國立虎尾科技大學 |

A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems./
作者:	Kadkhodaie Elyaderani, Mojtaba.
面頁冊數:	1 online resource (166 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Contained By:	Dissertation Abstracts International79-04B(E).
標題:	Electrical engineering. -
電子資源:	click for full text (PQDT)
ISBN:	9780355416190

A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems.
Kadkhodaie Elyaderani, Mojtaba.

A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems. - 1 online resource (166 pages)

Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Modern machine learning problems that emerge from real-world applications typically involve estimating high dimensional model parameters, whose number may be of the same order as or even significantly larger than the number of measurements. In such high dimensional settings, statistically-consistent estimation of true underlying models via classical approaches is often impossible, due to the lack of identifiability. A recent solution to this issue is through incorporating regularization functions into estimation procedures to promote intrinsic low-complexity structure of the underlying models. Statistical studies have established successful recovery of model parameters via structure-exploiting regularized estimators and computational efforts have examined efficient numerical procedures to accurately solve the associated optimization problems.

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

Mode of access: World Wide Web

ISBN: 9780355416190Subjects--Topical Terms:

596380
Electrical engineering.
Index Terms--Genre/Form:

554714
Electronic books.

A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems.
LDR:03522ntm a2200397Ki 4500 001 910843
005 20180517112612.5
006 m o u
007 cr mn||||a|a||
008 190606s2017 xx obm 000 0 eng d
020 $a 9780355416190
035 $a (MiAaPQ)AAI10636402
035 $a (MiAaPQ)umn:18652
035 $a AAI10636402
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Kadkhodaie Elyaderani, Mojtaba. $3 1182325
245 1 2 $a A Computational and Statistical Study of Convex and Nonconvex Optimization with Applications to Structured Source Demixing and Matrix Factorization Problems.
264 0 $c 2017
300 $a 1 online resource (166 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
500 $a Adviser: Jarvis D. Haupt.
502 $a Thesis (Ph.D.) $c University of Minnesota $d 2017.
504 $a Includes bibliographical references
520 $a Modern machine learning problems that emerge from real-world applications typically involve estimating high dimensional model parameters, whose number may be of the same order as or even significantly larger than the number of measurements. In such high dimensional settings, statistically-consistent estimation of true underlying models via classical approaches is often impossible, due to the lack of identifiability. A recent solution to this issue is through incorporating regularization functions into estimation procedures to promote intrinsic low-complexity structure of the underlying models. Statistical studies have established successful recovery of model parameters via structure-exploiting regularized estimators and computational efforts have examined efficient numerical procedures to accurately solve the associated optimization problems.
520 $a In this dissertation, we study the statistical and computational aspects of some regularized estimators that are successful in reconstructing high dimensional models. The investigated estimation frameworks are motivated by their applications in different areas of engineering, such as structural health monitoring and recommendation systems. In particular, the group Lasso recovery guarantees provided in Chapter 2 will bring insight into the application of this estimator for localizing material defects in the context of a structural diagnostics problem.
520 $a Chapter 3 describes the convergence study of an accelerated variant of the well-known alternating direction method of multipliers (ADMM) for minimizing strongly convex functions. The analysis is followed by several experimental evidence into the algorithm's applicability to a ranking problem.
520 $a Finally, Chapter 4 presents a local convergence analysis of regularized factorization-based estimators for reconstructing low-rank matrices. Interestingly, the analysis of this chapter reveals the interplay between statistical and computational aspects of such (non-convex) estimators. Therefore, it can be useful in a wide variety of problems that involve low-rank matrix estimation.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Electrical engineering. $3 596380
650 4 $a Operations research. $3 573517
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0544
690 $a 0796
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Minnesota. $b Electrical/Computer Engineering. $3 1182326
773 0 $t Dissertation Abstracts International $g 79-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10636402 $z click for full text (PQDT)