Statistical Analysis of Multi-Relational Network Recovery

Frontiers in Applied Mathematics and Statistics

Xueying Tang¹  Zhi Wang²  Jingchen Liu² 

[1] Department of Mathematics, University of Arizona, Tucson, AZ, United States;Department of Statistics, Columbia University, New York, NY, United States;

关键词: multi-relational network;    knowledge graph completion;    tail probability;    risk;    asymptotic analysis;    non-asymptotic analysis;   

DOI  :  10.3389/fams.2020.540225

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown