Multilevel neural simulation-based inference

TL;DR

This paper introduces a multilevel Monte Carlo approach to neural simulation-based inference, improving accuracy when using multiple simulators of different costs and fidelities under limited computational resources.

Contribution

It presents a novel multilevel Monte Carlo method for neural SBI that leverages multiple simulators to enhance inference accuracy efficiently.

Findings

Significant accuracy improvements with fixed computational budgets.

Theoretical analysis supports the efficiency of the multilevel approach.

Extensive experiments validate the method's effectiveness.

Abstract

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.