Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures

Excerpt

arXiv:2610.07485v1 Announce Type: new Abstract: We study estimating rare-event probabilities $I = \mathbb{P}(g(\mathbf{X}) > \gamma)$ with $\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$ and general $g : \mathbb{R}^d \to \mathbb{R}$. 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 r