Essays in problems in sequential decisions and large-scale randomized algorithms / Peichao Peng.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Peng, Peichao, author.

Contributor:

Steele, J. Michael, degree supervisor, degree committee member.

Foster, Dean, degree supervisor, degree committee member.

Zhao, Linda, 1969- degree committee member.

University of Pennsylvania. Department of Statistics, degree granting institution.

Language:

English

Subjects (All):

Penn dissertations--Statistics.

Statistics--Penn dissertations.

Local Subjects:

Penn dissertations--Statistics.

Statistics--Penn dissertations.

Physical Description:

ix, 94 leaves : illustrations ; 29 cm

Production:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2016.

Summary:

In 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, Guluru, based on subsampled randomized Hadamard transform, to solve a wide class of generalized linear models.

Notes:

Ph. D. University of Pennsylvania 2016.

Department: Statistics.

Supervisor: J. Michael Steele; Dean Foster.

Includes bibliographical references.

OCLC:

961021856