A bayesian model for collaborative filtering

Consider the general setup where a set of items have been partially rated by a set of judges, in the sense that not every item has been rated by every judge. For this setup, we propose a Bayesian approach for the problem of predicting the missing ratings from the observed ratings. This approach incorporates similarity by assuming the set of judges can be partitioned into groups which share the same ratings probability distribution. This leads to a predictive distribution of missing ratings based on the posterior distribution of the groupings and associated ratings probabilities. Markov chain Monte Carlo methods and a hybrid search algorithm are then used to obtain predictions of the missing ratings.