| Summary: | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Cataloged from student-submitted PDF version of thesis. === Includes bibliographical references (pages 121-128). === In this thesis, we tackle three challenges in recommender systems (RS): scalability, privacy and structured recommendations. We first develop a scalable primal dual algorithm for matrix completion based on trace norm regularization. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block coordinate descent algorithm for solving the dual problem with a few spectral constraints. Empirical results illustrate the effectiveness of our method in comparison to recently proposed alternatives. In addition, we extend the method to non-negative matrix factorization (NMF) and dictionary learning for sparse coding. Privacy is another important issue in RS. Indeed, there is an inherent trade-off between accuracy of recommendations and the extent to which users are willing to release information about their preferences. We explore a two-tiered notion of privacy where there is a small set of public users who are willing to share their preferences openly, and a large set of private users who require privacy guarantees. We show theoretically, and demonstrate empirically, that a moderate number of public users with no access to private user information already suffices for reasonable accuracy. Moreover, we introduce a new privacy concept for gleaning relational information from private users while maintaining a first order deniability. We demonstrate gains from controlled access to private user preferences. We further extend matrix completion to high-order tensors. We illustrate the problem of recommending a set of items to users as a tensor completion problem. We develop methods for directly controlling tensor factorizations in terms of the degree of nonlinearity (the number of non-uniform modes in rank-1 components) as well as the overall number of rank-1 components. Finally, we develop a tensor factorization for dependency parsing. Instead of manually selecting features, we use tensors to map high-dimensional sparse features into low dimensional (dense) features. Our parser achieves state of the art results across multiple languages. === by Yu Xin. === Ph. D.
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