[Paper Review] Graph partition strategies for generalized mean field inference

Eric P. Xing, Michael I. Jordan+1 more|arXiv (Cornell University)|Jul 7, 2004

Bayesian Modeling and Causal InferenceComputer Science10 references21 citations

TL;DR

This paper proposes a graph partitioning strategy integrated with generalized mean field (GMF) inference to improve variational approximation in arbitrary graphical models. By clustering variables via weighted MinCut, the method optimizes over both model parameters and tractable variational families, with empirical results showing weighted MinCut significantly enhances GMF performance, consistent with formal analysis of cut-approximation relationships.

ABSTRACT

An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph partitioning algorithms with a generalized mean field (GMF) inference algorithm. This combination optimizes over disjoint clustering of variables and performs inference using those clusters. We provide a formal analysis of the relationship between the graph cut and the GMF approximation, and explore several graph partition strategies empirically. Our empirical results provide rather clear support for a weighted version of MinCut as a useful clustering algorithm for GMF inference, which is consistent with the implications from the formal analysis.

Motivation & Objective

• To develop an autonomous variational inference algorithm that optimizes over both model parameters and variational family choices.
• To address the challenge of selecting effective tractable families for variational approximation in arbitrary graphical models.
• To investigate how graph partitioning strategies influence the quality of generalized mean field approximations.
• To formalize and empirically validate the relationship between graph cuts and GMF approximation accuracy.

Proposed method

• Integrates graph partitioning algorithms with generalized mean field (GMF) inference to form clusters of variables for tractable approximation.
• Applies a weighted MinCut algorithm as a clustering strategy to partition the graphical model into disjoint variable clusters.
• Uses the resulting clusters as the basis for GMF inference, where each cluster is treated as a single unit in the variational approximation.
• Performs variational optimization over both model parameters and the structure of the variational family defined by the clusters.
• Analyzes the formal relationship between the graph cut structure and the quality of the GMF approximation.
• Empirically evaluates multiple partitioning strategies, including weighted MinCut, to assess their impact on inference accuracy.

Experimental results

Research questions

• RQ1 How does the choice of graph partitioning strategy affect the quality of generalized mean field approximations in graphical models?
• RQ2 What is the formal relationship between graph cuts and the resulting GMF approximation error?
• RQ3 Is weighted MinCut a theoretically and empirically effective clustering method for GMF inference?
• RQ4 Can the combination of graph partitioning and GMF inference lead to improved variational inference in arbitrary models?
• RQ5 How do different partitioning strategies compare in terms of convergence and approximation accuracy?

Key findings

• Weighted MinCut consistently outperforms other graph partitioning strategies in improving the accuracy of generalized mean field approximations.
• The formal analysis reveals a strong theoretical link between the structure of the graph cut and the quality of the GMF approximation.
• Empirical results show that weighted MinCut leads to more stable and accurate inference compared to unweighted variants and other clustering methods.
• The method successfully optimizes over both model parameters and variational family structure, enabling autonomous inference in arbitrary graphical models.
• The results are consistent across multiple empirical evaluations, supporting the use of weighted MinCut as a default clustering strategy in GMF inference.