Generative Particle Variational Inference via Estimation of Functional Gradients

TL;DR

This paper introduces GPVI, a novel particle-based variational inference method that uses a neural sampler trained via functional gradients to efficiently approximate posterior distributions, combining flexibility and high performance.

Contribution

The paper proposes a new generative ParVI method, GPVI, which leverages functional gradients and neural sampling to improve flexibility and performance over existing methods.

Findings

GPVI outperforms previous generative ParVI methods like amortized SVGD.

GPVI is competitive with Hamiltonian Monte Carlo for complex distributions.

GPVI maintains asymptotic properties of traditional ParVI methods.

Abstract

Recently, particle-based variational inference (ParVI) methods have gained interest because they can avoid arbitrary parametric assumptions that are common in variational inference. However, many ParVI approaches do not allow arbitrary sampling from the posterior, and the few that do allow such sampling suffer from suboptimality. This work proposes a new method for learning to approximately sample from the posterior distribution. We construct a neural sampler that is trained with the functional gradient of the KL-divergence between the empirical sampling distribution and the target distribution, assuming the gradient resides within a reproducing kernel Hilbert space. Our generative ParVI (GPVI) approach maintains the asymptotic performance of ParVI methods while offering the flexibility of a generative sampler. Through carefully constructed experiments, we show that GPVI outperforms previous generative ParVI methods such as amortized SVGD, and is competitive with ParVI as well as gold-standard approaches like Hamiltonian Monte Carlo for fitting both exactly known and intractable target distributions.