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 and provably makes the smallest change in the latent joint distribution to accommodate new data. This simple method requires no likelihood or simulator derivatives and its fit is insensitive to prior strength, removing the need to balance observed data fit with prior belief. We demonstrate this MaxEnt approach and compare with other likelihood-free inference methods across three systems; a linear simulator with Gaussian noise, a point particle moving in a gravitational field, and finally a compartmental mode of epidemic spread. We demonstrate that our method compares favorably, and in some cases exceeds the performance of other methods.