It is a dimensionality reduction approach for finding a lowdimensional representation with certain preferred characteristics of highdimensional tensor data through direct mapping, without going through vectorization. The term tensor in MSL refers to multidimensional arrays. Examples of tensor data include images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D). The mapping from a highdimensional tensor space to a lowdimensional tensor space or vector space is named as multilinear projection. MSL methods are higherorder generalizations of linear subspace learning methods such as principal component analysis (PCA), linear discriminant analysis (LDA) and canonical correlation analysis (CCA). In the literature, MSL is also referred to as tensor subspace learning or tensor subspace analysis. Research on MSL has progressed from heuristic exploration in 2000s (decade) to systematic investigation in 2010s. 
Multilingual Question Answering (mQA) 
In this paper, we present the mQA model, which is able to answer questions about the content of an image. The answer can be a sentence, a phrase or a single word. Our model contains four components: a LongShort Term Memory (LSTM) to extract the question representation, a Convolutional Neural Network (CNN) to extract the visual representation, a LSTM for storing the linguistic context in an answer, and a fusing component to combine the information from the first three components and generate the answer. We construct a Freestyle Multilingual Image Question Answering (FMIQA) dataset to train and evaluate our mQA model. It contains over 120,000 images and 250,000 freestyle Chinese questionanswer pairs and their English translations. The quality of the generated answers of our mQA model on this dataset are evaluated by human judges through a Turing Test. Specifically, we mix the answers provided by humans and our model. The human judges need to distinguish our model from the human. They will also provide a score (i.e. 0, 1, 2, the larger the better) indicating the quality of the answer. We propose strategies to monitor the quality of this evaluation process. The experiments show that in 64.7% of cases, the human judges cannot distinguish our model from humans. The average score is 1.454 (1.918 for human). 
Multimodal Attribute Extraction  The broad goal of information extraction is to derive structured information from unstructured data. However, most existing methods focus solely on text, ignoring other types of unstructured data such as images, video and audio which comprise an increasing portion of the information on the web. To address this shortcoming, we propose the task of multimodal attribute extraction. Given a collection of unstructured and semistructured contextual information about an entity (such as a textual description, or visual depictions) the task is to extract the entity’s underlying attributes. In this paper, we provide a dataset containing mixedmedia data for over 2 million product items along with 7 million attributevalue pairs describing the items which can be used to train attribute extractors in a weakly supervised manner. We provide a variety of baselines which demonstrate the relative effectiveness of the individual modes of information towards solving the task, as well as study human performance. 
Multimodal Learning  The information in real world usually comes as different modalities. For example, images are usually associated with tags and text explanations; texts contain images to more clearly express the main idea of the article. Different modalities are characterized by very different statistical properties. For instance, images are usually represented as pixel intensities or outputs of feature extractors, while texts are represented as discrete word count vectors. Due to the distinct statistical properties of different information resources, it is very important to discover the relationship between different modalities. Multimodal learning is a good model to represent the joint representations of different modalities. The multimodal learning model is also capable to fill missing modality given the observed ones. The multimodal learning model combines two deep Boltzmann machines each corresponds to one modality. An additional hidden layer is placed on top of the two Boltzmann Machines to give the joint representation. 
Multimodal Machine Learning  Our experience of the world is multimodal – we see objects, hear sounds, feel texture, smell odors, and taste flavors. Modality refers to the way in which something happens or is experienced and a research problem is characterized as multimodal when it includes multiple such modalities. In order for Artificial Intelligence to make progress in understanding the world around us, it needs to be able to interpret such multimodal signals together. Multimodal machine learning aims to build models that can process and relate information from multiple modalities. It is a vibrant multidisciplinary field of increasing importance and with extraordinary potential. Instead of focusing on specific multimodal applications, this paper surveys the recent advances in multimodal machine learning itself and presents them in a common taxonomy. We go beyond the typical early and late fusion categorization and identify broader challenges that are faced by multimodal machine learning, namely: representation, translation, alignment, fusion, and colearning. This new taxonomy will enable researchers to better understand the state of the field and identify directions for future research. 
Multinomial Probit Bayesian Additive Regression Trees (MPBART) 
mpbart 
MultiObjective Optimization  Multiobjective optimization (also known as multiobjective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multiobjective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of tradeoffs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multiobjective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multiobjective optimization problem, no single solution exists that simultaneously optimizes each objective. In that case, the objective functions are said to be conflicting, and there exists a (possibly infinite) number of Pareto optimal solutions. A solution is called nondominated, Pareto optimal, Pareto efficient or noninferior, if none of the objective functions can be improved in value without degrading some of the other objective values. Without additional subjective preference information, all Pareto optimal solutions are considered equally good (as vectors cannot be ordered completely). Researchers study multiobjective optimization problems from different viewpoints and, thus, there exist different solution philosophies and goals when setting and solving them. The goal may be to find a representative set of Pareto optimal solutions, and/or quantify the tradeoffs in satisfying the different objectives, and/or finding a single solution that satisfies the subjective preferences of a human decision maker (DM). 
Multiobjective Programming  Multiobjective optimization (also known as multiobjective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making, that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multiobjective optimization has been applied in many fields of science, including engineering, economics and logistics (see the section on applications for detailed examples) where optimal decisions need to be taken in the presence of tradeoffs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multiobjective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multiobjective optimization problem, there does not exist a single solution that simultaneously optimizes each objective. In that case, the objective functions are said to be conflicting, and there exists a (possibly infinite) number of Pareto optimal solutions. A solution is called nondominated, Pareto optimal, Pareto efficient or noninferior, if none of the objective functions can be improved in value without degrading some of the other objective values. Without additional subjective preference information, all Pareto optimal solutions are considered equally good (as vectors cannot be ordered completely). Researchers study multiobjective optimization problems from different viewpoints and, thus, there exist different solution philosophies and goals when setting and solving them. The goal may be to find a representative set of Pareto optimal solutions, and/or quantify the tradeoffs in satisfying the different objectives, and/or finding a single solution that satisfies the subjective preferences of a human decision maker (DM). 
MultiParameter Regression (MPR) 
mpr 
Multiple Correspondence Analysis (MCA) 
In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a lowdimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA is an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables. GDAtools 
Multiple Criteria Decision Making (MCDM) 
Multiplecriteria decisionmaking or multiplecriteria decision analysis (MCDA) is a subdiscipline of operations research that explicitly considers multiple criteria in decisionmaking environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider. In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences. Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiplecriteria decisionmaking discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decisionmaking software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy. 
Multiple Factor Analysis (MFA) 
Multiple factor analysis (MFA) is a factorial method devoted to the study of tables in which a group of individuals is described by a set of variables (quantitative and / or qualitative) structured in groups. It may be seen as an extension of: • Principal component analysis (PCA) when variables are quantitative, • Multiple correspondence analysis (MCA) when variables are qualitative, • Factor analysis of mixed data (FAMD) when the active variables belong to the two types. FactoMineR,MFAg 
Multiple Instance Learning (MIL) 
Multiple instance learning (MIL) is a form of weakly supervised learning where training instances are arranged in sets, called bags, and a label is provided for the entire bag. This formulation is gaining interest because it naturally fits various problems and allows to leverage weakly labeled data. Consequently, it has been used in diverse application fields such as computer vision and document classification. However, learning from bags raises important challenges that are unique to MIL. This paper provides a comprehensive survey of the characteristics which define and differentiate the types of MIL problems. Until now, these problem characteristics have not been formally identified and described. As a result, the variations in performance of MIL algorithms from one data set to another are difficult to explain. In this paper, MIL problem characteristics are grouped into four broad categories: the composition of the bags, the types of data distribution, the ambiguity of instance labels, and the task to be performed. Methods specialized to address each category are reviewed. Then, the extent to which these characteristics manifest themselves in key MIL application areas are described. Finally, experiments are conducted to compare the performance of 16 stateoftheart MIL methods on selected problem characteristics. This paper provides insight on how the problem characteristics affect MIL algorithms, recommendations for future benchmarking and promising avenues for research. 
Multiple Response Permutation Procedure (MRPP) 
Multiple Response Permutation Procedure (MRPP) provides a test of whether there is a significant difference between two or more groups of sampling units. vegan,Blossom 
MultipleCriteria Decision Analysis (MCDA) 

MultipleOutput Regression  Predicting multivariate responses in multiple linear regression. Multioutput Decision Tree Regression Multiple Output Regression 
Multiplicative Integration (MI) 
We introduce a general and simple structural design called Multiplicative Integration (MI) to improve recurrent neural networks (RNNs). MI changes the way in which information from difference sources flows and is integrated in the computational building block of an RNN, while introducing almost no extra parameters. The new structure can be easily embedded into many popular RNN models, including LSTMs and GRUs. We empirically analyze its learning behaviour and conduct evaluations on several tasks using different RNN models. Our experimental results demonstrate that Multiplicative Integration can provide a substantial performance boost over many of the existing RNN models. 
Multipolar Analytics  The layercake bestpractice model of analytics (operational systems and external data feeding data marts and a data warehouse, with BI tools as the cherry on the top) is rapidly becoming obsolete. It’s being replaced by a new, multipolar model where data is collected and analyzed in multiple places, according to the type of data and analysis required: • New HTAP systems (traditional operational data and realtime analytics) • Traditional data warehouses (finance, budgets, corporate KPIs, etc.) • Hadoop/Spark (sensor and polystructured data, longterm storage and analysis) • Standalone BI systems (personal and departmental analytics, including spreadsheets) 
Multiregression Dynamic Models (MDM) 
Multiregression dynamic models are defined to preserve certain conditional independence structures over time across a multivariate time series. They are nonGaussian and yet they can often be updated in closed form. The first two moments of their onestepahead forecast distribution can be easily calculated. Furthermore, they can be built to contain all the features of the univariate dynamic linear model and promise more efficient identification of causal structures in a time series than has been possible in the past multdyn 
MultiRelevance Transfer Learning (MRTL) 
Transfer learning aims to faciliate learning tasks in a labelscarce target domain by leveraging knowledge from a related source domain with plenty of labeled data. Often times we may have multiple domains with little or no labeled data as targets waiting to be solved. Most existing efforts tackle target domains separately by modeling the `sourcetarget’ pairs without exploring the relatedness between them, which would cause loss of crucial information, thus failing to achieve optimal capability of knowledge transfer. In this paper, we propose a novel and effective approach called MultiRelevance Transfer Learning (MRTL) for this purpose, which can simultaneously transfer different knowledge from the source and exploits the shared common latent factors between target domains. Specifically, we formulate the problem as an optimization task based on a collective nonnegative matrix trifactorization framework. The proposed approach achieves both sourcetarget transfer and targettarget leveraging by sharing multiple decomposed latent subspaces. Further, an alternative minimization learning algorithm is developed with convergence guarantee. Empirical study validates the performance and effectiveness of MRTL compared to the stateoftheart methods. 
MultiResolution Scanning (MRS) 
MRS 
MultiRobot Transfer Learning  Multirobot transfer learning allows a robot to use data generated by a second, similar robot to improve its own behavior. The potential advantages are reducing the time of training and the unavoidable risks that exist during the training phase. Transfer learning algorithms aim to find an optimal transfer map between different robots. In this paper, we investigate, through a theoretical study of singleinput singleoutput (SISO) systems, the properties of such optimal transfer maps. We first show that the optimal transfer learning map is, in general, a dynamic system. The main contribution of the paper is to provide an algorithm for determining the properties of this optimal dynamic map including its order and regressors (i.e., the variables it depends on). The proposed algorithm does not require detailed knowledge of the robots’ dynamics, but relies on basic system properties easily obtainable through simple experimental tests. We validate the proposed algorithm experimentally through an example of transfer learning between two different quadrotor platforms. Experimental results show that an optimal dynamic map, with correct properties obtained from our proposed algorithm, achieves 6070% reduction of transfer learning error compared to the cases when the data is directly transferred or transferred using an optimal static map. 
MultiScale Deep Neural Network (MSDNN) 
Salient object detection is a fundamental problem and has been received a great deal of attentions in computer vision. Recently deep learning model became a powerful tool for image feature extraction. In this paper, we propose a multiscale deep neural network (MSDNN) for salient object detection. The proposed model first extracts global highlevel features and context information over the whole source image with recurrent convolutional neural network (RCNN). Then several stacked deconvolutional layers are adopted to get the multiscale feature representation and obtain a series of saliency maps. Finally, we investigate a fusion convolution module (FCM) to build a final pixel level saliency map. The proposed model is extensively evaluated on four salient object detection benchmark datasets. Results show that our deep model significantly outperforms other 12 stateoftheart approaches. 
Multiset Dimension  We introduce a variation of the metric dimension, called the multiset dimension. The representation multiset of a vertex $v$ with respect to $W$ (which is a subset of the vertex set of a graph $G$), $r_m (vW)$, is defined as a multiset of distances between $v$ and the vertices in $W$ together with their multiplicities. If $r_m (u W) \neq r_m(vW)$ for every pair of distinct vertices $u$ and $v$, then $W$ is called a resolving set of $G$. If $G$ has a resolving set, then the cardinality of a smallest resolving set is called the multiset dimension of $G$, denoted by $md(G)$. If $G$ does not contain a resolving set, we write $md(G) = \infty$. We present basic results on the multiset dimension. We also study graphs of given diameter and give some sufficient conditions for a graph to have an infinite multiset dimension. 
MultiState Adaptive Dynamic Principal Component Analysis  mvMonitoring 
MultiState Morkov Model  
MultiTask Multiple Kernel Relationship Learning (MKMTRL) 
This paper presents a novel multitask multiplekernel learning framework that efficiently learns the kernel weights leveraging the relationship across multiple tasks. The idea is to automatically infer this task relationship in the \textit{RKHS} space corresponding to the given base kernels. The problem is formulated as a regularizationbased approach called \textit{MultiTask Multiple Kernel Relationship Learning} (\textit{MKMTRL}), which models the task relationship matrix from the weights learned from latent feature spaces of taskspecific base kernels. Unlike in previous work, the proposed formulation allows one to incorporate prior knowledge for simultaneously learning several related task. We propose an alternating minimization algorithm to learn the model parameters, kernel weights and task relationship matrix. In order to tackle largescale problems, we further propose a twostage \textit{MKMTRL} online learning algorithm and show that it significantly reduces the computational time, and also achieves performance comparable to that of the joint learning framework. Experimental results on benchmark datasets show that the proposed formulations outperform several stateoftheart multitask learning methods. 
Multivariate Adaptive Regression Splines (MARS) 
Multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a nonparametric regression technique and can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables. earth 
Multivariate Count Autoregression  We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and loglinear models. For studying the properties of such processes we develop a novel conceptual framework which is based on copulas. However, our approach does not impose the copula on a vector of counts; instead the joint distribution is determined by imposing a copula function on a vector of associated continuous random variables. This specific construction avoids conceptual difficulties resulting from the joint distribution of discrete random variables yet it keeps the properties of the Poisson process marginally. We employ Markov chain theory and the notion of weak dependence to study ergodicity and stationarity of the models we consider. We obtain easily verifiable conditions for both linear and loglinear models under both theoretical frameworks. Suitable estimating equations are suggested for estimating unknown model parameters. The large sample properties of the resulting estimators are studied in detail. The work concludes with some simulations and a real data example. 
Multivariate Imputation by Chained Equations (MICE) 
Multivariate imputation by chained equations (MICE) is a particular multiple imputation technique (Raghunathan et al., 2001; Van Buuren, 2007). MICE operates under the assumption that given the variables used in the imputation procedure, the missing data are Missing At Random (MAR), which means that the probability that a value is missing depends only on observed values and not on unobserved values (Schafer & Graham, 2002). In other words, after controlling for all of the available data (i.e., the variables included in the imputation model) “any remaining missingness is completely random” (Graham, 2009). Implementing MICE when data are not MAR could result in biased estimates. In the remainder of this paper, we assume that the MICE procedures are used with data that are MAR. mice 
Multivariate Locally Stationary Wavelet Analysis (mvLSW) 
mvLSW 
Multivariate Ordinal Regression Model  mvord 
Multivariate Process Capability Indices (MPCI) 
MPCI 
Multivariate Range Boxes  dynRB 
Multivariate Response Regression Models  
Multivariate Statistics  Multivariate statistics is a form of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical implementation of multivariate statistics to a particular problem may involve several types of univariate and multivariate analysis in order to understand the relationships between variables and their relevance to the actual problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both: 1. how these can be used to represent the distributions of observed data; 2. how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problem involving multivariate data, for example simple linear regression and multiple regression, are NOT usually considered as special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables. 
Multiway Data Analysis  Multiway data analysis is a method of analyzing large data sets by representing the data as a multidimensional array. The proper choice of array dimensions and analysis techniques can reveal patterns in the underlying data undetected by other methods. 
MuProp  Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes it possible to learn very complex distributions. However, as backpropagation is not directly applicable to stochastic networks that include discrete sampling operations within their computational graph, training such networks remains difficult. We present MuProp, an unbiased gradient estimator for stochastic networks, designed to make this task easier. MuProp improves on the likelihoodratio estimator by reducing its variance using a control variate based on the firstorder Taylor expansion of a meanfield network. Crucially, unlike prior attempts at using backpropagation for training stochastic networks, the resulting estimator is unbiased and well behaved. 
Murphy Diagram  In the context of probability forecasts for binary weather events, displays of this type have a rich tradition that can be traced to Thompson and Brier (1955) and Murphy (1977). More recent examples include the papers by Schervish (1989), Richardson (2000), Wilks (2001), Mylne (2002), and Berrocal et al. (2010), among many others. Murphy (1977) distinguished three kinds of diagrams that reflect the economic decisions involved. The negatively oriented expense diagram shows the mean raw loss or expense of a given forecast scheme; the positively oriented value diagram takes the unconditional or climatological forecast as reference and plots the difference in expense between this reference forecast and the forecast at hand, and lastly, the relativevalue diagram plots the ratio of the utility of a given forecast and the utility of an oracle forecast. The displays introduced above are similar to the value diagrams of Murphy, and we refer to them as Murphy diagrams. Murphy diagrams in R 
Mutual Information Neural Estimator (MINE) 
We argue that the estimation of the mutual information between high dimensional continuous random variables is achievable by gradient descent over neural networks. This paper presents a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size. MINE is backpropable and we prove that it is strongly consistent. We illustrate a handful of applications in which MINE is succesfully applied to enhance the property of generative models in both unsupervised and supervised settings. We apply our framework to estimate the information bottleneck, and apply it in tasks related to supervised classification problems. Our results demonstrate substantial added flexibility and improvement in these settings. 
mxnet  MXNet is a deep learning framework designed for both efficiency and flexibility. It allows you to mix symbolic and imperative programming to maximize efficiency and productivity. At its core, MXNet contains a dynamic dependency scheduler that automatically parallelizes both symbolic and imperative operations on the fly. A graph optimization layer on top of that makes symbolic execution fast and memory efficient. MXNet is portable and lightweight, scaling effectively to multiple GPUs and multiple machines. MXNet is also more than a deep learning project. It is also a collection of blue prints and guidelines for building deep learning systems, and interesting insights of DL systems for hackers. mxnet 
MXNETMPI  Existing Deep Learning frameworks exclusively use either Parameter Server(PS) approach or MPI parallelism. In this paper, we discuss the drawbacks of such approaches and propose a generic framework supporting both PS and MPI programming paradigms, coexisting at the same time. The key advantage of the new model is to embed the scaling benefits of MPI parallelism into the loosely coupled PS task model. Apart from providing a practical usage model of MPI in cloud, such framework allows for novel communication avoiding algorithms that do parameter averaging in Stochastic Gradient Descent(SGD) approaches. We show how MPI and PS models can synergestically apply algorithms such as Elastic SGD to improve the rate of convergence against existing approaches. These new algorithms directly help scaling SGD clusterwide. Further, we also optimize the critical component of the framework, namely global aggregation or allreduce using a novel concept of tensor collectives. These treat a group of vectors on a node as a single object allowing for the existing single vector algorithms to be directly applicable. We back our claims with sufficient emperical evidence using large scale ImageNet 1K data. Our framework is built upon MXNET but the design is generic and can be adapted to other popular DL infrastructures. 
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