Determining the Number of Latent Factors in Statistical Multi-Relational Learning.

TitleDetermining the Number of Latent Factors in Statistical Multi-Relational Learning.
Publication TypeJournal Article
Year of Publication2019
AuthorsShi, Chengchun, Wenbin Lu, and Rui Song
JournalJ Mach Learn Res
Volume20
Date Published2019
ISSN1532-4435
Abstract

Statistical relational learning is primarily concerned with learning and inferring relationships between entities in large-scale knowledge graphs. Nickel et al. (2011) proposed a RESCAL tensor factorization model for statistical relational learning, which achieves better or at least comparable results on common benchmark data sets when compared to other state-of-the-art methods. Given a positive integer , RESCAL computes an -dimensional latent vector for each entity. The latent factors can be further used for solving relational learning tasks, such as collective classification, collective entity resolution and link-based clustering. The focus of this paper is to determine the number of latent factors in the RESCAL model. Due to the structure of the RESCAL model, its log-likelihood function is not concave. As a result, the corresponding maximum likelihood estimators (MLEs) may not be consistent. Nonetheless, we design a specific pseudometric, prove the consistency of the MLEs under this pseudometric and establish its rate of convergence. Based on these results, we propose a general class of information criteria and prove their model selection consistencies when the number of relations is either bounded or diverges at a proper rate of the number of entities. Simulations and real data examples show that our proposed information criteria have good finite sample properties.

DOI10.1214/009053606000001217
Alternate JournalJ Mach Learn Res
Original PublicationDetermining the number of latent factors in statistical multi-relational learning.
PubMed ID31983896
PubMed Central IDPMC6980192
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
Project: