{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/151664"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/151664","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space","abstract":"Variational inference (VI) seeks to approximate a target distribution π by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates π by minimizing the Kullback–Leibler (KL) divergence to π 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 π is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when π is only log-smooth. Additionally, in the setting where the potential admits a representation as the average of many smooth component functionals, we develop and analyze a variance-reduced extension to (Stochastic) FB–GVI with improved complexity guarantees.","abstract_html":"Variational inference (VI) seeks to approximate a target distribution π by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates π by minimizing the Kullback–Leibler (KL) divergence to π 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 π is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when π is only log-smooth. Additionally, in the setting where the potential admits a representation as the average of many smooth component functionals, we develop and analyze a variance-reduced extension to (Stochastic) FB–GVI with improved complexity guarantees.","abstract_has_math":false,"creators":["Diao, Michael Ziyang"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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Of key interest in statistics and machine learning is Gaussian VI, which approximates π by minimizing the Kullback–Leibler (KL) divergence to π 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 π is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when π is only log-smooth. Additionally, in the setting where the potential admits a representation as the average of many smooth component functionals, we develop and analyze a variance-reduced extension to (Stochastic) FB–GVI with improved complexity guarantees."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space"]}]}],"canonical_facts":{"dc:contributor.advisor":["Moitra, Ankur","Chewi, Sinho"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["Diao, Michael Ziyang"],"dc:date.accessioned":["2023-07-31T19:57:22Z"],"dc:date.available":["2023-07-31T19:57:22Z"],"dc:date.issued":["2023-06"],"dc:description.abstract":["Variational inference (VI) seeks to approximate a target distribution π by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates π by minimizing the Kullback–Leibler (KL) divergence to π 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 π is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when π is only log-smooth. Additionally, in the setting where the potential admits a representation as the average of many smooth component functionals, we develop and analyze a variance-reduced extension to (Stochastic) FB–GVI with improved complexity guarantees."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/151664"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:21:00Z"}