2026-09-19T03:29:19Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1139322026-06-16T18:55:26Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Asuman Ozdaglar and Devavrat Shah.
Lee, Christina (Christina Esther)
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2018-03-02T21:39:48Z
2018-03-02T21:39:48Z
2017
2017
http://hdl.handle.net/1721.1/113932
1023861300
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.
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 255-264).
Similarity based collaborative filtering for matrix completion is a popular heuristic that has been used widely across industry in the previous decades to build recommendation systems, due to its simplicity and scalability. However, despite its popularity, there has been little theoretical foundation explaining its widespread success. In this thesis, we prove theoretical guarantees for collaborative filtering under a nonparametric latent variable model, which arises from the natural property of "exchangeability", i.e. invariance under relabeling of the dataset. The analysis suggests that similarity based collaborative filtering can be viewed as kernel regression for latent variable models, where the features are not directly observed and the kernel must be estimated from the data. In addition, while classical collaborative filtering typically requires a dense dataset, this thesis proposes a new collaborative filtering algorithm which compares larger radius neighborhoods of data to compute similarities, and show that the estimate converges even for very sparse datasets, which has implications towards sparse graphon estimation. The algorithms can be applied in a variety of settings, such as recommendations for online markets, analysis of social networks, or denoising crowdsourced labels.
by Christina E. Lee.
Ph.D.
264 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Latent variable model estimation via collaborative filtering
Thesis
application/pdf
false
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="5134b383-4583-462e-8195-6593500c9662">
<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>Latent variable model estimation via collaborative filtering</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2017</PublicationDate>
<Authors>
<Author>
<DisplayName>Lee, Christina (Christina Esther)</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>Similarity based collaborative filtering for matrix completion is a popular heuristic that has been used widely across industry in the previous decades to build recommendation systems, due to its simplicity and scalability. However, despite its popularity, there has been little theoretical foundation explaining its widespread success. In this thesis, we prove theoretical guarantees for collaborative filtering under a nonparametric latent variable model, which arises from the natural property of "exchangeability", i.e. invariance under relabeling of the dataset. The analysis suggests that similarity based collaborative filtering can be viewed as kernel regression for latent variable models, where the features are not directly observed and the kernel must be estimated from the data. In addition, while classical collaborative filtering typically requires a dense dataset, this thesis proposes a new collaborative filtering algorithm which compares larger radius neighborhoods of data to compute similarities, and show that the estimate converges even for very sparse datasets, which has implications towards sparse graphon estimation. The algorithms can be applied in a variety of settings, such as recommendations for online markets, analysis of social networks, or denoising crowdsourced labels.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>