Nonparametric learning of heterogeneous graphical model on network-linked data

• URL: http://arxiv.org/abs/2507.01473v1
• Date: Wed, 02 Jul 2025 08:37:15 GMT
• Title: Nonparametric learning of heterogeneous graphical model on network-linked data
• Authors: Yuwen Wang, Changyu Liu, Xin He, Junhui Wang,
• Abstract summary: This paper proposes a nonparametric graphical model that accommodates heterogeneous graph structures without imposing any distributional assumptions.<n>It transforms the graph learning task into solving a finite-dimensional linear equation system by leveraging the properties of vector-valued kernel Hilbert space.<n>Its effectiveness is also demonstrated through a variety of simulated examples and a real application to the statistician coauthorship dataset.
• Score: 19.215806260939473
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex datasets such as network-linked data. This paper proposes a nonparametric graphical model that addresses these limitations by accommodating heterogeneous graph structures without imposing any specific distributional assumptions. The proposed estimation method effectively integrates network embedding with nonparametric graphical model estimation. It further transforms the graph learning task into solving a finite-dimensional linear equation system by leveraging the properties of vector-valued reproducing kernel Hilbert space. Moreover, theoretical guarantees are established for the proposed method in terms of the estimation consistency and exact recovery of the heterogeneous graph structures. Its effectiveness is also demonstrated through a variety of simulated examples and a real application to the statistician coauthorship dataset.

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