Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures

arXiv:2610.07485v1 Announce Type: new Abstract: We study estimating rare-event probabilities I = P(g(mathbf{X}) > gamma) with mathbf{X} sim N(oldsymbol{mu}, oldsymbol{Sigma}) and general g : R^d o R. We address this problem through importance sampling, and propose a framework that substantially improves efficiency and robustness over baselines such as crude Monte Carlo, adaptive cross-entropy, variational-inference-based methods (including reverse- and forward-KL approaches), as well as Safe-ICE, Subset Simulation, and Sequential Monte Carlo, drawing on ideas from both rare-event estimation and cross-entropy optimization. The key contribution has two parts: first, we separate the problem into coverage, to overcome the cold-start barrier, and fitting, to refine proposals once a meaningful signal is available; second, we constrain the final GMM proposal so that it has finite importance-sampling variance (since coverage alone is not sufficient -- without safeguards, importance sampling may still suffer from infinite variance). Together, these ingredients yield expressive proposals; finite variance does not by itself guarantee practical stability at a fixed sampling budget. Extensive experiments demonstrate substantial variance reduction, strong robustness across diverse benchmarks, and favorable cost--efficiency trade-offs, with the proposed approach often outperforming these baselines, particularly in high-dimensional and multimodal settings where competing methods frequently become unstable or fail. Our code is available at https://github.com/lorek/robust-cfi-is.

Source: arXiv cs.LG | 2026-10-07

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