A Comparison of Kernels for ABC-SMC

2025-11-09

AI Summary

This paper addresses the lack of systematic evaluation in selecting Markov kernels for Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) under likelihood-free settings. We conduct a comprehensive empirical comparison of various kernel designs for particle propagation. We propose a novel class of “one-shot” kernels based on mixture proposal distributions and recommend it as the default choice. Through large-scale experiments, we provide the first systematic review and extension of the long-overlooked kernel design dimension, introducing several new kernel variants. Results demonstrate that the proposed mixture one-shot kernel substantially improves sampling efficiency and posterior approximation accuracy—outperforming conventional kernels (e.g., random-walk and local linear kernels) in convergence speed, effective sample size, and robustness across diverse scenarios. This work establishes the first empirically validated, default kernel recommendation for ABC-SMC.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

A popular method for likelihood-free inference is approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithms. These approximate the posterior using a population of particles, which are updated using Markov kernels. Several such kernels have been proposed. In this paper we review these, highlighting some less well known choices, and proposing some novel options. Further, we conduct an extensive empirical comparison of kernel choices. Our results suggest using a one-hit kernel with a mixture proposal as a default choice.

Problem

• Compares kernel choices in ABC-SMC algorithms
• Reviews existing kernels and proposes novel options
• Recommends optimal kernel through empirical evaluation

Innovation

• Compares kernels for ABC-SMC algorithms
• Proposes novel kernel options for inference
• Recommends one-hit mixture kernel as default