Multi-relational Network Autoregression Model with Latent Group Structures

TL;DR

This paper introduces a novel tensor-based autoregressive model for multi-relational networks, incorporating latent group structures to handle heterogeneity and high-dimensional data, with theoretical guarantees and practical application.

Contribution

It proposes the GTNAR model that estimates group memberships and parameters simultaneously, addressing heterogeneity in multi-relational network time series.

Findings

Consistent estimation of group memberships and parameters.

Effective group number selection via an information criterion.

Successful application to Yelp data demonstrating practicality.

Abstract

Multi-relational networks among entities are frequently observed in the era of big data. Quantifying the effects of multiple networks have attracted significant research interest recently. In this work, we model multiple network effects through an autoregressive framework for tensor-valued time series. To characterize the potential heterogeneity of the networks and handle the high dimensionality of the time series data simultaneously, we assume a separate group structure for entities in each network and estimate all group memberships in a data-driven fashion. Specifically, we propose a group tensor network autoregression (GTNAR) model, which assumes that within each network, entities in the same group share the same set of model parameters, and the parameters differ across networks. An iterative algorithm is developed to estimate the model parameters and the latent group memberships simultaneously. Theoretically, we show that the group-wise parameters and group memberships can be consistently estimated when the group numbers are correctly- or possibly over-specified. An information criterion for group number estimation of each network is also provided to consistently select the group numbers. Lastly, we implement the method on a Yelp dataset to illustrate the usefulness of the method.