# A generalized likelihood-weighted optimal sampling algorithm for rare-event probability quantification

arXiv: https://arxiv.org/abs/2310.14457 · HTML: https://mlsanity.com/paper/2310.14457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 22 Oct 2023.

## Builds on (most cited first, 12 of 12)

- [Accelerated Evaluation of Automated Vehicles Safety in Lane Change Scenarios Based on Importance Sampling Techniques](https://mlsanity.com/paper/1605.04965/) (2016)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems](https://mlsanity.com/paper/1804.07240/) (2018)
- [Output-weighted and relative entropy loss functions for deep learning precursors of extreme events](https://mlsanity.com/paper/2112.00825/) (2021)
- [Adaptive Safety Evaluation for Connected and Automated Vehicles with Sparse Control Variates](https://mlsanity.com/paper/2212.00517/) (2022)
- [Output-weighted optimal sampling for Bayesian regression and rare event statistics using few samples](https://mlsanity.com/paper/1907.07552/) (2019)
- [Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs](https://mlsanity.com/paper/2102.10085/) (2021)
- [An adaptive multi-fidelity sampling framework for safety analysis of connected and automated vehicles](https://mlsanity.com/paper/2210.14114/) (2022)
- [Sequential Bayesian experimental design for estimation of extreme-event probability in stochastic dynamical systems](https://mlsanity.com/paper/2102.11108/) (2021)
- [Extreme event probability estimation using PDE-constrained optimization and large deviation theory, with application to tsunamis](https://mlsanity.com/paper/2007.13930/) (2020)
- [Optimization under rare chance constraints](https://mlsanity.com/paper/2011.06052/) (2020)
- [Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems](https://mlsanity.com/paper/2306.15159/) (2023)

## Abstract (arXiv)

In this work, we introduce a new acquisition function for sequential sampling to efficiently quantify rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. Our acquisition is a generalization of the likelihood-weighted (LW) acquisition that was initially designed for the same purpose and then extended to many other applications. The improvement in our acquisition comes from the generalized form with two additional parameters, by varying which one can target and address two weaknesses of the original LW acquisition: (1) that the input space associated with rare-event responses is not sufficiently stressed in sampling; (2) that the surrogate model (generated from samples) may have significant deviation from the true ItR function, especially for cases with complex ItR function and limited number of samples. In addition, we develop a critical procedure in Monte-Carlo discrete optimization of the acquisition function, which achieves orders of magnitude acceleration compared to existing approaches for such type of problems. The superior performance of our new acquisition to the original LW acquisition is demonstrated in a number of test cases, including some cases that were designed to show the effectiveness of the original LW acquisition. We finally apply our method to an engineering example to quantify the rare-event roll-motion statistics of a ship in a random sea.