发表机构
University of Wrocław; Tooploox; TRAILS; University of Warsaw; Warsaw University of Technology; IDEAS Research Institute; Wrocław University of Science and Technology（弗罗茨瓦夫大学; Tooploox; TRAILS; 华沙大学; 华沙理工大学; IDEAS研究所; 弗罗茨瓦夫理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对稀有事件概率估计，提出基于约束高斯混合的重要性采样框架，通过覆盖与拟合两阶段及有限方差约束，显著提升效率与鲁棒性，优于多种基线方法。
AI 中文摘要
我们研究估计稀有事件概率 $I = \mathbb{P}(g(\mathbf{X}) > \gamma)$ 的问题，其中 $\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$，$g: \mathbb{R}^d \to \mathbb{R}$ 为一般函数。我们通过重要性采样解决该问题，并提出一个框架，该框架在效率和鲁棒性上显著优于基线方法，如原始蒙特卡洛、自适应交叉熵、基于变分推断的方法（包括反向和正向KL方法），以及Safe-ICE、子集模拟和序列蒙特卡洛，借鉴了稀有事件估计和交叉熵优化的思想。关键贡献包含两部分：首先，我们将问题分解为覆盖（coverage）和拟合（fitting）两个阶段，覆盖阶段用于克服冷启动障碍，拟合阶段用于在获得有意义信号后细化提议分布；其次，我们约束最终的GMM提议分布，使其具有有限的重要性采样方差（因为仅靠覆盖不足以保证——若无保护措施，重要性采样仍可能遭受无限方差）。这些要素共同产生表达力强的提议分布；有限方差本身并不能保证在固定采样预算下的实际稳定性。大量实验表明，该方法显著降低方差，在多样化基准上表现出强鲁棒性，并具有有利的成本-效率权衡，所提方法通常优于这些基线，特别是在高维和多模态设置中，竞争方法经常变得不稳定或失败。我们的代码可在 https://this https URL 获取。
英文摘要
We study estimating rare-event probabilities $I = \mathbb{P}(g(\mathbf{X}) > γ)$ with $\mathbf{X} \sim \mathcal{N}(\boldsymbolμ, \boldsymbolΣ)$ 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 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.
CommentsAccepted at NeurIPS 2026
