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Robust Simulation Based Inference Through Robust Optimal Transport
[Submitted on 18 May 2026 (v1), last revised 5 Jun 2026 (this ve · 2026-06-09 · via stat updates on arXiv.org

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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.

Submission history

From: Peter Jacobs [view email]
[v1] Mon, 18 May 2026 17:57:07 UTC (613 KB)
[v2] Fri, 5 Jun 2026 19:13:14 UTC (614 KB)

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