# Scalable Importance Sampling in High Dimensions with Low-Rank Mixture Proposals

arXiv: https://arxiv.org/abs/2505.13335 · HTML: https://mlsanity.com/paper/2505.13335/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 9 of 9)

- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [On GANs and GMMs](https://mlsanity.com/paper/1805.12462/) (2018)
- [Accelerated Evaluation of Automated Vehicles Safety in Lane Change Scenarios Based on Importance Sampling Techniques](https://mlsanity.com/paper/1605.04965/) (2016)
- [Solving Stabilize-Avoid Optimal Control via Epigraph Form and Deep Reinforcement Learning](https://mlsanity.com/paper/2305.14154/) (2023)
- [Efficient Black-box Assessment of Autonomous Vehicle Safety](https://mlsanity.com/paper/1912.03618/) (2019)
- [Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling](https://mlsanity.com/paper/2310.09194/) (2023)

## Abstract (arXiv)

Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal distribution, importance sampling allows for more sample-efficient estimation of rare events or tails of distributions. A common choice of proposal density is a Gaussian mixture model (GMM). However, estimating full-rank GMM covariance matrices in high dimensions is a challenging task due to numerical instabilities. In this work, we propose using mixtures of probabilistic principal component analyzers (MPPCA) as the parametric proposal density for importance sampling methods. MPPCA models are a type of low-rank mixture model that can be fit quickly using expectation-maximization, even in high-dimensional spaces. We validate our method on three simulated systems, demonstrating consistent gains in sample efficiency and quality of failure distribution characterization.