Estimating confidence of individual user predictions in item-based recommender systems

This paper focuses on recommender systems based on item-item collaborative filtering (CF). Although research on item-based methods is not new, current literature does not provide any reliable insight on how to estimate confidence of recommendations. The goal of this paper is to fill this gap, by investigating the conditions under which item-based recommendations will succeed or fail for a specific user. We formalize the item-based CF problem as an eigenvalue problem, where estimated ratings are equivalent to the true (unknown) ratings multiplied by a user-specific eigenvalue of the similarity matrix. We show that the magnitude of the eigenvalue related to a user is proportional to the accuracy of recommendations for that user. We define a confidence parameter called the eigenvalue confidence index, analogous to the eigenvalue of the similarity matrix, but simpler to be computed. We also show how to extend the eigenvalue confidence index to matrix-factorization algorithms. A comprehensive set of experiments on five datasets show that the eigenvalue confidence index is effective in predicting, for each user, the quality of recommendations. On average, our confidence index is 3 times more correlated with MAP with respect to previous confidence estimates.