Statistical Analysis of Multi-Relational Network Recovery

TL;DR

This paper develops asymptotic theories and error bounds for latent variable models in large multi-relational networks, demonstrating estimator consistency and near-optimality as network size grows.

Contribution

It introduces new asymptotic results and error bounds for penalized maximum likelihood estimators in large-scale multi-relational network models.

Findings

Establishes consistency of estimators as network size increases.

Provides non-asymptotic error bounds via large deviations analysis.

Shows estimators are nearly minimax optimal.

Abstract

In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum likelihood estimators when the size of the network tends to infinity. The basic technique is to develop a non-asymptotic error bound for the maximum likelihood estimators through large deviations analysis of random fields. We also show that these estimators are nearly optimal in terms of minimax risk.