Diversity-inducing probability measures for machine learning

Subset selection problems arise in machine learning within kernel approximation, experimental design, and numerous other applications. In such applications, one often seeks to select diverse subsets of items to represent the population. One way to select such diverse subsets is to sample according to Diversity-Inducing Probability Measures (DIPMs) that assign higher probabilities to more diverse subsets. DIPMs underlie several recent breakthroughs in mathematics and theoretical computer science, but their power has not yet been explored for machine learning. In this thesis, we investigate DIPMs, their mathematical properties, sampling algorithms, and applications. Perhaps the best known instance of a DIPM is a Determinantal Point Process (DPP). DPPs originally arose in quantum physics, and are known to have deep relations to linear algebra, combinatorics, and geometry. We explore applications of DPPs to kernel matrix approximation and kernel ridge regression.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Li, Chengtao,Ph. D.Massachusetts Institute of Technology.

Advisor dc:contributor.advisor

• Suvrit Sra and Stefanie Jegelka.

• Electrical Engineering and Computer Science.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/121724

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/121724