Approximate Bayesian Computation with the Sliced-Wasserstein Distance

TL;DR

This paper introduces Sliced-Wasserstein ABC, a new approximate Bayesian computation method that improves scalability and accuracy by using the Sliced-Wasserstein distance, with proven consistency and demonstrated benefits on synthetic and real data.

Contribution

It proposes a novel ABC approach based on the Sliced-Wasserstein distance, addressing scalability issues of Wasserstein-ABC and providing theoretical guarantees.

Findings

Shows asymptotic consistency of the method

Demonstrates improved computational efficiency

Validates effectiveness on synthetic and image denoising data

Abstract

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which the simulated data are close to the observations in terms of summary statistics. These statistics are defined beforehand and might induce a loss of information, which has been shown to deteriorate the quality of the approximation. To overcome this problem, Wasserstein-ABC has been recently proposed, and compares the datasets via the Wasserstein distance between their empirical distributions, but does not scale well to the dimension or the number of samples. We propose a new ABC technique, called Sliced-Wasserstein ABC and based on the Sliced-Wasserstein distance, which has better computational and statistical properties. We derive two theoretical results showing the asymptotical consistency of our approach, and we illustrate its advantages on synthetic data and an image denoising task.