Simulation-based science often requires a distribution over simulator parameters whose push-forward reproduces a set of real observations: this is the source distribution estimation (SDE) problem. Existing methods fit the source against a likelihood surrogate trained once from a fixed proposal prior. Their objective is therefore stated only in terms of the surrogate instead of the true simulator, which may fail for inaccurate areas in parameter space where the surrogate was never trained. We instead solve SDE by expectation maximization: an E-step trains an amortized posterior on fresh simulations from the current source estimate, and an M-step refits the source to the average of that posterior over the observed data. We give two parameterizations, (1) separate source and posterior flows and (2) a single shared conditional flow. We evaluate our method on three benchmark tasks under both broad and misspecified initial priors. Both improve on existing fixed surrogate approaches and on iterated variants of each, most clearly on Lotka--Volterra, where no baseline falls below 0.96 data-space C2ST while our methods reach 0.64-0.68 in three of four initial-prior settings.
In this article we describe Cohort Organized Learning (CoOL), a method for clustering data without explicit distance or similarity computations. Herein, we will describe CoOL, derive the gradients determined by expectation maximization to train the networks, show how to monitor convergence during training and evaluate the clusters after training, and discuss a series of examples and use cases. We also discuss CoOL's limitations and future prospects on related tasks. Because CoOL uses neural networks to estimate the clusters, it can be used to cluster any data that can be made compatible and we illustrate this on vector data and images.