Besides the probabilistic item similarity functions discussed in Computing Item Similarity, several fully probabilistic formulations of collaborative filtering have been proposed and gained some currency. These
methods generally aim to build probabilistic models of user behavior
and use those models to predict future behavior. The core idea of proba-
bilistic methods is to compute either P(i|u), the probability that user u
will purchase or view item i, or the probability distribution P(ru,i|u)
over user u’s rating of item i (and the related problem E[ru,i], the
expected value of u’s rating of i).