Autor: |
Ghosh, Soumyadip, Lu, Yingdong, Nowicki, Tomasz, Zhang, Edith |
Rok vydání: |
2022 |
Předmět: |
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Druh dokumentu: |
Working Paper |
Popis: |
The mean field variational inference (MFVI) formulation restricts the general Bayesian inference problem to the subspace of product measures. We present a framework to analyze MFVI algorithms, which is inspired by a similar development for general variational Bayesian formulations. Our approach enables the MFVI problem to be represented in three different manners: a gradient flow on Wasserstein space, a system of Fokker-Planck-like equations and a diffusion process. Rigorous guarantees are established to show that a time-discretized implementation of the coordinate ascent variational inference algorithm in the product Wasserstein space of measures yields a gradient flow in the limit. A similar result is obtained for their associated densities, with the limit being given by a quasi-linear partial differential equation. A popular class of practical algorithms falls in this framework, which provides tools to establish convergence. We hope this framework could be used to guarantee convergence of algorithms in a variety of approaches, old and new, to solve variational inference problems. |
Databáze: |
arXiv |
Externí odkaz: |
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