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Variational algorithms for biclustering models

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2015年 89卷 12-24页

作者： Duy Vu Aitkin, Murray Univ Melbourne Dept Math & Stat Melbourne Vic 3010 Australia

Biclustering is an important tool in exploratory statistical analysis which can be used to detect latent row and column groups of different response patterns. However, few studies include covariate data directly into their biclustering models to explain these variations. A novel biclustering framework that considers both stochastic block structures and covariate effects is proposed to address this modeling problem. Fast approximation estimation algorithms are also developed to deal with a large number of latent variables and covariate coefficients. These algorithms are derived from the variational generalized expectation-maximization (em) framework where the goal is to increase, rather than maximize, the likelihood lower bound in both E and M steps. The utility of the proposed biclustering framework is demonstrated through two block modeling applications in model-based collaborative filtering and microarray analysis. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Biclustering Stochastic block models em algorithms generalized em algorithms Variational em algorithms MM algorithms

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MODEL-BASED CLUSTERING OF LARGE NETWORKS

引用

ANNALS OF APPLIED STATISTICS 2013年第2期7卷 1010-1039页

作者： Vu, Duy Q. Hunter, David R. Schweinberger, Michael Univ Melbourne Dept Math & Stat Melbourne Vic 3010 Australia Penn State Univ Dept Stat University Pk PA 16802 USA Rice Univ Dept Stat Houston TX 77251 USA

We describe a network clustering framework, based on finite mixture models, that can be applied to discrete-valued networks with hundreds of thousands of nodes and billions of edge variables. Relative to other recent model-based clustering work for networks, we introduce a more flexible modeling framework, improve the variational-approximation estimation algorithm, discuss and implement standard error estimation via a parametric bootstrap approach, and apply these methods to much larger data sets than those seen elsewhere in the literature. The more flexible framework is achieved through introducing novel parameterizations of the model, giving varying degrees of parsimony, using exponential family models whose structure may be exploited in various theoretical and algorithmic ways. The algorithms are based on variational generalized em algorithms, where the E-steps are augmented by a minorization-maximization (MM) idea. The bootstrapped standard error estimates are based on an efficient Monte Carlo network simulation idea. Last, we demonstrate the usefulness of the model-based clustering framework by applying it to a discrete-valued network with more than 131,000 nodes and 17 billion edge variables.

关键词： Social networks stochastic block models finite mixture models em algorithms generalized em algorithms variational em algorithms MM algorithms

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