Low-Budget Simulation-Based Inference with Bayesian Neural Networks

TL;DR

This paper introduces a Bayesian neural network approach for simulation-based inference that remains accurate and well-calibrated even with very limited data, making it suitable for expensive simulations.

Contribution

It develops a new family of Bayesian neural network priors tailored for inference, enabling reliable posterior estimation with as few as 10 simulations.

Findings

Well-calibrated posteriors with as few as 10 simulations

Effective in cosmology with expensive single simulations

Produces informative posterior estimates with limited data

Abstract

Simulation-based inference methods have been shown to be inaccurate in the data-poor regime, when training simulations are limited or expensive. Under these circumstances, the inference network is particularly prone to overfitting, and using it without accounting for the computational uncertainty arising from the lack of identifiability of the network weights can lead to unreliable results. To address this issue, we propose using Bayesian neural networks in low-budget simulation-based inference, thereby explicitly accounting for the computational uncertainty of the posterior approximation. We design a family of Bayesian neural network priors that are tailored for inference and show that they lead to well-calibrated posteriors on tested benchmarks, even when as few as $O(10)$ simulations are available. This opens up the possibility of performing reliable simulation-based inference using very expensive simulators, as we demonstrate on a problem from the field of cosmology where single simulations are computationally expensive. We show that Bayesian neural networks produce informative and well-calibrated posterior estimates with only a few hundred simulations.