Permutations accelerate Approximate Bayesian Computation

TL;DR

permABC is a novel framework that leverages permutation-based matching and sequential strategies to significantly improve the scalability and efficiency of Approximate Bayesian Computation in high-dimensional, hierarchical models.

Contribution

We introduce permABC, a permutation-based ABC framework with new sequential strategies that enhance scalability and robustness in complex models.

Findings

Demonstrates improved computational efficiency in synthetic experiments.

Achieves more accurate inference in a COVID-19 epidemic model across 94 regions.

Shows robustness in high-dimensional hierarchical settings.

Abstract

Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in hierarchical or high-dimensional models. In this paper, we introduce permABC, a new ABC framework designed for settings with both global and local parameters, where observations are grouped into exchangeable compartments. Building upon the Sequential Monte Carlo ABC (ABC-SMC) framework, permABC exploits the exchangeability of compartments through permutation-based matching, significantly improving computational efficiency. We then develop two further, complementary sequential strategies: Over Sampling, which facilitates early-stage acceptance by temporarily increasing the number of simulated compartments, and Under Matching, which relaxes the acceptance condition by matching only subsets of the data. These techniques allow for robust and scalable inference even in high-dimensional regimes. Through synthetic and real-world experiments -- including a hierarchical Susceptible-Infectious-Recover model of the early COVID-19 epidemic across 94 French departments -- we demonstrate the practical gains in accuracy and efficiency achieved by our approach.