An efficient parallel block coordinate descent algorithm for large-scale precision matrix estimation using graphics processing units
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, Young-Geun | - |
dc.contributor.author | Lee, Seunghwan | - |
dc.contributor.author | Yu, Donghyeon | - |
dc.date.accessioned | 2022-04-19T08:42:22Z | - |
dc.date.available | 2022-04-19T08:42:22Z | - |
dc.date.issued | 2022-03 | - |
dc.identifier.issn | 0943-4062 | - |
dc.identifier.issn | 1613-9658 | - |
dc.identifier.uri | https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/145870 | - |
dc.description.abstract | Large-scale sparse precision matrix estimation has attracted wide interest from the statistics community. The convex partial correlation selection method (CONCORD) developed by Khare et al. (J R Stat Soc Ser B (Stat Methodol) 77(4):803-825, 2015) has recently been credited with some theoretical properties for estimating sparse precision matrices. The CONCORD obtains its solution by a coordinate descent algorithm (CONCORD-CD) based on the convexity of the objective function. However, since a coordinate-wise update in CONCORD-CD is inherently serial, a scale-up is nontrivial. In this paper, we propose a novel parallelization of CONCORD-CD, namely, CONCORD-PCD. CONCORD-PCD partitions the off-diagonal elements into several groups and updates each group simultaneously without harming the computational convergence of CONCORD-CD. We guarantee this by employing the notion of edge coloring in graph theory. Specifically, we establish a nontrivial correspondence between scheduling the updates of the off-diagonal elements in CONCORD-CD and coloring the edges of a complete graph. It turns out that CONCORD-PCD simultanoeusly updates off-diagonal elements in which the associated edges are colorable with the same color. As a result, the number of steps required for updating off-diagonal elements reduces from p(p - 1)/2 to p - 1 (for even p) or p (for odd p), where p denotes the number of variables. We prove that the number of such steps is irreducible In addition, CONCORD-PCD is tailored to single-instruction multiple-data (SIMD) parallelism. A numerical study shows that the SIMD-parallelized PCD algorithm implemented in graphics processing units boosts the CONCORD-CD algorithm multiple times. The method is available in the R package pcdconcord. | - |
dc.format.extent | 25 | - |
dc.language | 영어 | - |
dc.language.iso | ENG | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.title | An efficient parallel block coordinate descent algorithm for large-scale precision matrix estimation using graphics processing units | - |
dc.type | Article | - |
dc.publisher.location | 독일 | - |
dc.identifier.doi | 10.1007/s00180-021-01127-x | - |
dc.identifier.scopusid | 2-s2.0-85110205487 | - |
dc.identifier.wosid | 000673886400001 | - |
dc.identifier.bibliographicCitation | COMPUTATIONAL STATISTICS, v.37, no.1, pp 419 - 443 | - |
dc.citation.title | COMPUTATIONAL STATISTICS | - |
dc.citation.volume | 37 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 419 | - |
dc.citation.endPage | 443 | - |
dc.type.docType | Article | - |
dc.description.isOpenAccess | N | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Statistics & Probability | - |
dc.subject.keywordPlus | INVERSE COVARIANCE ESTIMATION | - |
dc.subject.keywordPlus | SPARSE | - |
dc.subject.keywordPlus | CONVERGENCE | - |
dc.subject.keywordPlus | LASSO | - |
dc.subject.keywordPlus | REGRESSION | - |
dc.subject.keywordPlus | SELECTION | - |
dc.subject.keywordPlus | INSIGHTS | - |
dc.subject.keywordAuthor | CONCORD | - |
dc.subject.keywordAuthor | Edge coloring | - |
dc.subject.keywordAuthor | Parallel coordinate descent | - |
dc.subject.keywordAuthor | Graphical model | - |
dc.subject.keywordAuthor | GPU-parallel computation | - |
dc.identifier.url | https://arxiv.org/pdf/2106.09382.pdf | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
Sookmyung Women's University. Cheongpa-ro 47-gil 100 (Cheongpa-dong 2ga), Yongsan-gu, Seoul, 04310, Korea02-710-9127
Copyright©Sookmyung Women's University. All Rights Reserved.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.