A Latent Logistic Regression Model with Graph Data

TL;DR

This paper introduces a latent logistic regression model for network data that accounts for node influence, using a latent indicator, with an EM algorithm for estimation and tests for dependence.

Contribution

It proposes a novel latent logistic regression model with a latent indicator for network influence, along with a score test and EM algorithm for parameter estimation.

Findings

Model effectively captures network dependence in binary responses.

Simulation studies demonstrate accurate parameter estimation.

Real data analysis confirms model's practical utility.

Abstract

Recently, graph (network) data is an emerging research area in artificial intelligence, machine learning and statistics. In this work, we are interested in whether node's labels (people's responses) are affected by their neighbor's features (friends' characteristics). We propose a novel latent logistic regression model to describe the network dependence with binary responses. The key advantage of our proposed model is that a latent binary indicator is introduced to indicate whether a node is susceptible to the influence of its neighbour. A score-type test is proposed to diagnose the existence of network dependence. In addition, an EM-type algorithm is used to estimate the model parameters under network dependence. Extensive simulations are conducted to evaluate the performance of our method. Two public datasets are used to illustrate the effectiveness of the proposed latent logistic regression model.