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

Shi, Chengchun, Lu, Wenbin and Song, Rui (2019) Determining the number of latent factors in statistical multi-relational learning. Journal of Machine Learning Research, 20. 1 - 38. ISSN 1532-4435

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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.

Item Type: Article
Official URL:
Additional Information: © 2019 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 15 Oct 2019 12:27
Last Modified: 20 Oct 2021 00:59

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