2026-09-19T11:40:14Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1516642023-08-01T04:13:17Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Moitra, Ankur
Chewi, Sinho
Diao, Michael Ziyang
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2023-07-31T19:57:22Z
2023-07-31T19:57:22Z
2023-06
2023-06-06T16:35:08.204Z
https://hdl.handle.net/1721.1/151664
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.
M.Eng.
Massachusetts Institute of Technology
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Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space
Thesis
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Master
Master of Engineering in Electrical Engineering and Computer Science
Publication
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<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>
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