A regression framework for studying relationships among attributes under network interference

TL;DR

This paper introduces a scalable, interpretable regression framework for analyzing relationships among attributes in networks with interdependent outcomes, supported by theoretical guarantees and demonstrated through simulations and social media data.

Contribution

It presents a novel regression framework that models complex dependencies in network data with provable convergence and scalability, integrating interpretability with computational efficiency.

Findings

Framework effectively captures attribute relationships in networks

Scalable optimization via convex methods demonstrated

Theoretical convergence guarantees established

Abstract

To understand how the interconnected and interdependent world of the twenty-first century operates and make model-based predictions, joint probability models for networks and interdependent outcomes are needed. We propose a comprehensive regression framework for networks and interdependent outcomes with multiple advantages, including interpretability, scalability, and provable theoretical guarantees. The regression framework can be used for studying relationships among attributes of connected units and captures complex dependencies among connections and attributes, while retaining the virtues of linear regression, logistic regression, and other regression models by being interpretable and widely applicable. On the computational side, we show that the regression framework is amenable to scalable statistical computing based on convex optimization of pseudo-likelihoods using minorization-maximization methods. On the theoretical side, we establish convergence rates for pseudo-likelihood estimators based on a single observation of dependent connections and attributes. We demonstrate the regression framework using simulations and an application to hate speech on the social media platform X.