Learning Summary Statistics for Bayesian Inference with Autoencoders

TL;DR

This paper proposes using deep autoencoders to learn effective summary statistics for approximate Bayesian computation, improving posterior approximation for complex stochastic models.

Contribution

It introduces a novel autoencoder-based method that encodes all relevant parameter information while excluding noise, enhancing ABC performance.

Findings

Autoencoders effectively learn informative summary statistics.

The method improves posterior approximation accuracy.

Validation on different stochastic models confirms effectiveness.

Abstract

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.