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Topics in Optimization and Learning.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topics in Optimization and Learning./
Author:	Bohorquez, Cindy Catherine Orozco .
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	137 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
Subject:	Sample size. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28812925
ISBN:	9798494456779

Topics in Optimization and Learning.
Bohorquez, Cindy Catherine Orozco .

Topics in Optimization and Learning. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 137 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--Stanford University, 2021.

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

Optimization algorithms that learn from data have been around for a long time. Nevertheless, the ever-changing nature of computational resources, the development of modern theoretical tools, and the availability of new kinds of data keep us wondering what is possible in this field. This work gives us a fresh look at three classical problems: point-set registration, multi-resolution analysis, and tensor factorization. First, we explore how the least unsquared loss ensures exact recovery of the optimal rotation between two point clouds under gross corruption. We also show a phase transition of the probability of exact recovery when the least unsquared loss is optimized over convex sets containing the special orthogonal group. Second, we present a neural network architecture inspired in the non-standard wavelet form, called BCR-net. The BCR-net uses significantly fewer parameters than standard neural networks and shows promising behavior compressing non-linear integral operators. Lastly, we discuss the implications of defining a factorization-preserving algebra to evaluate functions over high-dimensional tensors. We focus on what makes tensors in tensor ring form challenging to work with, and we give insights on how to overcome these challenges.

ISBN: 9798494456779Subjects--Topical Terms:

3642155
Sample size.

Topics in Optimization and Learning.
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100 1 $a Bohorquez, Cindy Catherine Orozco . $3 3689305
245 1 0 $a Topics in Optimization and Learning.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 137 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Ying, Lexing;Darve, Eric;Gerritsen, Margot.
502 $a Thesis (Ph.D.)--Stanford University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a Optimization algorithms that learn from data have been around for a long time. Nevertheless, the ever-changing nature of computational resources, the development of modern theoretical tools, and the availability of new kinds of data keep us wondering what is possible in this field. This work gives us a fresh look at three classical problems: point-set registration, multi-resolution analysis, and tensor factorization. First, we explore how the least unsquared loss ensures exact recovery of the optimal rotation between two point clouds under gross corruption. We also show a phase transition of the probability of exact recovery when the least unsquared loss is optimized over convex sets containing the special orthogonal group. Second, we present a neural network architecture inspired in the non-standard wavelet form, called BCR-net. The BCR-net uses significantly fewer parameters than standard neural networks and shows promising behavior compressing non-linear integral operators. Lastly, we discuss the implications of defining a factorization-preserving algebra to evaluate functions over high-dimensional tensors. We focus on what makes tensors in tensor ring form challenging to work with, and we give insights on how to overcome these challenges.
590 $a School code: 0212.
650 4 $a Sample size. $3 3642155
650 4 $a Motivation. $3 532704
650 4 $a Applied mathematics. $3 2122814
650 4 $a Wavelet transforms. $3 3681479
650 4 $a Optimization. $3 891104
650 4 $a Neural networks. $3 677449
650 4 $a Multiplication & division. $3 3680536
650 4 $a Phase transitions. $3 3560387
650 4 $a Numerical analysis. $3 517751
650 4 $a Homogenization. $3 3561160
650 4 $a Data science. $3 3689306
650 4 $a Registration. $3 3682192
650 4 $a Algorithms. $3 536374
650 4 $a Performance evaluation. $3 3562292
650 4 $a Artificial intelligence. $3 516317
650 4 $a Computer science. $3 523869
650 4 $a Mathematics. $3 515831
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710 2 $a Stanford University. $3 754827
773 0 $t Dissertations Abstracts International $g 83-05B.
790 $a 0212
791 $a Ph.D.
792 $a 2021
793 $a English
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