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A Propagation Framework for Network Regression

Yingying Ma, Chenlei Leng

TL;DR

Network Propagation Regression (NPR) provides a unified, interpretable framework for network-dependent regression by modeling outcomes as covariates diffused across multi-step network paths. It yields estimable, scalable procedures via ordinary least squares (for continuous outcomes) or standard GLMs, with theoretical guarantees of consistency and asymptotic normality under mild conditions and a statistically principled method to select the effective propagation radius. Extensions to binary and survival outcomes (network logistic regression and network Cox models) preserve interpretability while handling diverse data types. Empirical results from simulations and social media sentiment analysis show NPR robustly outperforms traditional approaches under misspecification and offers practical, scalable inference for network-diffusion processes.

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.

A Propagation Framework for Network Regression

TL;DR

Network Propagation Regression (NPR) provides a unified, interpretable framework for network-dependent regression by modeling outcomes as covariates diffused across multi-step network paths. It yields estimable, scalable procedures via ordinary least squares (for continuous outcomes) or standard GLMs, with theoretical guarantees of consistency and asymptotic normality under mild conditions and a statistically principled method to select the effective propagation radius. Extensions to binary and survival outcomes (network logistic regression and network Cox models) preserve interpretability while handling diverse data types. Empirical results from simulations and social media sentiment analysis show NPR robustly outperforms traditional approaches under misspecification and offers practical, scalable inference for network-diffusion processes.

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.
Paper Structure (19 sections, 7 theorems, 28 equations, 3 figures, 4 tables)

This paper contains 19 sections, 7 theorems, 28 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contributions
  4. The Network Propagation Model
  5. Model Formulation
  6. Estimation
  7. Determining the Relevant Neighborhood Order
  8. A Unified Framework
  9. Network Logistic Regression Model
  10. Network Cox Proportional Hazards Model
  11. Simulation
  12. Data Generation Mechanisms
  13. Performance Evaluation
  14. Finite-Sample Performance of Hypothesis Tests
  15. Social Media Sentiment Analysis
  16. ...and 4 more sections

Key Result

Proposition 1

For any row-normalized adjacency matrix $W$ and any positive integer $k$,

Figures (3)

  • Figure 1: Robustness comparison between the network propagation and cohesion models. Left: Data generated from the network cohesion model (Setting 4). Our method achieves competitive performance, demonstrating robustness to model misspecification. Right: Data generated from the network propagation model (Setting 3). Our method consistently outperforms the cohesion model, which exhibits overfitting for small network sizes.
  • Figure 2: Frequencies of emotion-related keywords (left) and emotion categories (right) in user comments.
  • Figure 3: Histograms of in-degrees (left) and out-degrees (right) for the social media comment network.

Theorems & Definitions (8)

  • Proposition 1
  • Theorem 1: Estimation Consistency
  • Theorem 2: Asymptotic Normality
  • Corollary 1: Variance Estimator Consistency
  • Theorem 3: High-Dimensional Asymptotics for Wald Statistic
  • Remark 1
  • Theorem 4: Asymptotic Normality for Binary Responses
  • Theorem 5: Asymptotic Normality for Network Cox Model