Essays in Problems in Sequential Decisions and Large-Scale Randomized Algorithms

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dc.contributor.advisorMichael Steele
dc.contributor.advisorDean Foster
dc.contributor.authorPeng, Peichao
dc.date2023-05-17T16:05:33.000
dc.date.accessioned2023-05-22T16:51:40Z
dc.date.available2016-04-28T00:00:00Z
dc.date.copyright2016-11-29T00:00:00-08:00
dc.date.issued2016-01-01
dc.date.submitted2016-11-29T13:00:08-08:00
dc.description.abstractIn the first part of this dissertation, we consider two problems in sequential decision making. The first problem we consider is sequential selection of a monotone subsequence from a random permutation. We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length $n$. The second problem we consider deals with the multiplicative relaxation or constriction of the classical problem of the number of records in a sequence of $n$ independent and identically distributed observations. In the relaxed case, we find a central limit theorem (CLT) with a different normalization than Renyi's classical CLT, and in the constricted case we find convergence in distribution to an unbounded random variable. In the second part of this dissertation, we put forward two large-scale randomized algorithms. We propose a two-step sensing scheme for the low-rank matrix recovery problem which requires far less storage space and has much lower computational complexity than other state-of-art methods based on nuclear norm minimization. We introduce a fast iterative reweighted least squares algorithm, \textit{Guluru}, based on subsampled randomized Hadamard transform, to solve a wide class of generalized linear models.
dc.description.degreeDoctor of Philosophy (PhD)
dc.format.extent103 p.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/28805
dc.languageen
dc.legacy.articleid3727
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=3727&context=edissertations&unstamped=1
dc.provenanceReceived from ProQuest
dc.rightsPeichao Peng
dc.source.issue1941
dc.source.journalPublicly Accessible Penn Dissertations
dc.source.statuspublished
dc.subject.otherStatistics and Probability
dc.titleEssays in Problems in Sequential Decisions and Large-Scale Randomized Algorithms
dc.typeDissertation/Thesis
digcom.contributor.authorisAuthorOfPublication|email:ppeichao@wharton.upenn.edu|institution:University of Pennsylvania|Peng, Peichao
digcom.date.embargo2016-04-28T00:00:00-07:00
digcom.identifieredissertations/1941
digcom.identifier.contextkey9424801
digcom.identifier.submissionpathedissertations/1941
digcom.typedissertation
dspace.entity.typePublication
relation.isAuthorOfPublicationce1f3708-7f94-49a5-9104-76cfec051e65
relation.isAuthorOfPublication.latestForDiscoveryce1f3708-7f94-49a5-9104-76cfec051e65
upenn.graduate.groupStatistics
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