Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation
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arXiv
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| Format: | Preprint |
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2026
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| author | Renganathan, Ashwin Booth, Annie S. |
| author_facet | Renganathan, Ashwin Booth, Annie S. |
| contents | We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a surrogate model for the limit state and then construct an IS proposal to estimate failure probability using separate oracle evaluations, we propose a \emph{single stage} approach where a Gaussian process surrogate and a surrogate for the optimal (zero-variance) IS density are trained from shared evaluations of the oracle, making better use of a limited budget. With such an approach, small failure probabilities can be learned with relatively few oracle evaluations. We propose \emph{kernel density estimation adaptive importance sampling} (\texttt{KDE-AIS}), which combines Gaussian process surrogates with kernel density estimation to adaptively construct the IS proposal density, leading to sample efficient estimation of failure probabilities. We show that \texttt{KDE-AIS} density asymptotically converges to the optimal zero-variance IS density in total variation. Empirically, \texttt{KDE-AIS} enables accurate and sample efficient estimation of failure probabilities compared to the state of the art, including previous work on Gaussian process based adaptive importance sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20959 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation Renganathan, Ashwin Booth, Annie S. Computation Probability We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a surrogate model for the limit state and then construct an IS proposal to estimate failure probability using separate oracle evaluations, we propose a \emph{single stage} approach where a Gaussian process surrogate and a surrogate for the optimal (zero-variance) IS density are trained from shared evaluations of the oracle, making better use of a limited budget. With such an approach, small failure probabilities can be learned with relatively few oracle evaluations. We propose \emph{kernel density estimation adaptive importance sampling} (\texttt{KDE-AIS}), which combines Gaussian process surrogates with kernel density estimation to adaptively construct the IS proposal density, leading to sample efficient estimation of failure probabilities. We show that \texttt{KDE-AIS} density asymptotically converges to the optimal zero-variance IS density in total variation. Empirically, \texttt{KDE-AIS} enables accurate and sample efficient estimation of failure probabilities compared to the state of the art, including previous work on Gaussian process based adaptive importance sampling. |
| title | Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation |
| topic | Computation Probability |
| url | https://arxiv.org/abs/2603.20959 |