Determining the number of latent factors in statistical multi-relational learning

Chengchun Shi, Wenbin Lu and Rui Song

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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 s, RESCAL computes an s-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.

Keywords: information criteria; knowledge graph; model selection consistency; RESCAL model; statistical relational learning; tensor factorization (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2019
New Economics Papers: this item is included in nep-ecm
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Published in Journal of Machine Learning Research, 2019, 20, pp. 1 - 38. ISSN: 1532-4435

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:102110

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