AUTHOR=Wang Zhi , Tang Xueying , Liu Jingchen 

TITLE=Statistical Analysis of Multi-Relational Network Recovery

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=6

YEAR=2020

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2020.540225

DOI=10.3389/fams.2020.540225

ISSN=2297-4687

ABSTRACT=<p>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.</p>