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Space-Filling Designs and Big Data S...

University of California, Los Angeles.

Space-Filling Designs and Big Data Subsampling.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Space-Filling Designs and Big Data Subsampling.
Author:	Wang, Lin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2019
Description:	80 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Notes:	Advisor: Xu, Hongquan.
Contained By:	Dissertations Abstracts International81-03B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13900373
ISBN:	9781085676977

Space-Filling Designs and Big Data Subsampling.
Wang, Lin.

Space-Filling Designs and Big Data Subsampling. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 80 p.

Source: Dissertations Abstracts International, Volume: 81-03, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2019.

This item must not be sold to any third party vendors.

Space-filling designs are commonly used in computer experiments and other scenarios for investigating complex systems, but the construction of such designs is challenging. In this thesis, we construct a series of maximin-distance Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin L1-distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns. The procedure is further extended to the construction of multi-level nonregular fractional factorial designs which have better properties than regular designs. Existing research on the construction of nonregular designs focuses on two-level designs. We construct a novel class of multilevel nonregular designs by permuting levels of regular designs via the Williams transformation. The constructed designs can reduce aliasing among effects without increasing the run size. They are more efficient than regular designs for studying quantitative factors. In addition, we explore the application of experimental design strategies to data-driven problems and develop a subsampling framework for big data linear regression. The subsampling procedure inherits optimality from the design matrices and therefore minimizes the mean squared error of coefficient estimations for sufficiently large data. It works especially well for the problem of label-constrained regression where a large covariate dataset is available but only a small set of labels are observable. The subsampling procedure can also be used for big data reduction where computation and storage issues are the primary concern.

ISBN: 9781085676977Subjects--Topical Terms:

182057
Statistics.

Space-Filling Designs and Big Data Subsampling.
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300 $a 80 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
500 $a Advisor: Xu, Hongquan.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Space-filling designs are commonly used in computer experiments and other scenarios for investigating complex systems, but the construction of such designs is challenging. In this thesis, we construct a series of maximin-distance Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin L1-distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns. The procedure is further extended to the construction of multi-level nonregular fractional factorial designs which have better properties than regular designs. Existing research on the construction of nonregular designs focuses on two-level designs. We construct a novel class of multilevel nonregular designs by permuting levels of regular designs via the Williams transformation. The constructed designs can reduce aliasing among effects without increasing the run size. They are more efficient than regular designs for studying quantitative factors. In addition, we explore the application of experimental design strategies to data-driven problems and develop a subsampling framework for big data linear regression. The subsampling procedure inherits optimality from the design matrices and therefore minimizes the mean squared error of coefficient estimations for sufficiently large data. It works especially well for the problem of label-constrained regression where a large covariate dataset is available but only a small set of labels are observable. The subsampling procedure can also be used for big data reduction where computation and storage issues are the primary concern.
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