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Geometric Methods for Robust Data Analysis in High Dimension.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Geometric Methods for Robust Data Analysis in High Dimension./
Author:	Anderson, Joseph Timothy.
Description:	1 online resource (178 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369838626

Geometric Methods for Robust Data Analysis in High Dimension.
Anderson, Joseph Timothy.

Geometric Methods for Robust Data Analysis in High Dimension. - 1 online resource (178 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Data-driven applications are growing. Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics. These applications rely on large quantities of data gathered from automated sensors and user input. Furthermore, the dimensionality of many datasets is extreme: more details are being gathered about single user interactions or sensor readings. All of these applications encounter problems with a common theme: use observed data to make inferences about the world. Our work obtains the first provably efficient algorithms for Independent Component Analysis (ICA) in the presence of heavy-tailed data. The main tool in this result is the centroid body (a well-known topic in convex geometry), along with optimization and random walks for sampling from a convex body. This is the first algorithmic use of the centroid body and it is of independent theoretical interest, since it effectively replaces the estimation of covariance from samples, and is more generally accessible.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369838626Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Geometric Methods for Robust Data Analysis in High Dimension.
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245 1 0 $a Geometric Methods for Robust Data Analysis in High Dimension.
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300 $a 1 online resource (178 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Advisers: Luis Rademacher; Anastasios Sidiropolous.
502 $a Thesis (Ph.D.) $c The Ohio State University $d 2017.
504 $a Includes bibliographical references
520 $a Data-driven applications are growing. Machine learning and data analysis now finds both scientific and industrial application in biology, chemistry, geology, medicine, and physics. These applications rely on large quantities of data gathered from automated sensors and user input. Furthermore, the dimensionality of many datasets is extreme: more details are being gathered about single user interactions or sensor readings. All of these applications encounter problems with a common theme: use observed data to make inferences about the world. Our work obtains the first provably efficient algorithms for Independent Component Analysis (ICA) in the presence of heavy-tailed data. The main tool in this result is the centroid body (a well-known topic in convex geometry), along with optimization and random walks for sampling from a convex body. This is the first algorithmic use of the centroid body and it is of independent theoretical interest, since it effectively replaces the estimation of covariance from samples, and is more generally accessible.
520 $a We demonstrate that ICA is itself a powerful geometric primitive. That is, having access to an efficient algorithm for ICA enables us to efficiently solve other important problems in machine learning. The first such reduction is a solution to the open problem of efficiently learning the intersection of n + 1 halfspaces in Rn, posed in [43]. This reduction relies on a non-linear transformation of samples from such an intersection of halfspaces (i.e. a simplex) to samples which are approximately from a linearly transformed product distribution. Through this transformation of samples, which can be done efficiently, one can then use an ICA algorithm to recover the vertices of the intersection of halfspaces.
520 $a Finally, we again use ICA as an algorithmic primitive to construct an efficient solution to the widely-studied problem of learning the parameters of a Gaussian mixture model. Our algorithm again transforms samples from a Gaussian mixture model into samples which fit into the ICA model and, when processed by an ICA algorithm, result in recovery of the mixture parameters. Our algorithm is effective even when the number of Gaussians in the mixture grows with the ambient dimension, even polynomially in the dimension. In addition to the efficient parameter estimation, we also obtain a complexity lower bound for a low-dimension Gaussian mixture model.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Computer science. $3 573171
655 7 $a Electronic books. $2 local $3 554714
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690 $a 0984
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The Ohio State University. $b Computer Science and Engineering. $3 1180873
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10610128 $z click for full text (PQDT)