Pliable rejection sampling

2026-04-24

AI Summary

Traditional rejection sampling suffers from low efficiency due to high rejection rates, while existing adaptive approaches often compromise generality or lack theoretical guarantees. This work proposes Probabilistic Rejection Sampling (PRS), which for the first time integrates kernel density estimation into the rejection sampling framework. By adaptively learning the proposal distribution, PRS maintains approximate independence and identical distribution of generated samples while providing a provable lower bound on the number of accepted samples. The method effectively reconciles broad applicability with rigorous probabilistic performance guarantees, thereby overcoming the longstanding trade-off between efficiency and generality inherent in conventional rejection sampling techniques.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.

Problem

• rejection sampling
• high rejection rate
• adaptive sampling
• performance guarantees
• sampling proposal

Innovation

• rejection sampling
• kernel estimator
• adaptive sampling
• sample acceptance guarantee
• i.i.d. sampling