Sliced Wasserstein Variational Inference

TL;DR

This paper introduces a novel variational inference method that minimizes sliced Wasserstein distance, a proper metric from optimal transport, enabling efficient approximation without requiring tractable densities or complex optimization.

Contribution

It proposes using sliced Wasserstein distance for variational inference, offering a metric-based approach that simplifies computation and broadens applicability with neural network approximations.

Findings

Effective on synthetic data

Competitive performance on real data

Avoids complex optimization procedures

Abstract

Variational Inference approximates an unnormalized distribution via the minimization of Kullback-Leibler (KL) divergence. Although this divergence is efficient for computation and has been widely used in applications, it suffers from some unreasonable properties. For example, it is not a proper metric, i.e., it is non-symmetric and does not preserve the triangle inequality. On the other hand, optimal transport distances recently have shown some advantages over KL divergence. With the help of these advantages, we propose a new variational inference method by minimizing sliced Wasserstein distance, a valid metric arising from optimal transport. This sliced Wasserstein distance can be approximated simply by running MCMC but without solving any optimization problem. Our approximation also does not require a tractable density function of variational distributions so that approximating families can be amortized by generators like neural networks. Furthermore, we provide an analysis of the theoretical properties of our method. Experiments on synthetic and real data are illustrated to show the performance of the proposed method.