Rare Event Probability Learning by Normalizing Flows
This addresses inefficiencies in rare event probability estimation for domains relying on Monte Carlo methods, though it is incremental as it builds on existing normalizing flow techniques.
The paper tackles the problem of accurately estimating low-probability rare events, proposing NOFIS, a method that uses normalizing flows and importance sampling to achieve superior performance over baselines in 10 test cases.
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.