Simulation-based inference with approximately correct parameters via maximum entropy

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 settings 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 molecular dynamics simulation of a protein.

Automated summary

In this paper, a MaxEnt-based approach for inferring input parameters of simulators is proposed, which is suitable for sparse data and approximately correct models. This method can fit new data by making the smallest change in the latent joint distribution without relying on likelihood or model derivatives, and it is insensitive to prior strength. The assumption that data is fit in expectation is required, making it applicable to scenarios with few data points, and it improves algorithm efficiency through sample reweighting.