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.

翻译：摘要：富含节点信息的异质性网络数据在跨学科研究中日益普遍，然而如何精确建模复杂的节点异质性并同时筛选出具有影响力的节点属性，仍是一个开放性的挑战。当节点异质性与高维个体特征显著影响网络形成时，该问题在经济与社会学的众多应用中至关重要。我们提出了一种具有统计依据的统一深度神经网络方法，用于对具有高维节点属性的随机网络中的节点异质性进行建模，即“NetworkNet”。NetworkNet的一项关键创新在于其定制化的神经架构：该架构显式参数化了由属性驱动的异质性，同时嵌入了一种可扩展的属性选择机制。NetworkNet能够一致地估计两种潜在的异质性函数——即节点扩展性与节点流行性，并同步执行数据驱动的属性选择以提取具有影响力的节点属性。通过将经典统计网络建模与深度学习相统一，NetworkNet在保留深度神经网络表达能力的同时，兼具方法可解释性、算法可扩展性以及具备非渐近近似误差界的统计严谨性。实证模拟表明，该方法在异质性估计与高维属性选择方面均表现出强大性能。我们进一步将NetworkNet应用于一个大规模的统计学者合作引用网络，揭示了研究领域动态演进与学术影响力的新见解。