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arXiv 2210.01489cs.LG
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核结构图的生成模型与学习算法

Generative Models and Learning Algorithms for Core-Periphery Structured Graphs

Indian Institute of Science(印度科学学院)

Sravanthi Gurugubelli, Sundeep Prabhakar Chepuri

摘要:

我们考虑核心-外围结构图,这些图分别具有一组密集连接和稀疏连接的节点,称为核心节点和外围节点。所谓的节点的核心得分与其成为核心节点的可能性有关。在本文中,我们专注于学习一个图的节点属性和连通性结构的核心分数。为此,我们提出了两类概率图模型:仿射和非线性。首先,我们描述仿射生成模型来模拟节点属性对其核心分数的依赖性,这决定了图的结构。接下来,我们讨论了非线性生成模型,其中节点属性的偏相关性通过潜在核心分数影响图结构。我们开发的算法,用于推断模型参数和核心分数的图形时,图形结构和节点属性。当只有图的节点属性可用时,我们共同学习核心-外围结构图及其核心分数。我们提供了几个合成和真实世界的数据集上的数值实验结果,以证明所开发的模型和算法的有效性。

英文摘要:

We consider core-periphery structured graphs, which are graphs with a group of densely and sparsely connected nodes, respectively, referred to as core and periphery nodes. The so-called core score of a node is related to the likelihood of it being a core node. In this paper, we focus on learning the core scores of a graph from its node attributes and connectivity structure. To this end, we propose two classes of probabilistic graphical models: affine and nonlinear. First, we describe affine generative models to model the dependence of node attributes on its core scores, which determine the graph structure. Next, we discuss nonlinear generative models in which the partial correlations of node attributes influence the graph structure through latent core scores. We develop algorithms for inferring the model parameters and core scores of a graph when both the graph structure and node attributes are available. When only the node attributes of graphs are available, we jointly learn a core-periphery structured graph and its core scores. We provide results from numerical experiments on several synthetic and real-world datasets to demonstrate the efficacy of the developed models and algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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