Quantile Matrix Factorization for Collaborative Filtering

Matrix Factorization-based algorithms are among the state-of-the-art in Collaborative Filtering methods. In many of these models, a least squares loss functional is implicitly or explicitly minimized and thus the resulting estimates correspond to the conditional mean of the potential rating a user might give to an item. However they do not provide any information on the uncertainty and the confidence of the Recommendation. We introduce a novel Matrix Factorization algorithm that estimates the conditional quantiles of the ratings. Experimental results demonstrate that the introduced model performs well and can potentially be a very useful tool in Recommender Engines by providing a direct measure of the quality of the prediction.