|Title||Determining the Number of Latent Factors in Statistical Multi-Relational Learning.|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||Shi, Chengchun, Wenbin Lu, and Rui Song|
|Journal||J Mach Learn Res|
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.
|Alternate Journal||J Mach Learn Res|
|Original Publication||Determining the number of latent factors in statistical multi-relational learning.|
|PubMed Central ID||PMC6980192|
|Grant List||P01 CA142538 / CA / NCI NIH HHS / United States|
Determining the Number of Latent Factors in Statistical Multi-Relational Learning.