Movie Rating Recommender System using PMRF

Recommendation algorithms are used by systems that provide users with speedy customized experience. Users give ratings to movies based on the extent they like them on websites like IMDB, MovieLens, Rotten Tomatoes. In this paper, we try to predict ratings for movies user has not given yet, based on the ratings user has given to other movies in past. We want to discuss this movie recommendation problem as an inference problem that can be represented using Pairwise Markov Random Fields (PMRF). Applying PMRF to movie ratings and calculating marginal probabilities for unseen movie ratings yields exponential time complexity. For this reason, we have utilized Belief Propagation algorithm, which only increases time complexity linearly with number of items. This approach is basically a collaborative filtering approach where the items are represented as nodes and the similarities among the users are predicted in their rating behavior based on their past ratings. We can use this approach to only provide real-time update for a single active user without affecting the others, keeping complexity linear for a single user. The prediction of the ratings is not linear, but is exponential in complexity with increasing variables, so Belief Propagation and inference via message passing are preferred among the nodes of the model. We apply a deterministic method to calculate the similarities, as well as show a learning approach for more accuracy in similarities of the active user with others. We also evaluate our results via various error comparing schemes.