  Factorization machines (FMs) are a powerful tool for regression and
classification in the context of sparse observations, that has been
successfully applied to collaborative filtering, especially when side
information over users or items is available. Bayesian formulations of FMs have
been proposed to provide confidence intervals over the predictions made by the
model, however they usually involve Markov-chain Monte Carlo methods that
require many samples to provide accurate predictions, resulting in slow
training in the context of large-scale data. In this paper, we propose a
variational formulation of factorization machines that allows us to derive a
simple objective that can be easily optimized using standard mini-batch
stochastic gradient descent, making it amenable to large-scale data. Our
algorithm learns an approximate posterior distribution over the user and item
parameters, which leads to confidence intervals over the predictions. We show,
using several datasets, that it has comparable or better performance than
existing methods in terms of prediction accuracy, and provide some applications
in active learning strategies, e.g., preference elicitation techniques.
