NetworkNet: A Deep Neural Network Approach for Random Networks with Sparse Nodal Attributes and Complex Nodal Heterogeneity

TL;DR

NetworkNet is a deep neural network method designed to model complex heterogeneity in random networks with high-dimensional nodal attributes, offering interpretability, scalability, and effective attribute selection.

Contribution

It introduces a novel neural architecture that explicitly models nodal heterogeneity and performs scalable attribute selection, bridging classical network models with deep learning.

Findings

Strong performance in heterogeneity estimation and attribute selection in simulations.

Effective application to a large-scale author-citation network reveals new insights.

Provides a non-asymptotic error bound combining statistical rigor with deep learning.

Abstract

Heterogeneous network data with rich nodal information become increasingly prevalent across multidisciplinary research, yet accurately modeling complex nodal heterogeneity and simultaneously selecting influential nodal attributes remains an open challenge. This problem is central to many applications in economics and sociology, when both nodal heterogeneity and high-dimensional individual characteristics highly affect network formation. We propose a statistically grounded, unified deep neural network approach for modeling nodal heterogeneity in random networks with high-dimensional nodal attributes, namely ``NetworkNet''. A key innovation of NetworkNet lies in a tailored neural architecture that explicitly parameterizes attribute-driven heterogeneity, and at the same time, embeds a scalable attribute selection mechanism. NetworkNet consistently estimates two types of latent heterogeneity functions, i.e., nodal expansiveness and popularity, while simultaneously performing data-driven attribute selection to extract influential nodal attributes. By unifying classical statistical network modeling with deep learning, NetworkNet delivers the expressive power of DNNs with methodological interpretability, algorithmic scalability, and statistical rigor with a non-asymptotic approximation error bound. Empirically, simulations demonstrate strong performance in both heterogeneity estimation and high-dimensional attribute selection. We further apply NetworkNet to a large-scale author-citation network among statisticians, revealing new insights into the dynamic evolution of research fields and scholarly impact.