Nonparametric learning of heterogeneous graphical model on network-linked data

TL;DR

This paper introduces a nonparametric graphical model for network-linked data that captures heterogeneous structures without distributional assumptions, combining network embedding with kernel methods and providing theoretical guarantees.

Contribution

It proposes a novel nonparametric estimation approach that integrates network embedding and kernel methods to learn heterogeneous graphical models without distributional assumptions.

Findings

The method achieves consistent estimation of heterogeneous graph structures.

The approach enables exact recovery of the underlying graph in simulations.

Application to coauthorship data demonstrates practical effectiveness.

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.