A Logistic Factorization Model for Recommender Systems with Multinomial Responses

In this paper, 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.