2025/05/19 by Liam A. Kruse, Marc R. Schlichting, Kruse, Liam A. +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Probability and Risk Models #Robotics (cs.RO)
paper · pdf · doi:10.48550/arxiv.2505.13335
openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.