A Propagation Framework for Network Regression

2026-01-15

AI Summary

Existing network regression methods often rely on ad hoc estimators or strong decay assumptions, limiting their ability to handle diverse data types uniformly and compromising robustness. This work proposes a Network Propagation Regression (NPR) framework that models the response variable as a function of covariates propagated through a network, simultaneously capturing both direct and indirect effects. NPR enables unified modeling for continuous, binary, multinomial, and survival outcomes, offering an interpretable, computationally efficient framework compatible with standard estimation techniques such as ordinary least squares and generalized linear models. It also provides formal hypothesis tests for the order of network influence. Theoretical analysis establishes consistency and asymptotic normality under mild conditions. Simulations and an empirical application to social media sentiment analysis demonstrate that NPR outperforms benchmark methods under model misspecification, exhibiting both robustness and practical utility.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Classification and Regression
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• network regression
• propagation
• indirect effects
• model misspecification
• network data

Innovation

• Network Propagation Regression
• network regression
• indirect effects
• ordinary least squares
• model robustness