BibTeX

@article{2605.18741v1,
Author        = {Peter Matthew Jacobs and Lekha Patel and Anirban Bhattacharya and Debdeep Pati},
Title         = {Robust Simulation Based Inference Through Robust Optimal Transport},
Eprint        = {2605.18741v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.ME},
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.},
Year          = {2026},
Month         = {May},
Url           = {http://arxiv.org/abs/2605.18741v1},
File          = {2605.18741v1.pdf}
}