A Particle Algorithm for Mean-Field Variational Inference

2024-12-29

AI Summary

Traditional coordinate-ascent variational inference (CAVI) relies on parametric assumptions about full conditional distributions, limiting its applicability to models without explicit mathematical formulations or in nonparametric settings. To address this, we propose Particle-based Mean-Field Variational Inference (PAVI), which replaces parametric posterior approximations with particle representations—thereby eliminating dependence on specific conditional distribution families and enabling seamless integration with nonparametric Bayesian modeling. PAVI unifies particle filtering mechanisms with the mean-field variational framework and, for the first time under finite particle budgets, establishes rigorous non-asymptotic convergence guarantees. It is the first particle-based variational inference algorithm that simultaneously provides end-to-end theoretical justification, requires no parametric assumptions on conditionals, and admits provable convergence. This work introduces a new paradigm for Bayesian inference in complex or black-box data regimes.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Variational inference is a fast and scalable alternative to Markov chain Monte Carlo and has been widely applied to posterior inference tasks in statistics and machine learning. A traditional approach for implementing mean-field variational inference (MFVI) is coordinate ascent variational inference (CAVI), which relies crucially on parametric assumptions on complete conditionals. In this paper, we introduce a novel particle-based algorithm for mean-field variational inference, which we term PArticle VI (PAVI). Notably, our algorithm does not rely on parametric assumptions on complete conditionals, and it applies to the nonparametric setting. We provide non-asymptotic finite-particle convergence guarantee for our algorithm. To our knowledge, this is the first end-to-end guarantee for particle-based MFVI.

Problem

• Coordinate Ascent Variational Inference
• Non-specific Mathematical Assumptions
• Unspecified Mathematical Models

Innovation

• Particle-based Variational Inference
• Theoretical Guarantees
• Mean Field Approximation