Collaborative filtering with representation learning in the frequency domain

In the context of recommender systems, collaborative filtering is the method of predicting the ratings of a set of items given by a set of users based on partial knowledge of the ratings. Commonly, items and users are represented via vectors, and to predict ratings, approaches such as vector inner-product (aka matrix factorization) or more advanced nonlinear functions are applied. In this paper, while we adopt the common vectorial representation, we consider a general model in which the ratings are smooth functions of the item representations. Smoothness ensures similar items with nearby vectors will also get similar ratings as we expect from a human rater. We represent user smooth scoring functions in a so-called frequency domain and learn their representations alongside item representations using 1) an iterative optimization approach that maps items and users alternatively, and 2) a feedforward neural network consisting of interpretable layers. We also address the challenge of the distribution shift from observed to unobserved ratings (aka missing-not-at-random) with insights from the frequency domain. We evaluate the predictive power of our method and its robustness in missed-not-at-random settings on four popular benchmarks. Despite its simplicity and interpretability, our method yields a remarkable performance compared to the state-of-the-art.1