{"id":158717,"date":"2009-01-01T00:00:00","date_gmt":"2009-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/inference-algorithms-and-learning-theory-for-bayesian-sparse-factor-analysis\/"},"modified":"2018-10-16T20:43:40","modified_gmt":"2018-10-17T03:43:40","slug":"inference-algorithms-and-learning-theory-for-bayesian-sparse-factor-analysis","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/inference-algorithms-and-learning-theory-for-bayesian-sparse-factor-analysis\/","title":{"rendered":"Inference algorithms and learning theory for Bayesian sparse factor analysis"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational Bayes (VB) algorithms as well as a novel hybrid of VB and Expectation Propagation (EP). For the case of a single latent factor we derive a theory for learning performance using the replica method. We compare the MCMC and VB\/EP algorithm results with simulated data to the theoretical prediction. The results for MCMC agree closely with the theory as expected. Results for VB\/EP are slightly sub-optimal but show that the new algorithm is effective for sparse inference. In large-scale problems MCMC is infeasible due to computational limitations and the VB\/EP algorithm then provides a very useful computationally efficient alternative.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bayesian sparse factor analysis has many applications; for example, it has been applied to the problem of inferring a sparse regulatory network from gene expression data. We describe a number of inference algorithms for Bayesian sparse factor analysis using a slab and spike mixture prior. These include well-established Markov chain Monte Carlo (MCMC) and variational [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"International Workshop on Statistical-Mechanical Informatics 2009, Journal of Physics: Conference Series","msr_chapter":"","msr_edition":"International Workshop on Statistical-Mechanical Informatics 2009, Journal of Physics: Conference Series","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Workshop on Statistical-Mechanical Informatics 2009, Journal of Physics: 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