Proximal Gradient Algorithms for Gaussian Variational Inference:Optimization in the Bures–Wasserstein Space
Name
diao-diao-meng-eecs-2023-thesis.pdf
Description
Thesis PDF
Size
864.78 KB
Format
Adobe PDF
Checksum (MD5)
dfb09c716a79965429556e415cf355a3
Author(s)
Diao, Michael Ziyang
Advisor(s)
Moitra, Ankur
Chewi, Sinho
Date Issued
June 2023
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
In Copyright - Educational Use Permitted
Copyright retained by author(s)
Persistent DSpace Link
