Efficient Semi-Implicit Variational Inference

TL;DR

This paper introduces CI-VI, a scalable and efficient solver for semi-implicit variational inference that handles bias in nonlinear expectations, with proven convergence and successful application to complex posteriors.

Contribution

We develop a novel optimizer for SIVI that manages bias in nonlinear nested expectations and demonstrate its convergence and effectiveness in complex models.

Findings

Converges to a stationary point with rate O(t^{-4/5})

Effectively approximates complex posteriors in NLP datasets

Handles bias in nonlinear nested expectations

Abstract

In this paper, we propose CI-VI an efficient and scalable solver for semi-implicit variational inference (SIVI). Our method, first, maps SIVI's evidence lower bound (ELBO) to a form involving a nonlinear functional nesting of expected values and then develops a rigorous optimiser capable of correctly handling bias inherent to nonlinear nested expectations using an extrapolation-smoothing mechanism coupled with gradient sketching. Our theoretical results demonstrate convergence to a stationary point of the ELBO in general non-convex settings typically arising when using deep network models and an order of $O(t^{-\frac{4}{5}})$ gradient-bias-vanishing rate. We believe these results generalise beyond the specific nesting arising from SIVI to other forms. Finally, in a set of experiments, we demonstrate the effectiveness of our algorithm in approximating complex posteriors on various data-sets including those from natural language processing.