Zelig |
A framework that brings together an abundance of common statistical models found across packages into a unified interface, and provides a common architecture for estimation and interpretation, as well as bridging functions to absorb increasingly more models into the collective library. Zelig allows each individual package, for each statistical model, to be accessed by a common uniformly structured call and set of arguments. Moreover, Zelig automates all the surrounding building blocks of a statistical work-flow–procedures and algorithms that may be essential to one user’s application but which the original package developer did not use in their own research and might not themselves support. These include bootstrapping, jackknifing, and re-weighting of data. In particular, Zelig automatically generates predicted and simulated quantities of interest (such as relative risk ratios, average treatment effects, first differences and predicted and expected values) to interpret and visualize complex models. zeligverse,Zelig |

ZenLDA |
This paper presents our recent efforts, zenLDA, an efficient and scalable Collapsed Gibbs Sampling system for Latent Dirichlet Allocation training, which is thought to be challenging that both data parallelism and model parallelism are required because of the Big sampling data with up to billions of documents and Big model size with up to trillions of parameters. zenLDA combines both algorithm level improvements and system level optimizations. It first presents a novel CGS algorithm that balances the time complexity, model accuracy and parallelization flexibility. The input corpus in zenLDA is represented as a directed graph and model parameters are annotated as the corresponding vertex attributes. The distributed training is parallelized by partitioning the graph that in each iteration it first applies CGS step for all partitions in parallel, followed by synchronizing the computed model each other. In this way, both data parallelism and model parallelism are achieved by converting them to graph parallelism. We revisited the tradeoff between system efficiency and model accuracy and presented approximations such as unsynchronized model, sparse model initialization and ‘converged’ token exclusion. zenLDA is built on GraphX in Spark that provides distributed data abstraction (RDD) and expressive APIs to simplify the programming efforts and simultaneously hides the system complexities. This enables us to implement other CGS algorithm with a few lines of code change. To better fit in distributed data-parallel framework and achieve comparable performance with contemporary systems, we also presented several system level optimizations to push the performance limit. zenLDA was evaluated it against web-scale corpus, and the result indicates that zenLDA can achieve about much better performance than other CGS algorithm we implemented, and simultaneously achieve better model accuracy. |

Zero Inflation |
In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e. a distribution that allows for frequent zero-valued observations. The zero-inflated Poisson model concerns a random event containing excess zero-count data in unit time. For example, the number of insurance claims within a population for a certain type of risk would be zero-inflated by those people who have not taken out insurance against the risk and thus are unable to claim. The zero-inflated Poisson (ZIP) model employs two components that correspond to two zero generating processes. The first process is governed by a binary distribution that generates structural zeros. The second process is governed by a Poisson distribution that generates counts, some of which may be zero. |

Zero/One Inflated Beta Regression( ZOIB) |
A general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. ➚ “Beta Regression” zoib |

Zero-Shot Learning( ZSL) |
Zero-shot learning (ZSL) is a challenging task aiming at recognizing novel classes without any training instances. Zero-Shot Learning by Generating Pseudo Feature Representations |

Zipf’s Law |
Zipf’s law, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. |

ZNN |
Convolutional networks (ConvNets) have become a popular approach to computer vision. It is important to accelerate ConvNet training, which is computationally costly. We propose a novel parallel algorithm based on decomposition into a set of tasks, most of which are convolutions or FFTs. Applying Brent’s theorem to the task dependency graph implies that linear speedup with the number of processors is attainable within the PRAM model of parallel computation, for wide network architectures. To attain such performance on real shared-memory machines, our algorithm computes convolutions converging on the same node of the network with temporal locality to reduce cache misses, and sums the convergent convolution outputs via an almost wait-free concurrent method to reduce time spent in critical sections. We implement the algorithm with a publicly available software package called ZNN. Benchmarking with multi-core CPUs shows that ZNN can attain speedup roughly equal to the number of physical cores. We also show that ZNN can attain over 90x speedup on a many-core CPU (Xeon Phi Knights Corner). These speedups are achieved for network architectures with widths that are in common use. The task parallelism of the ZNN algorithm is suited to CPUs, while the SIMD parallelism of previous algorithms is compatible with GPUs. Through examples, we show that ZNN can be either faster or slower than certain GPU implementations depending on specifics of the network architecture, kernel sizes, and density and size of the output patch. ZNN may be less costly to develop and maintain, due to the relative ease of general-purpose CPU programming. |

Z-Score |
In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, “normalizing” can refer to many types of ratios; see normalization (statistics) for more). |

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