Conformal matrix factorization based recommender system

Recommender systems can be viewed as prediction systems wherein one can predict the rating a user would give to a particular item. Typically, items having the highest predicted ratings will be recommended to the user. Matrix Factorization techniques are the most widely used methods in predicting the missing ratings of a user-item rating matrix due to their efficiency and accuracy in prediction. However, users do not know how certain these predictions are. Hence, it is important to associate a confidence measure to the predictions which tells the users how certain the system is in making the predictions. Confidence is a very useful concept in recommender systems which can help users in making decisions about which movies to watch, which books to buy and so on. Different approaches have been proposed to estimate the confidence in recommender systems but none of them provide a guarantee on the error rate of these predictions. Conformal Prediction is a framework which makes it possible to control the number of erroneous predictions by selecting a suitable confidence level which can be varied depending on the application. In this paper, we propose Conformal Matrix Factorization (CMF) and show different ways of adapting conformal prediction to matrix factorization. Nonconformity measure is a key concept of conformal prediction which needs to be defined by careful investigation of the underlying algorithm. We propose and analyse different nonconformity measures based on matrix factorization and experimentally show that the accuracy of the best nonconformity measure is very close to the accuracy of the underlying algorithm.We show that the proposed method yields promising results in terms of prediction accuracy along with confidence measure.