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dc.contributor.advisorSuvrit Sra and Stefanie Jegelka.en_US
dc.contributor.authorLi, Chengtao,Ph. D.Massachusetts Institute of Technology.en_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2019-07-17T20:57:57Z
dc.date.available2019-07-17T20:57:57Z
dc.date.copyright2019en_US
dc.date.issued2019en_US
dc.identifier.urihttps://hdl.handle.net/1721.1/121724
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 163-176).en_US
dc.description.abstractSubset 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.en_US
dc.description.abstractIn these applications, DPPs deliver strong approximation guarantees and obtain superior performance compared to existing methods. We further develop an MCMC sampling algorithm accelerated by Gauss-type quadratures for DPPs. The algorithm runs several orders of magnitude faster than the existing ones. DPPs lie in a larger class of DIPMs called Strongly Rayleigh (SR) Measures. Instances of SR measures display a strong negative dependence property known as negative association, and as such can be used to model subset diversity. We study mathematical properties of SR measures, and construct the first provably fast-mixing Markov chain that samples from general SR measures. As a special case, we consider an SR measure called Dual Volume Sampling (DVS), for which we present the first poly-time sampling algorithm.en_US
dc.description.abstractWhile all considered distributions over subsets are unconstrained, those of interest in the real world usually come with constraints due to prior knowledge, resource limitations or personal preferences. Hence we investigate sampling from constrained versions of DIPMs. Specifically, we consider DIPMs with cardinality constraints and matroid base constraints and construct poly-time approximate sampling algorithms for them. Such sampling algorithms will enable practical uses of constrained DIPMs in real world.en_US
dc.description.statementofresponsibilityby Chengtao Li.en_US
dc.format.extent176 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT 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.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleDiversity-inducing probability measures for machine learningen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.identifier.oclc1102048939en_US
dc.description.collectionPh.D. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Scienceen_US
dspace.imported2019-07-17T20:57:53Zen_US
mit.thesis.degreeDoctoralen_US
mit.thesis.departmentEECSen_US


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