Robust Simulation Based Inference Through Robust Optimal Transport

TL;DR

This paper introduces a robust simulation-based inference method using a novel optimal transport divergence that remains reliable under model misspecification and contamination.

Contribution

It develops a new robust optimal transport divergence, a stochastic optimization algorithm, and a parallelized SBI method with bootstrap for uncertainty quantification.

Findings

The divergence is mathematically robust against geometric and Total Variation contamination.

The proposed SBI method performs well on complex benchmark tasks.

The algorithm guarantees convergence in estimating the divergence.

Abstract

When a statistical model $\{P_{\theta} : \theta \in \Theta\}$ lacks analytically tractable likelihoods, parametric statistical inference based on data generated from an unknown underlying distribution $P$ can still be performed as long as simulations from the model are possible. This approach is called Simulation Based Inference (SBI). Statistical models are rarely exactly correct (that is, $P \notin \{P_{\theta}: \theta \in \Theta\}$), and Robust SBI focuses on inferring a reasonable parameter even under model mis-specification. We focus on the setting where $P$ possesses potentially both geometric and Total Variation type discrepancies from $P_{\theta^*}$. For this problem, we use a Kullback-Liebler informed robust Optimal Transport divergence, motivated by Empirical Likelihood considerations. We introduce a stochastic sub-gradient ascent algorithm with a convergence guarantee for estimating the semi-discrete version of this robust Optimal Transport divergence, and design a parallelized SBI algorithm which employs the regular bootstrap on top of minimum semi-discrete robust Optimal Transport for parameter uncertainty quantification. We demonstrate mathematically why the divergence is robust under a joint geometric plus Total Variation type contamination and then illustrate the robustness of inferences on a complex benchmark SBI task.