Spectral Bayesian network theory

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2023-10-01 DOI:10.1016/j.laa.2023.06.003

Luke Duttweiler, Sally W. Thurston, Anthony Almudevar

引用次数: 1

Abstract

A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often lead to many ‘likely’ network structures. In this paper, we lay the groundwork for an approach that focuses on learning global properties of the DAG rather than exact edges. This is done by defining the structural hypergraph of a BN, which is shown to be related to the inverse-covariance matrix of the network. Spectral bounds are derived for the normalized inverse-covariance matrix, which are shown to be closely related to the maximum indegree of the associated BN.

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谱贝叶斯网络理论

贝叶斯网络(BN)是一种概率模型，它使用有向无环图(DAG)表示一组变量。当前从数据中学习BN结构的算法侧重于估计特定DAG的边缘，并且通常会导致许多“可能的”网络结构。在本文中，我们为一种专注于学习DAG全局属性而不是精确边的方法奠定了基础。这是通过定义BN的结构超图来实现的，它被证明与网络的逆协方差矩阵相关。为归一化逆协方差矩阵导出了谱界，它被证明与相关BN的最大度密切相关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.