Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation
Julius Vetter Guy Moss Cornelius Schröder Richard Gao Jakob H. Macke
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 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 neuron model from
experimental datasets with thousands of measurements. In summary, we propose a
principled framework for inferring unique source distributions of scientific
simulator parameters while retaining as much uncertainty as possible.