论文标题
光谱贝叶斯网络理论
Spectral Bayesian Network Theory
论文作者
论文摘要
贝叶斯网络（BN）是一个概率模型，它使用有向的无环图（DAG）表示一组变量。从数据中学习BN结构的当前算法集中于估计特定DAG的边缘，并且通常会导致许多“可能的”网络结构。在本文中，我们为一种侧重于学习DAG的全球属性而不是精确边缘的方法奠定了基础。这是通过定义BN的结构超图来完成的，BN显示与网络的逆稳定性矩阵有关。光谱边界是针对归一化的反合率矩阵得出的，该矩阵与相关BN的最大indegree密切相关。
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.
