Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation

Julius Vetter, Guy Moss, Cornelius Schröder, Richard Gao, Jakob H. Macke

Keywords: source distribution estimation, maximum entropy, Sliced-Wasserstein distance, empirical Bayes, simulation-based inference

TL;DR: We propose a sample-based, maximum entropy approach to the source distribution estimation problem.

Abstract: Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid sources, we propose an approach which targets the maximum entropy distribution, i.e., prioritizes retaining as much uncertainty as possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein distance to measure the discrepancy between the dataset and simulations - and thus suitable for simulators with intractable likelihoods. We benchmark our method on several tasks, and show that it can recover source distributions with substantially higher entropy than recent source estimation methods, without sacrificing the fidelity of the simulations. Finally, to demonstrate the utility of our approach, we infer source distributions for parameters of the Hodgkin-Huxley model from experimental datasets with hundreds of single-neuron measurements. In summary, we propose a principled method for inferring source distributions of scientific simulator parameters while retaining as much uncertainty as possible.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 15224