Simulation-Based Inference with Approximately Correct Parameters via Maximum Entropy

TL;DR

This paper introduces a MaxEnt-based method for inferring simulator parameters from sparse data without requiring likelihoods or derivatives, effective across diverse systems.

Contribution

It presents a likelihood-free inference approach using maximum entropy that is simple, robust, and insensitive to prior strength, suitable for small data regimes.

Findings

Outperforms existing likelihood-free methods in various systems

Requires no likelihood or derivatives, simplifying implementation

Asymptotic runtime is independent of prior dimension

Abstract

Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models, which is common when trying to use an existing model to infer latent variables with observed data. This approach is based on the principle of maximum entropy (MaxEnt) and provably makes the smallest change in the latent joint distribution to fit new data. This method requires no likelihood or model derivatives and its fit is insensitive to prior strength, removing the need to balance observed data fit with prior belief. The method requires the ansatz that data is fit in expectation, which is true in some settings and may be reasonable in all with few data points. The method is based on sample reweighting, so its asymptotic run time is independent of prior distribution dimension. We demonstrate this MaxEnt approach and compare with other likelihood-free inference methods across three systems: a point particle moving in a gravitational field, a compartmental model of epidemic spread and finally molecular dynamics simulation of a protein.