# Achieving Efficiency in Black Box Simulation of Distribution Tails with Self-structuring Importance Samplers

arXiv: https://arxiv.org/abs/2102.07060 · HTML: https://mlsanity.com/paper/2102.07060/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 100 references that are in the map.
- First posted on arXiv 14 Feb 2021.

## Builds on (most cited first, 15 of 15)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Large-Scale Methods for Distributionally Robust Optimization](https://mlsanity.com/paper/2010.05893/) (2020)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Fairness risk measures](https://mlsanity.com/paper/1901.08665/) (2019)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)
- [Accelerated Evaluation of Automated Vehicles Safety in Lane Change Scenarios Based on Importance Sampling Techniques](https://mlsanity.com/paper/1605.04965/) (2016)
- [Applying Deep Learning to the Newsvendor Problem](https://mlsanity.com/paper/1607.02177/) (2016)
- [PROVEN: Certifying Robustness of Neural Networks with a Probabilistic Approach](https://mlsanity.com/paper/1812.08329/) (2018)
- [Accelerated Evaluation of Automated Vehicles Using Piecewise Mixture Models](https://mlsanity.com/paper/1701.08915/) (2017)
- [Deep Probabilistic Accelerated Evaluation: A Robust Certifiable Rare-Event Simulation Methodology for Black-Box Safety-Critical Systems](https://mlsanity.com/paper/2006.15722/) (2020)
- [Rare-Event Simulation for Neural Network and Random Forest Predictors](https://mlsanity.com/paper/2010.04890/) (2020)
- [Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives](https://mlsanity.com/paper/2008.09818/) (2020)
- [Rare-Event Simulation for Distribution Networks](https://mlsanity.com/paper/1706.05602/) (2017)

## Built on by (most cited first, 6 of 6)

- [Certifiable Deep Importance Sampling for Rare-Event Simulation of Black-Box Systems](https://mlsanity.com/paper/2111.02204/) (2021)
- [Importance Sampling-Guided Meta-Training for Intelligent Agents in Highly Interactive Environments](https://mlsanity.com/paper/2407.15839/) (2024)
- [Stochastic Optimization with Optimal Importance Sampling](https://mlsanity.com/paper/2504.03560/) (2025)
- [Efficient Black-Box Importance Sampling for VaR and CVaR Estimation](https://mlsanity.com/paper/2106.10236/) (2021)
- [Reliability Sensitivity with Response Gradient](https://mlsanity.com/paper/2510.09315/) (2025)
- [An Extreme Value Perspective on Learning Stress Laws](https://mlsanity.com/paper/2607.10700/) (2026)

## Abstract (arXiv)

This paper presents a novel Importance Sampling (IS) scheme for estimating distribution tails of performance measures modeled with a rich set of tools such as linear programs, integer linear programs, piecewise linear/quadratic objectives, feature maps specified with deep neural networks, etc. The conventional approach of explicitly identifying efficient changes of measure suffers from feasibility and scalability concerns beyond highly stylized models, due to their need to be tailored intricately to the objective and the underlying probability distribution. This bottleneck is overcome in the proposed scheme with an elementary transformation which is capable of implicitly inducing an effective IS distribution in a variety of models by replicating the concentration properties observed in less rare samples. This novel approach is guided by developing a large deviations principle that brings out the phenomenon of self-similarity of optimal IS distributions. The proposed sampler is the first to attain asymptotically optimal variance reduction across a spectrum of multivariate distributions despite being oblivious to the specifics of the underlying model. Its applicability is illustrated with contextual shortest path and portfolio credit risk models informed by neural networks