A Missing Information Loss function for implicit feedback datasets

Latent factor models for Recommender Systems with implicit feedback typically treat unobserved user-item interactions (i.e. missing information) as negative feedback. This is frequently done either through negative sampling (point--wise loss) or with a ranking loss function (pair-- or list--wise estimation). Since a zero preference recommendation is a valid solution for most common objective functions, regarding unknown values as actual zeros results in users having a zero preference recommendation for most of the available items. In this paper we propose a novel objective function, the \emph{Missing Information Loss} (MIL), that explicitly forbids treating unobserved user-item interactions as positive or negative feedback. We apply this loss to both traditional Matrix Factorization and user--based Denoising Autoencoder, and compare it with other established objective functions such as cross-entropy (both point- and pair-wise) or the recently proposed multinomial log-likelihood. MIL achieves competitive performance in ranking-aware metrics when applied to three datasets. Furthermore, we show that such a relevance in the recommendation is obtained while displaying popular items less frequently (up to a $20 \%$ decrease with respect to the best competing method). This debiasing from the recommendation of popular items favours the appearance of infrequent items (up to a $50 \%$ increase of long-tail recommendations), a valuable feature for Recommender Systems with a large catalogue of products.