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A Regularization Perspective on Spec...

Liao, Zhenyu.

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A Regularization Perspective on Spectral Sparsification.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A Regularization Perspective on Spectral Sparsification./
作者:	Liao, Zhenyu.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	80 p.
附註:	Source: Dissertations Abstracts International, Volume: 81-06, Section: B.
Contained By:	Dissertations Abstracts International81-06B.
標題:	Computer science. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13424514
ISBN:	9781392668023

A Regularization Perspective on Spectral Sparsification.
Liao, Zhenyu.

A Regularization Perspective on Spectral Sparsification. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 80 p.

Source: Dissertations Abstracts International, Volume: 81-06, Section: B.

Thesis (Ph.D.)--Boston University, 2019.

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

In this thesis, we study how to obtain faster algorithms for spectral graph sparsifi-cation by applying continuous optimization techniques. Spectral sparsification is thetask of reducing the number of edges in a graph while maintaining a spectral ap-proximation to the original graph. Our key conceptual contribution is the connectionbetween spectral sparsification and regret minimization in online matrix games, i.e.,online convex programming over the positive semidefinite cone. While this connec-tion was previously noted [24, 47], we formally reduce graph sparsification to a matrixregret minimization problem, which we solve by applying mirror descent with a non-entropic regularizer. In this way, we not only obtain a new proof of the existenceof linear-sized spectral sparsifiers, originally given by [19], but improve the runningtime from Ω(n4)([19, 54]) to almost quadratic. More generally, our framework canalso be applied for the matrix multi-armed bandit online learning problem to reducethe regret bound to the optimalO(√nT), compared to theO(√nTlog(n) given bythe traditional matrix-entropy regulariz.

ISBN: 9781392668023Subjects--Topical Terms:

523869
Computer science.

A Regularization Perspective on Spectral Sparsification.
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520 $a In this thesis, we study how to obtain faster algorithms for spectral graph sparsifi-cation by applying continuous optimization techniques. Spectral sparsification is thetask of reducing the number of edges in a graph while maintaining a spectral ap-proximation to the original graph. Our key conceptual contribution is the connectionbetween spectral sparsification and regret minimization in online matrix games, i.e.,online convex programming over the positive semidefinite cone. While this connec-tion was previously noted [24, 47], we formally reduce graph sparsification to a matrixregret minimization problem, which we solve by applying mirror descent with a non-entropic regularizer. In this way, we not only obtain a new proof of the existenceof linear-sized spectral sparsifiers, originally given by [19], but improve the runningtime from Ω(n4)([19, 54]) to almost quadratic. More generally, our framework canalso be applied for the matrix multi-armed bandit online learning problem to reducethe regret bound to the optimalO(√nT), compared to theO(√nTlog(n) given bythe traditional matrix-entropy regulariz.
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