Open Access
December 2018 Multilayer tensor factorization with applications to recommender systems
Xuan Bi, Annie Qu, Xiaotong Shen
Ann. Statist. 46(6B): 3308-3333 (December 2018). DOI: 10.1214/17-AOS1659


Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this article, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested latent factors to accommodate between-subjects dependency. One major advantage is that the proposed method is able to address the “cold-start” issue in the absence of information from new customers, new products or new contexts. Specifically, it provides more effective recommendations through sub-group information. To achieve scalable computation, we develop a new algorithm for the proposed method, which incorporates a maximum block improvement strategy into the cyclic blockwise-coordinate-descent algorithm. In theory, we investigate algorithmic properties for convergence from an arbitrary initial point and local convergence, along with the asymptotic consistency of estimated parameters. Finally, the proposed method is applied in simulations and IRI marketing data with 116 million observations of product sales. Numerical studies demonstrate that the proposed method outperforms existing competitors in the literature.


Download Citation

Xuan Bi. Annie Qu. Xiaotong Shen. "Multilayer tensor factorization with applications to recommender systems." Ann. Statist. 46 (6B) 3308 - 3333, December 2018.


Received: 1 July 2017; Revised: 1 September 2017; Published: December 2018
First available in Project Euclid: 11 September 2018

zbMATH: 06965689
MathSciNet: MR3852653
Digital Object Identifier: 10.1214/17-AOS1659

Primary: 62M20
Secondary: 68T05 , 90C26

Keywords: Cold-start problem , context-aware recommender system , maximum block improvement , nonconvex optimization , tensor completion

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.46 • No. 6B • December 2018
Back to Top