Robust Simulation Based Inference Through Robust Optimal Transport
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910233082724352 |
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| author | Jacobs, Peter Matthew Patel, Lekha Bhattacharya, Anirban Pati, Debdeep |
| author_facet | Jacobs, Peter Matthew Patel, Lekha Bhattacharya, Anirban Pati, Debdeep |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18741 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Simulation Based Inference Through Robust Optimal Transport Jacobs, Peter Matthew Patel, Lekha Bhattacharya, Anirban Pati, Debdeep Methodology Computation 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. |
| title | Robust Simulation Based Inference Through Robust Optimal Transport |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2605.18741 |