Rating Proportion-Aware Binomial Matrix Factorization for Collaborative Filtering

Addressing biases in observed data is a major challenge in statistical and machine learning applications. This challenge also exists in recommendation systems, and various methods based on causal inference are being investigated. We investigate a collaborative filtering technique that robustly predicts ratings from biased observation. Utilizing the proportion of unbiased ratings in the different data sources, we extend collaborative filtering by adding a term for the proportion of ratings estimates from collaborative filtering to be closer to the proportion of ratings in unbiased data. Our aim is to obtain less biased estimates from observations that include bias. The proposed method is based on collaborative filtering with binomial matrix factorization, which treats observations and predictions as discrete variables. By treating the proportion of ratings in the unbiased case as a probability distribution, we introduce a constraint term that minimizes the KL divergence with the estimates by collaborative filtering. The binomial matrix factorization allows for direct calculation of the KL term due to the discrete assumption. The simple extension by adding the constraint term can be straightforwardly combined with various existing methods, such as inverse propensity weighting matrix factorization. Experimental results show that the standalone proposed method improves MSE from the conventional method, and the proposed method combined with inverse propensity score weighting also still improves slightly.