A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this challenge and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as a series of quantitative experiments encompassing $10$ distinct test cases, which highlight NOFIS's superiority over baseline approaches.

翻译：罕见事件定义为其发生概率极低的事件。精确估计此类微小概率在多个领域中至关重要。传统的蒙特卡洛方法效率低下，需要大量样本才能获得可靠估计。受归一化流精确采样能力的启发，我们重新审视这一挑战，提出归一化流辅助重要性采样方法，简称NOFIS。NOFIS首先通过最小化KL散度损失，学习与预定义嵌套子事件相关的一系列提议分布。随后，利用最后一个提议分布结合重要性采样，估计罕见事件概率。通过全面的定性可视化结果，我们验证了所学习提议分布的最优性；同时，包含$10$个不同测试案例的系列定量实验也证实了NOFIS方法相较于基线方法的优越性。