Variational inference (VI) seeks to approximate a target distribution \\(\\pi\\) by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates \\(\\pi\\) by minimizing the Kullback-Leibler (KL) divergence to \\(\\pi\\) over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when \\(\\pi\\) is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when \\(\\pi\\) is only log-smooth.<\/p>\n","protected":false},"excerpt":{"rendered":"
Variational inference (VI) seeks to approximate a target distribution by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates by minimizing the Kullback-Leibler (KL) divergence to over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) […]<\/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":"","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":"ICML 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