We introduce a unified and computationally efficient framework for regression on network data, addressing limitations of existing models that require specialized estimation procedures or impose restrictive decay assumptions. Our Network Propagation Regression (NPR) models outcomes as functions of covariates propagated through network connections, capturing both direct and indirect effects. NPR is estimable via ordinary least squares for continuous outcomes and standard routines for binary, categorical, and time-to-event data, all within a single interpretable framework. We establish consistency and asymptotic normality under weak conditions and develop valid hypothesis tests for the order of network influence. Simulation studies demonstrate that NPR consistently outperforms established approaches, such as the linear-in-means model and regression with network cohesion, especially under model misspecification. An application to social media sentiment analysis highlights the practical utility and robustness of NPR in real-world settings.

翻译：本文提出了一种统一且计算高效的网络数据回归框架，旨在解决现有模型需要专门估计程序或施加严格衰减假设的局限性。我们提出的网络传播回归（NPR）模型将结果变量建模为通过网络连接传播的协变量的函数，从而同时捕捉直接和间接效应。对于连续型结果变量，NPR可通过普通最小二乘法进行估计；对于二值、分类以及生存时间数据，则可通过标准流程进行估计，所有这些都包含在一个统一且可解释的框架内。我们在弱条件下建立了模型的一致性和渐近正态性，并针对网络影响的阶数开发了有效的假设检验。模拟研究表明，NPR始终优于现有方法，例如线性均值模型和网络凝聚回归，尤其是在模型设定错误的情况下。一项关于社交媒体情感分析的应用突显了NPR在实际场景中的实用性和鲁棒性。