  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.
