Probabilistic Inference and Learning with Stein's Method

2026-03-08

AI Summary

This work addresses the efficient construction and utilization of Stein methods for distributional metrics and optimization in probabilistic reasoning and learning. By establishing a general framework for constructing Stein discrepancies, it systematically analyzes their computability, separating properties, and capacity to detect and control convergence of probability measures. The study further elucidates the theoretical connection between Stein operators and Stein Variational Gradient Descent (SVGD). Beyond clarifying the foundational theoretical properties of Stein discrepancies, this research develops a unified framework that bridges variational inference and nonparametric distribution approximation, thereby providing a rigorous theoretical foundation and practical pathway for designing efficient and verifiable probabilistic learning algorithms.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein sets, and properties of these discrepancies such as computability, separation, convergence detection, and convergence control are discussed. Further, the connection between Stein operators and Stein variational gradient descent is set out in detail. The main definitions and results are precisely stated, and references to all proofs are provided.

Problem

• probabilistic inference
• Stein's method
• Stein discrepancy
• convergence control
• Stein variational gradient descent

Innovation

• Stein's method
• Stein discrepancy
• probabilistic inference
• Stein variational gradient descent
• convergence control