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All in the Exponential Family: Bregman Duality in Thermodynamic Variational Inference
Rob Brekelmans · Vaden Masrani · Frank Wood · Greg Ver Steeg · Aram Galstyan

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 06:00 PM -- 06:45 PM (PDT) @ Virtual

The recently proposed Thermodynamic Variational Objective (TVO) leverages thermodynamic integration to provide a family of variational inference objectives, which both tighten and generalize the ubiquitous Evidence Lower Bound (ELBO). However, the tightness of TVO bounds was not previously known, an expensive grid search was used to choose a ``schedule'' of intermediate distributions, and model learning suffered with ostensibly tighter bounds. In this work, we propose an exponential family interpretation of the geometric mixture curve underlying the TVO and various path sampling methods, which allows us to characterize the gap in TVO likelihood bounds as a sum of KL divergences. We propose to choose intermediate distributions using equal spacing in the moment parameters of our exponential family, which matches grid search performance and allows the schedule to adaptively update over the course of training. Finally, we derive a doubly reparameterized gradient estimator which improves model learning and allows the TVO to benefit from more refined bounds. To further contextualize our contributions, we provide a unified framework for understanding thermodynamic integration and the TVO using Taylor series remainders.

Author Information

Rob Brekelmans (University of Southern California)
Vaden Masrani (University of British Columbia)
Frank Wood (University of British Columbia)
Greg Ver Steeg (University of Southern California)
Aram Galstyan (USC Information Sciences Institute)

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