Rare Event Probability Learning by Normalizing Flows
Zhenggqi Gao Dinghuai Zhang Luca Daniel Duane S. Boning
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.