A Logistic Factorization Model for Recommender Systems With Multinomial Responses

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.本文面向分类评分推荐任务，提出一种双向多项逻辑回归模型。具体而言，我们将所有可选评分视作互斥事件，其概率由用户与物品的隐因子（latent factor）通过双向多项逻辑回归函数计算得到。所提方法不仅可适配分类评分任务，还能够统一整合协变量信息（covariate information）与用户、物品的隐因子，兼具双重优势。我们通过数值实验验证，在多种仿真实验配置与MovieLens数据集上，所提方法的表现始终优于五种常用协同过滤方法，分别为受限奇异值分解（restricted singular value decomposition）、软填充矩阵补全方法（soft-impute matrix completion method）、基于回归的隐因子模型（regression-based latent factor models）、受限玻尔兹曼机（restricted Boltzmann machine）以及分组专属推荐系统（group-specific recommender system）。本文的补充材料可在线获取。