Surrogate-Guided Adaptive Importance Sampling for Failure Probability Estimation

2026-03-21

AI Summary

This study addresses the challenge of sample efficiency in estimating small failure probabilities when the limit state function is computationally expensive. To this end, the authors propose a single-stage joint training framework that simultaneously constructs a Gaussian process surrogate model and an optimal importance sampling density. Departing from conventional two-stage approaches, the method leverages shared observational data and employs kernel density estimation to adaptively generate the sampling distribution—termed KDE-AIS—which asymptotically converges to the zero-variance optimal density in total variation distance. Numerical experiments demonstrate that KDE-AIS achieves higher estimation accuracy with fewer calls to the true model compared to existing methods, including Gaussian process-based adaptive importance sampling schemes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• failure probability estimation
• importance sampling
• surrogate modeling
• sample efficiency
• expensive oracle evaluations

Innovation

• adaptive importance sampling
• Gaussian process surrogate
• failure probability estimation
• kernel density estimation
• zero-variance IS density