Divide and conquer in ABC: Expectation-Progagation algorithms for likelihood-free inference

TL;DR

This paper introduces a divide-and-conquer Expectation-Propagation approach for likelihood-free inference in ABC, significantly reducing computational costs and allowing the use of local summary statistics to improve accuracy.

Contribution

It proposes a novel EP-based divide-and-conquer ABC method that enhances efficiency and accuracy by leveraging local summary statistics and parallel computation.

Findings

Faster than standard ABC algorithms

Reduces bias through local summary statistics

Effective in complex spatial extremes inference

Abstract

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n factors, and combine in some way n "local" ABC approximations of each factor. This has two advantages: (a) such an approach is typically much faster than standard ABC and (b) it makes it possible to use local summary statistics (i.e. summary statistics that depend only on the data-points that correspond to a single factor), rather than global summary statistics (that depend on the complete dataset). This greatly alleviates the bias introduced by summary statistics, and even removes it entirely in situations where local summary statistics are simply the identity function. We focus on EP (Expectation-Propagation), a convenient and powerful way to combine n local approximations into a global approximation. Compared to the EP- ABC approach of Barthelm\'e and Chopin (2014), we present two variations, one based on the parallel EP algorithm of Cseke and Heskes (2011), which has the advantage of being implementable on a parallel architecture, and one version which bridges the gap between standard EP and parallel EP. We illustrate our approach with an expensive application of ABC, namely inference on spatial extremes.