Yang, Fan2018-08-142018-08-142018-05https://hdl.handle.net/11299/199051University of Minnesota Ph.D. dissertation. 2018. Major: Statistics. Advisor: Xiaotong Shen. 1 computer file (PDF); 95 pages.Recommender systems aim to predict users’ ratings on items and suggest certain items to users that they are most likely to be interested in. Recent years there has been a lot of interest in developing recommender systems, especially personalized recommender systems to efficiently provide personalized services and increase conversion rates in commerce. Personalized recommender systems identify every individual’s preferences through analyzing users’ behavior, and sometimes also analyzing user and item feature information. Existing recommender system methods typically ignore the correlations between ratings given by a user. However, based on our observation the correlations can be strong. We propose a new personalized recommender system method that takes into account the correlation structure of ratings by a user. General precision matrices are estimated for the ratings of each user and clustered among users by supervised clustering. Moreover, in the proposed model we utilize user and item feature information, such as the demographic information of users and genres of movies. Individual preferences are estimated and grouped over users and items to find similar individuals that are close in nature. Computationally, we designed an algorithm applying the difference of convex method and the alternating direction method of multipliers to deal with the nonconvexity of the loss function and the fusion type penalty respectively. Theoretical rate of convergence is investigated for our new method. We also show theoretically that incorporating the correlation structure gives higher asymptotic efficiency of the estimators compared to ignoring it. Both simulation studies and Movielens data indicate that our method outperforms existing competitive recommender system methods.enCorrelation EstimationPersonalizedRecommender SystemSupervised ClusteringThesis or Dissertation