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 $20\mathrm{\%}$ 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 $50\mathrm{\%}$ increase of long-tail recommendations), a valuable feature for Recommender Systems with a large catalogue of products.