  Recommending items to users is a challenging task due to the large amount of
missing information. In many cases, the data solely consist of ratings or tags
voluntarily contributed by each user on a very limited subset of the available
items, so that most of the data of potential interest is actually missing.
Current approaches to recommendation usually assume that the unobserved data is
missing at random. In this contribution, we provide statistical evidence that
existing movie recommendation datasets reveal a significant positive
association between the rating of items and the propensity to select these
items. We propose a computationally efficient variational approach that makes
it possible to exploit this selection bias so as to improve the estimation of
ratings from small populations of users. Results obtained with this approach
applied to neighborhood-based collaborative filtering illustrate its potential
for improving the reliability of the recommendation.
