Robust Simulation Based Inference Through Robust Optimal Transport

2026-05-18

AI Summary

This work addresses the challenge of statistical inference under intractable likelihoods and composite contamination involving both geometric and total variation perturbations, where conventional methods often fail. The authors propose a robust optimal transport divergence grounded in empirical likelihood principles, enabling reliable parameter estimation and uncertainty quantification even when the model is misspecified but simulation-based data generation remains feasible. The approach integrates semi-discrete optimal transport, regularized bootstrap resampling, and stochastic subgradient optimization within a parallelizable simulation-based inference (SBI) framework that enjoys provable convergence guarantees. Theoretical analysis establishes the robustness of the proposed divergence under composite contamination, while experiments on challenging SBI benchmark tasks demonstrate its superior performance in terms of both robustness and statistical efficiency.

Abstract

When a statistical model $\{P_θ : θ\in Θ\}$ 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, $P \notin \{P_θ: θ\in Θ\}$), 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 $P_{θ^*}$. 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.

Problem

• Simulation Based Inference
• Robust Inference
• Model Misspecification
• Optimal Transport
• Statistical Divergence

Innovation

• Robust Simulation Based Inference
• Optimal Transport
• Model Misspecification
• Empirical Likelihood
• Stochastic Sub-gradient Ascent