A Logistic Factorization Model for Recommender Systems With Multinomial Responses

Yu Wang, Xuan Bi, Annie Qu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this article, we propose a two-way multinomial logistic model for recommender systems for categorical ratings. Specifically, we treat the possible ratings as mutually exclusive events, whose probability is determined by the latent factor of the users and the items through a two-way multinomial logistic function. The proposed method has a compatibility with categorical ratings and the advantage of incorporating both the covariate information and the latent factors of the users and items uniformly. We show numerically that the proposed method performs consistently better than five commonly used collaborative filtering methods, namely, the restricted singular value decomposition, the soft-impute matrix completion method, the regression-based latent factor models, the restricted Boltzmann machine, and the group-specific recommender system on various simulation setups and on MovieLens data. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)396-404
Number of pages9
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Apr 2 2020

Bibliographical note

Funding Information:
We would like to acknowledge support for this project from the National Science Foundation grants DMS-1415308, DMS-1613190, DMS-1821198, CPS-1329991 and AFOSR grant FA9550-15-1-0059. We greatly appreciate the comments and suggestions provided by the three anonymous reviewers, which improve the manuscript significantly.

Publisher Copyright:
© 2019, © 2019 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.


  • Cold-start problem
  • Collaborative filter
  • MovieLens


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