Entropic Mirror Monte Carlo

2026-02-03

AI Summary

This work addresses the well-known limitation of importance sampling, whose efficiency in high-dimensional, multimodal, or otherwise complex target distributions critically depends on the choice of the proposal distribution. To overcome this challenge, the authors propose a novel adaptive method for constructing effective proposal distributions. The approach integrates a global exploration mechanism with a delayed weighting strategy, enabling rapid resampling in regions where the proposal poorly matches the target and dynamically adjusting weights to enhance stability. Under mild assumptions, the algorithm is theoretically shown to achieve geometric convergence. Extensive numerical experiments demonstrate that the proposed method significantly outperforms existing approaches in both sampling efficiency and robustness across a range of challenging distributional scenarios.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.

Problem

• importance sampling
• proposal distribution
• multimodal distributions
• high-dimensional spaces
• Monte Carlo methods

Innovation

• adaptive importance sampling
• delayed weighting
• global exploration
• geometric convergence
• proposal distribution