Multilinear tensor regression for longitudinal relational data

TL;DR

This paper introduces a multilinear tensor regression model for analyzing longitudinal relational data, capturing dependencies like reciprocity and transitivity in social networks over time.

Contribution

It develops a novel tensor regression framework that models complex dependencies in multivariate relational data, including a tensor autoregression special case.

Findings

Model captures key relational patterns such as reciprocity and transitivity.

Tensor autoregression effectively models temporal dependencies in relational data.

The approach provides a parsimonious and flexible way to analyze complex network dynamics.

Abstract

A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between members of another pair. This article develops a type of regression model to estimate such effects in the context of longitudinal and multivariate relational data, or other data that can be represented in the form of a tensor. The model is based on a general multilinear tensor regression model, a special case of which is a tensor autoregression model in which the tensor of relations at one time point are parsimoniously regressed on relations from previous time points. This is done via a separable, or Kronecker-structured, regression parameter along with a separable covariance model. In the context of an analysis of longitudinal multivariate relational data, it is shown how the multilinear tensor regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity.