Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network
This addresses the problem of improving ABC efficiency and accuracy for researchers in computational statistics, though it is incremental as it builds on existing ABC methods with a novel application of neural networks.
The paper tackles the challenge of constructing effective summary statistics for Approximate Bayesian Computation (ABC) by automating the process using deep neural networks trained to predict parameters from generated data, resulting in summary statistics that match or exceed theoretically-motivated ones in posterior accuracy.
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.