K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

TL;DR

K2-ABC introduces a nonparametric approach to approximate Bayesian computation that leverages kernel embeddings and maximum mean discrepancy to compare data distributions without manually selecting summary statistics, improving inference accuracy.

Contribution

The paper proposes K2-ABC, a novel nonparametric ABC method using kernel embeddings and MMD, eliminating the need for manual summary statistic selection in complex models.

Findings

Effective in simulated scenarios

Successful application to biological data

Outperforms traditional ABC methods

Abstract

Complicated generative models often result in a situation where computing the likelihood of observed data is intractable, while simulating from the conditional density given a parameter value is relatively easy. Approximate Bayesian Computation (ABC) is a paradigm that enables simulation-based posterior inference in such cases by measuring the similarity between simulated and observed data in terms of a chosen set of summary statistics. However, there is no general rule to construct sufficient summary statistics for complex models. Insufficient summary statistics will "leak" information, which leads to ABC algorithms yielding samples from an incorrect (partial) posterior. In this paper, we propose a fully nonparametric ABC paradigm which circumvents the need for manually selecting summary statistics. Our approach, K2-ABC, uses maximum mean discrepancy (MMD) as a dissimilarity measure between the distributions over observed and simulated data. MMD is easily estimated as the squared difference between their empirical kernel embeddings. Experiments on a simulated scenario and a real-world biological problem illustrate the effectiveness of the proposed algorithm.