K2-ABC: Approximate Bayesian Computation with Kernel Embeddings

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.

References in corpus (2)

• Bayesian Indirect Inference Using a Parametric Auxiliary Model
• GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computation

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• Minimax Confidence Intervals for the Sliced Wasserstein Distance
• Summary Statistics in Approximate Bayesian Computation
• Approximating Bayes in the 21st Century
• DR-ABC: Approximate Bayesian Computation with Kernel-Based Distribution Regression
• Generalized Bayesian Likelihood-Free Inference
• A Parzen-based distance between probability measures as an alternative of summary statistics in Approximate Bayesian Computation
• Discrepancy geometry in approximate Bayesian inference: transport and risk perspectives