Deterministic annealing EM algorithm
Neural Networks
Learning in graphical models
Sparse graphical models for exploring gene expression data
Journal of Multivariate Analysis
CSB '04 Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Online dictionary learning for sparse coding
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
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We describe a class of sparse latent factor models, called graphical factor models (GFMs), and relevant sparse learning algorithms for posterior mode estimation. Linear, Gaussian GFMs have sparse, orthogonal factor loadings matrices, that, in addition to sparsity of the implied covariance matrices, also induce conditional independence structures via zeros in the implied precision matrices. We describe the models and their use for robust estimation of sparse latent factor structure and data/signal reconstruction. We develop computational algorithms for model exploration and posterior mode search, addressing the hard combinatorial optimization involved in the search over a huge space of potential sparse configurations. A mean-field variational technique coupled with annealing is developed to successively generate "artificial" posterior distributions that, at the limiting temperature in the annealing schedule, define required posterior modes in the GFM parameter space. Several detailed empirical studies and comparisons to related approaches are discussed, including analyses of handwritten digit image and cancer gene expression data.