Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network

TL;DR

This paper proposes a deep learning approach to automatically generate effective summary statistics for Approximate Bayesian Computation, improving posterior estimation accuracy across different models with minimal tuning.

Contribution

It introduces a neural network-based method to construct summary statistics that approximate posterior means, reducing reliance on manually crafted or known optimal statistics.

Findings

Method matches or exceeds traditional summary statistics in accuracy.

Applicable to models like Ising and moving-average with minimal tuning.

Enhances efficiency and accuracy of ABC procedures.

Abstract

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statistics are known, it is unclear which guiding principles can be used to construct effective summary statistics. In this paper we explore the possibility of automating the process of constructing summary statistics by training deep neural networks to predict the parameters from artificially generated data: the resulting summary statistics are approximately posterior means of the parameters. With minimal model-specific tuning, our method constructs summary statistics for the Ising model and the moving-average model, which match or exceed theoretically-motivated summary statistics in terms of the accuracies of the resulting posteriors.