arXiv subjects

Pei Heng

Publications and source records attributed to Pei Heng.

4 recordsLinked to original sources

arXiv2026

Decomposition for Bayesian Networks: Local and Parallel Inference

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

stat.ML↗

arXiv2026

An efficient recursive decomposition algorithm for undirected graphs

The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum cardinality search (MCS) ordering in general undirected graphs. Specifically, we prove that applying a convex extension to the node numbered $1$ and its neighborhood in an MCS ordering yields an atom in the graph. Furthermore, based on the MCS ordering, we introduce a recursive algorithm for decomposing an undirected graph into its atoms. This approach closely aligns with the results of chordal graph decomposition. As a result, minimal triangulation of the graph is no longer required, and the identification of clique minimal separators is avoided. In the experimental section, we combine the proposed decomposition algorithm with two existing convex expansion methods. The results show that both combinations significantly outperform the existing algorithms in terms of efficiency.

cs.DS↗

arXiv2026

Structural Dimension Reduction in Bayesian Networks

This work introduces a novel technique, named structural dimension reduction, to collapse a Bayesian network onto a minimum and localized one while ensuring that probabilistic inferences between the original and reduced networks remain consistent. To this end, we propose a new combinatorial structure in directed acyclic graphs called the directed convex hull, which has turned out to be equivalent to their minimum localized Bayesian networks. An efficient polynomial-time algorithm is devised to identify them by determining the unique directed convex hulls containing the variables of interest from the original networks. Experiments demonstrate that the proposed technique has high dimension reduction capability in real networks, and the efficiency of probabilistic inference based on directed convex hulls can be significantly improved compared with traditional methods such as variable elimination and belief propagation algorithms. The code of this study is open at \href{https://github.com/Balance-H/Algorithms}{https://github.com/Balance-H/Algorithms} and the proofs of the results in the main body are postponed to the appendix.

stat.ML↗

arXiv2025

Revisiting Madigan and Mosurski: Collapsibility via Minimal Separators

Collapsibility provides a principled approach for dimension reduction in contingency tables and graphical models. Madigan and Mosurski (1990) pioneered the study of minimal collapsible sets in decomposable models, but existing algorithms for general graphs remain computationally demanding. We show that a model is collapsible onto a target set precisely when that set contains at least one minimal separator between its non-adjacent vertices. This insight motivates the Close Minimal Separator Absorption (CMSA) algorithm, which constructs minimal collapsible sets using only local separator searches at very low costs. Simulations confirm substantial efficiency gains, making collapsibility analysis practical in high-dimensional settings.

stat.ME↗