{"id":149896,"date":"2002-01-01T00:00:00","date_gmt":"2002-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/vibes-a-variational-inference-engine-for-bayesian-networks\/"},"modified":"2018-10-16T21:45:32","modified_gmt":"2018-10-17T04:45:32","slug":"vibes-a-variational-inference-engine-for-bayesian-networks","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/vibes-a-variational-inference-engine-for-bayesian-networks\/","title":{"rendered":"VIBES: A variational inference engine for Bayesian networks"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In recent years several techniques have been proposed for modelling the low-dimensional manifolds, or `subspaces&#8217;, of natural images. Examples include principal component analysis (as used for instance in `eigen-faces&#8217;), independent component analysis, and auto-encoder neural networks. Such methods suffer from a number of restrictions such as the limitation to linear manifolds or the absence of a probabilistic representation. In this paper we exploit recent developments in the fields of variational inference and latent variable models to develop a novel and tractable probabilistic approach to modelling manifolds which can handle complex non-linearities. Our framework comprises a mixture of sub-space components in which both the number of components and the effective dimensionality of the sub-spaces are determined automatically as part of the Bayesian inference procedure. We illustrate our approach using two classical problems: modelling the manifold of face images and modelling the manifolds of hand-written digits.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In recent years several techniques have been proposed for modelling the low-dimensional manifolds, or `subspaces&#8217;, of natural images. Examples include principal component analysis (as used for instance in `eigen-faces&#8217;), independent component analysis, and auto-encoder neural networks. Such methods suffer from a number of restrictions such as the limitation to linear manifolds or the absence of [&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":"","msr_chapter":"","msr_edition":"Advances in Neural Information Processing Systems","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"793\u2013800","msr_page_range_start":"793","msr_page_range_end":"800","msr_series":"","msr_volume":"15","msr_copyright":"","msr_conference_name":"Advances in Neural Information Processing Systems","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"C. M. Bishop, J. M. Winn, D. 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