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Devavrat Shah. Li, Yihua, M. Eng. Massachusetts Institute of Technology Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2016-12-22T15:17:25Z 2016-12-22T15:17:25Z 2016 2016 http://hdl.handle.net/1721.1/105983 965786624 Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016. 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 37-39). Neighborhood-based Collaborative filtering (CF) methods have proven to be successful in practice and are widely applied in commercial recommendation systems. Yet theoretical understanding of their performance is lacking. In this work, we introduce a new framework of Blind Regression which assumes that there are latent features associated with input variables, and we observe outputs of some Lipschitz continuous function over those unobserved features. We apply our framework to the problem of matrix completion and give a nonparametric method which, similar to CF, combines the local estimates according to the distance between the neighbors. We use the sample variance of the difference in ratings between neighbors as the proximity of the distance. Through error analysis, we show that the minimum sample variance is a good proxy of the prediction error in the estimates. Experiments on real-world datasets suggests that our matrix completion algorithm outperforms classic user-user and item-item CF approaches. Finally, our framework easily extends to the setting of higher-order tensors and we present our algorithm for tensor completion. The result from real-world application of image inpainting demonstrates that our method is competitive with the state-of-the-art tensor factorization approaches in terms of predictive performance. by Yihua Li. M.Eng. x, 39 pages eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Blind regression : understanding collaborative filtering from matrix completion to tensor completion Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="f43cf2c0-cbc1-462c-b922-57c6867be4a2"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Blind regression : understanding collaborative filtering from matrix completion to tensor completion</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2016</PublicationDate> <Authors> <Author> <DisplayName>Li, Yihua, M. Eng. Massachusetts Institute of Technology</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>Neighborhood-based Collaborative filtering (CF) methods have proven to be successful in practice and are widely applied in commercial recommendation systems. Yet theoretical understanding of their performance is lacking. In this work, we introduce a new framework of Blind Regression which assumes that there are latent features associated with input variables, and we observe outputs of some Lipschitz continuous function over those unobserved features. We apply our framework to the problem of matrix completion and give a nonparametric method which, similar to CF, combines the local estimates according to the distance between the neighbors. We use the sample variance of the difference in ratings between neighbors as the proximity of the distance. Through error analysis, we show that the minimum sample variance is a good proxy of the prediction error in the estimates. Experiments on real-world datasets suggests that our matrix completion algorithm outperforms classic user-user and item-item CF approaches. Finally, our framework easily extends to the setting of higher-order tensors and we present our algorithm for tensor completion. The result from real-world application of image inpainting demonstrates that our method is competitive with the state-of-the-art tensor factorization approaches in terms of predictive performance.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>