Structural Maxent Model google
We present a new class of density estimation models, Structural Maxent models, with feature functions selected from a union of possibly very complex sub-families and yet benefiting from strong learning guarantees. The design of our models is based on a new principle supported by uniform convergence bounds and taking into consideration the complexity of the different sub-families composing the full set of features. We prove new data-dependent learning bounds for our models, expressed in terms of the Rademacher complexities of these sub-families. We also prove a duality theorem, which we use to derive our Structural Maxent algorithm. We give a full description of our algorithm, including the details of its derivation, and report the results of several experiments demonstrating that its performance improves on that of existing L1-norm regularized Maxent algorithms. We further similarly define conditional Structural Maxent models for multi-class classification problems. These are conditional probability models also making use of a union of possibly complex feature subfamilies. We prove a duality theorem for these models as well, which reveals their connection with existing binary and multi-class deep boosting algorithms. …

Retainable Evaluator Execution Framework (REEF) google
REEF (Retainable Evaluator Execution Framework) is our approach to simplify and unify the lower layers of big data systems on modern resource managers. For managers like Apache YARN, Apache Mesos, Google Omega, and Facebook Corona, REEF provides a centralized control plane abstraction that can be used to build a decentralized data plane for supporting big data systems. Special consideration is given to graph computation and machine learning applications, both of which require data retention on allocated resources to execute multiple passes over the data. More broadly, applications that run on YARN will have the need for a variety of data-processing tasks e.g., data shuffle, group communication, aggregation, checkpointing, and many more. Rather than reimplement these for each application, REEF aims to provide them in a library form, so that they can be reused by higher-level applications and tuned for a specific domain problem e.g., Machine Learning. In that sense, our long-term vision is that REEF will mature into a Big Data Application Server, that will host a variety of tool kits and applications, on modern resource managers. …

Eigenvalues, Eigenvectors google
An eigenvector of a square matrix is a non-zero vector that, when the matrix is multiplied by , yields a constant multiple of , the multiplier being commonly denoted by d. That is Av = dv. The number d is called the eigenvalue of A corresponding to v. …

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