Permutations accelerate Approximate Bayesian Computation

2025-07-08

AI Summary

To address the poor scalability of Approximate Bayesian Computation (ABC) in hierarchical high-dimensional models—particularly those featuring global and local parameters, with exchangeable observational units grouped into compartments—this paper introduces permABC. Built upon Sequential Monte Carlo ABC (ABC-SMC), permABC innovatively integrates three strategies: (i) permutation-based matching to exploit compartment-level exchangeability, (ii) oversampling of parameter proposals, and (iii) subset matching for efficient distance evaluation. These jointly enhance computational efficiency and robustness without compromising inferential accuracy. Experiments on synthetic data and real-world COVID-19 incidence data from 94 French administrative regions demonstrate that permABC substantially reduces computational cost compared to standard ABC methods, while improving both posterior estimation accuracy and stability. The framework establishes a new paradigm for scalable Bayesian inference in complex hierarchical models.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

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.

Problem

• Improving scalability of ABC in high-dimensional models
• Enhancing efficiency via permutation-based matching in ABC
• Enabling robust inference in hierarchical parameter settings

Innovation

• Permutation-based matching enhances ABC efficiency
• Over Sampling boosts early-stage acceptance rates
• Under Matching relaxes data subset requirements