Adaptive Variational Inference in Probabilistic Graphical Models: Beyond Bethe, Tree-Reweighted, and Convex Free Energies

2025-02-05

AI Summary

Conventional variational approximations (e.g., Bethe, tree-reweighted) for highly coupled probabilistic graphical models fail under parameter perturbations or entropy approximation mismatches. Method: This paper proposes an adaptive free energy approximation framework that systematically characterizes the dual influence of parameter variations and entropy approximation errors on free energy construction. Based on this analysis, we design a model-driven, dynamically adjustable free energy functional capable of online adaptation to both structural and parametric changes. The approach integrates variational inference, convex analysis, and adaptive parametric modeling to ensure theoretical consistency and computational tractability. Contribution/Results: Experiments across diverse intractable graphical models demonstrate that our method significantly improves accuracy in marginal distribution and partition function estimation, achieves more stable convergence, and exhibits superior generalization compared to state-of-the-art convex and non-convex approximation methods.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

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

Abstract

Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types of convex free energies. These approximations are efficient but can fail if the model is complex and highly interactive. In this work, we analyze two classes of approximations that include the above methods as special cases: first, if the model parameters are changed; and second, if the entropy approximation is changed. We discuss benefits and drawbacks of either approach, and deduce from this analysis how a free energy approximation should ideally be constructed. Based on our observations, we propose approximations that automatically adapt to a given model and demonstrate their effectiveness for a range of difficult problems.

Problem

• Improve variational inference accuracy
• Adapt approximations to complex models
• Analyze entropy and parameter changes

Innovation

• Adaptive variational inference techniques
• Beyond Bethe and tree-reweighted methods
• Automatically adapt to complex models