Vector Approximate Message Passing

The standard linear regression (SLR) problem is to recover a vector <inline-formula> <tex-math notation="LaTeX">\mathrm {x}^{0} </tex-math></inline-formula> from noisy linear observations <inline-formula> <tex-math notation="LaTeX">\mathrm {y}=...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	IEEE transactions on information theory Ročník 65; číslo 10; s. 6664 - 6684
Hlavní autoři:	Rangan, Sundeep, Schniter, Philip, Fletcher, Alyson K.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.10.2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Approximation algorithms Belief propagation compressive sensing Covariance matrices Evolution inference algorithms Iterative methods Linear regression Matrices (mathematics) Message passing Minimization random matrices Signal processing algorithms Singular value decomposition
ISSN:	0018-9448, 1557-9654
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	The standard linear regression (SLR) problem is to recover a vector <inline-formula> <tex-math notation="LaTeX">\mathrm {x}^{0} </tex-math></inline-formula> from noisy linear observations <inline-formula> <tex-math notation="LaTeX">\mathrm {y}=\mathrm {Ax}^{0}+\mathrm {w} </tex-math></inline-formula>. The approximate message passing (AMP) algorithm proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d. sub-Gaussian matrices A, its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. The AMP algorithm, however, is fragile in that even small deviations from the i.i.d. sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices A: those that are right-orthogonally invariant. After performing an initial singular value decomposition (SVD) of A, the per-iteration complexity of VAMP is similar to that of AMP. In addition, the fixed points of VAMP's state evolution are consistent with the replica prediction of the minimum mean-squared error derived by Tulino, Caire, Verdú, and Shamai. Numerical experiments are used to confirm the effectiveness of VAMP and its consistency with state-evolution predictions.
AbstractList	The standard linear regression (SLR) problem is to recover a vector [Formula Omitted] from noisy linear observations [Formula Omitted]. The approximate message passing (AMP) algorithm proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d. sub-Gaussian matrices A, its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. The AMP algorithm, however, is fragile in that even small deviations from the i.i.d. sub-Gaussian model can cause the algorithm to diverge. This paper considers a “vector AMP” (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices A: those that are right-orthogonally invariant. After performing an initial singular value decomposition (SVD) of A, the per-iteration complexity of VAMP is similar to that of AMP. In addition, the fixed points of VAMP’s state evolution are consistent with the replica prediction of the minimum mean-squared error derived by Tulino, Caire, Verdú, and Shamai. Numerical experiments are used to confirm the effectiveness of VAMP and its consistency with state-evolution predictions. The standard linear regression (SLR) problem is to recover a vector <inline-formula> <tex-math notation="LaTeX">\mathrm {x}^{0} </tex-math></inline-formula> from noisy linear observations <inline-formula> <tex-math notation="LaTeX">\mathrm {y}=\mathrm {Ax}^{0}+\mathrm {w} </tex-math></inline-formula>. The approximate message passing (AMP) algorithm proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d. sub-Gaussian matrices A, its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. The AMP algorithm, however, is fragile in that even small deviations from the i.i.d. sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices A: those that are right-orthogonally invariant. After performing an initial singular value decomposition (SVD) of A, the per-iteration complexity of VAMP is similar to that of AMP. In addition, the fixed points of VAMP's state evolution are consistent with the replica prediction of the minimum mean-squared error derived by Tulino, Caire, Verdú, and Shamai. Numerical experiments are used to confirm the effectiveness of VAMP and its consistency with state-evolution predictions.
Author	Schniter, Philip Fletcher, Alyson K. Rangan, Sundeep
Author_xml	– sequence: 1 givenname: Sundeep orcidid: 0000-0002-0925-8169 surname: Rangan fullname: Rangan, Sundeep email: srangan@nyu.edu organization: Department of Electrical and Computer Engineering, New York University, Brooklyn, NY, USA – sequence: 2 givenname: Philip orcidid: 0000-0003-0939-7545 surname: Schniter fullname: Schniter, Philip email: schniter.1@osu.edu organization: Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA – sequence: 3 givenname: Alyson K. surname: Fletcher fullname: Fletcher, Alyson K. email: akfletcher@ucla.edu organization: Department of Statistics, Mathematics, and Electrical Engineering, University of California at Los Angeles, Los Angeles, CA, USA
BookMark	eNp9kM1LAzEQxYNUsK3eBS9Fz7vOZJPN5liKH4WKHqrXELOzZUvdrUkK-t-b0uLBg6dh4L15v3kjNuj6jhi7RMgRQd8u58ucA-qcaywLqU_YEKVUmS6lGLAhAFaZFqI6Y6MQ1mkVEvmQXb-Ri72fTLdb33-1HzbS5IlCsCuavNgQ2m51zk4buwl0cZxj9np_t5w9Zovnh_lsushcioyZrLmskVwDhZNAqnaCo3bAG3yvrS6FlY0qnbDK1VUC4bIiAkyoIIVDXozZzeFuIvncUYhm3e98lyIN55prpUHppCoPKuf7EDw1xrXRxrbvorftxiCYfR8m9WH2fZhjH8kIf4xbn_713_9Zrg6Wloh-5ZVK0An8B_4EavU
CODEN	IETTAW
CitedBy_id	crossref_primary_10_1109_TVT_2025_3531355 crossref_primary_10_1109_TGRS_2022_3221185 crossref_primary_10_1109_TWC_2021_3088125 crossref_primary_10_1186_s13634_024_01151_1 crossref_primary_10_1121_10_0003625 crossref_primary_10_1109_TVT_2022_3147532 crossref_primary_10_1016_j_phycom_2021_101554 crossref_primary_10_1016_j_dsp_2025_105410 crossref_primary_10_1121_10_0028525 crossref_primary_10_1109_TIP_2022_3186749 crossref_primary_10_1214_19_AOS1923 crossref_primary_10_1109_TWC_2022_3179600 crossref_primary_10_1016_j_neucom_2023_01_092 crossref_primary_10_1214_23_AOS2257 crossref_primary_10_1109_TSP_2022_3213414 crossref_primary_10_1109_TCOMM_2021_3094509 crossref_primary_10_1109_TSP_2023_3322830 crossref_primary_10_1109_TSP_2023_3327609 crossref_primary_10_1214_24_AAP2056 crossref_primary_10_1109_TVT_2024_3377716 crossref_primary_10_1109_TVT_2021_3133111 crossref_primary_10_1109_TCOMM_2024_3395337 crossref_primary_10_1109_ACCESS_2020_3030932 crossref_primary_10_1109_JSAC_2020_3018799 crossref_primary_10_1109_LSP_2020_2976155 crossref_primary_10_3390_rs16071209 crossref_primary_10_3390_app10124397 crossref_primary_10_1109_TSP_2025_3575919 crossref_primary_10_1016_j_eswa_2022_119220 crossref_primary_10_1109_TSP_2024_3509413 crossref_primary_10_1109_TGCN_2022_3146188 crossref_primary_10_1103_PhysRevResearch_7_013081 crossref_primary_10_1109_ACCESS_2025_3572283 crossref_primary_10_1109_TCOMM_2021_3078563 crossref_primary_10_1109_TWC_2024_3446189 crossref_primary_10_1109_TVT_2020_2986271 crossref_primary_10_1121_10_0024608 crossref_primary_10_1214_21_AOS2101 crossref_primary_10_1109_TWC_2022_3153106 crossref_primary_10_1214_23_AOP1628 crossref_primary_10_1109_ACCESS_2021_3098638 crossref_primary_10_1109_TCOMM_2023_3240689 crossref_primary_10_1109_TIT_2020_3025272 crossref_primary_10_1109_TSP_2020_2983827 crossref_primary_10_3390_e23050539 crossref_primary_10_1109_TSP_2019_2943224 crossref_primary_10_1109_TIT_2025_3560070 crossref_primary_10_1109_TWC_2022_3206608 crossref_primary_10_1109_LWC_2024_3366590 crossref_primary_10_1109_TCI_2025_3527140 crossref_primary_10_1109_TVT_2022_3206254 crossref_primary_10_1007_s11235_025_01263_5 crossref_primary_10_1109_TWC_2023_3293315 crossref_primary_10_1109_JSTSP_2024_3511403 crossref_primary_10_1109_LSP_2024_3460478 crossref_primary_10_1109_TSP_2023_3310279 crossref_primary_10_1109_TIT_2023_3321575 crossref_primary_10_1109_TSP_2024_3385576 crossref_primary_10_1109_TVT_2020_3022916 crossref_primary_10_1109_TCOMM_2021_3059456 crossref_primary_10_1109_JSAC_2025_3531570 crossref_primary_10_1109_TCOMM_2024_3354205 crossref_primary_10_1109_TIT_2022_3182018 crossref_primary_10_1007_s42979_025_04352_z crossref_primary_10_1109_TIT_2024_3396472 crossref_primary_10_1109_OJCOMS_2024_3463202 crossref_primary_10_1109_TCOMM_2024_3354201 crossref_primary_10_1109_TIT_2022_3222913 crossref_primary_10_7717_peerj_cs_2582 crossref_primary_10_1109_TIT_2024_3509476 crossref_primary_10_1109_TWC_2022_3228326 crossref_primary_10_1109_LCOMM_2020_2981073 crossref_primary_10_1109_MVT_2021_3116420 crossref_primary_10_1109_TIT_2023_3321340 crossref_primary_10_1109_TWC_2024_3407586 crossref_primary_10_1117_1_APN_2_6_066005 crossref_primary_10_1109_COMST_2023_3326399 crossref_primary_10_1109_JSEN_2024_3419053 crossref_primary_10_1109_TCOMM_2022_3207813 crossref_primary_10_1109_TIT_2022_3186166 crossref_primary_10_1109_TIT_2022_3163342 crossref_primary_10_1109_TCCN_2021_3072895 crossref_primary_10_1109_OJCOMS_2025_3578473 crossref_primary_10_1007_s00440_024_01309_w crossref_primary_10_1109_TVT_2021_3055849 crossref_primary_10_1007_s11277_024_11581_7 crossref_primary_10_1109_LCOMM_2025_3542388 crossref_primary_10_1109_TGRS_2023_3268132 crossref_primary_10_1109_TVT_2022_3187746 crossref_primary_10_1109_TIT_2022_3194855 crossref_primary_10_1109_TSP_2023_3328064 crossref_primary_10_1109_TIT_2022_3157665 crossref_primary_10_3390_e25121667 crossref_primary_10_3390_s23104678 crossref_primary_10_1109_JSAC_2021_3126056 crossref_primary_10_1109_TWC_2023_3328361 crossref_primary_10_1137_23M1625846 crossref_primary_10_1109_TWC_2023_3314075 crossref_primary_10_1109_TVT_2021_3111081 crossref_primary_10_1109_LWC_2024_3385405 crossref_primary_10_1109_TWC_2021_3094970 crossref_primary_10_1109_TCOMM_2023_3262304 crossref_primary_10_1109_TWC_2023_3326468 crossref_primary_10_3390_electronics11162578 crossref_primary_10_1109_JSAC_2023_3276765 crossref_primary_10_1109_TCOMM_2022_3182369 crossref_primary_10_1109_TSP_2023_3301137 crossref_primary_10_1109_TIT_2021_3049172 crossref_primary_10_1088_1742_5468_ab4bbb crossref_primary_10_1109_TIT_2019_2947058 crossref_primary_10_1109_LCOMM_2023_3346914 crossref_primary_10_1016_j_sigpro_2020_107601 crossref_primary_10_1109_TCOMM_2023_3325479 crossref_primary_10_1109_TIT_2024_3455228 crossref_primary_10_1109_JOE_2023_3337349 crossref_primary_10_1137_19M1310013 crossref_primary_10_1121_10_0036346 crossref_primary_10_1088_1742_5468_ad0220 crossref_primary_10_1109_ACCESS_2019_2950901 crossref_primary_10_1109_TSP_2020_3044847 crossref_primary_10_1109_TSP_2024_3512575 crossref_primary_10_1109_TCOMM_2021_3063236 crossref_primary_10_1109_TIT_2023_3311408 crossref_primary_10_1109_TIT_2020_2981910 crossref_primary_10_1109_TVT_2025_3556519 crossref_primary_10_1016_j_dsp_2024_104387 crossref_primary_10_1093_imaiai_iaae024 crossref_primary_10_1109_TIT_2021_3077471 crossref_primary_10_3390_e22101121 crossref_primary_10_1109_TCOMM_2021_3126619 crossref_primary_10_3390_s21144760 crossref_primary_10_1109_JOE_2023_3330523 crossref_primary_10_54097_p90khg63 crossref_primary_10_1109_JSTSP_2024_3491580 crossref_primary_10_1016_j_phycom_2025_102616 crossref_primary_10_1088_2632_2153_abfbbb crossref_primary_10_1109_TSP_2023_3269151 crossref_primary_10_1121_10_0036139 crossref_primary_10_1109_ACCESS_2019_2941233 crossref_primary_10_1109_TCOMM_2020_3048942 crossref_primary_10_1214_25_AAP2186 crossref_primary_10_1088_2632_2153_ac7d3b crossref_primary_10_1016_j_sigpro_2020_107583 crossref_primary_10_1109_TWC_2024_3481494 crossref_primary_10_1016_j_phycom_2023_102018 crossref_primary_10_1109_TIP_2020_3044472 crossref_primary_10_1016_j_sigpro_2022_108750 crossref_primary_10_1109_TIT_2021_3114351 crossref_primary_10_1109_TSP_2022_3211672 crossref_primary_10_1121_10_0022376 crossref_primary_10_3390_e27060616 crossref_primary_10_1109_TIT_2023_3291615 crossref_primary_10_1109_LWC_2022_3152323 crossref_primary_10_1109_JSAC_2020_3036947 crossref_primary_10_1109_TVT_2023_3319562 crossref_primary_10_1109_LSP_2021_3065600 crossref_primary_10_1109_LCOMM_2021_3103420 crossref_primary_10_1109_TCOMM_2024_3475270 crossref_primary_10_1109_TIT_2024_3458953 crossref_primary_10_1109_TCCN_2024_3414577 crossref_primary_10_1109_TWC_2024_3506555 crossref_primary_10_1109_JSAC_2020_3000822 crossref_primary_10_1109_TWC_2024_3416375 crossref_primary_10_1109_TCOMM_2023_3294960 crossref_primary_10_1109_TSP_2025_3572903 crossref_primary_10_1002_ett_4566 crossref_primary_10_1109_ACCESS_2023_3244780 crossref_primary_10_1111_iere_12577 crossref_primary_10_1109_TCOMM_2022_3160540
Cites_doi	10.1109/ISIT.2016.7541287 10.1109/ITWKSPS.2010.5503193 10.1073/pnas.0909892106 10.1109/ISIT.2016.7541382 10.1002/cpa.20042 10.1109/ICASSP.2015.7178325 10.1561/0100000001 10.1017/CBO9780511794308.010 10.1109/TIT.2010.2094817 10.1109/ISIT.2011.6033942 10.1109/ALLERTON.2016.7852290 10.1109/TIT.2013.2250578 10.1137/090771806 10.1109/ISIT.2016.7541400 10.1109/ISIT.2014.6875083 10.1109/ISIT.2013.6620309 10.1007/978-3-642-55925-9_36 10.1103/PhysRevE.64.056131 10.1109/ISIT.2015.7282734 10.1109/ACCESS.2017.2653119 10.1109/ISIT.2014.6874830 10.1109/83.661182 10.1214/14-AAP1010 10.1080/14786437708235992 10.1109/JSTSP.2015.2496908 10.1109/ISIT.2017.8006578 10.1109/ISIT.2014.6875146 10.1109/ISIT.2014.6874828
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019
DBID	97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D
DOI	10.1109/TIT.2019.2916359
DatabaseName	IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Technology Research Database
Database_xml	– sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Computer Science
EISSN	1557-9654
EndPage	6684
ExternalDocumentID	10_1109_TIT_2019_2916359 8713501
Genre	orig-research
GrantInformation_xml	– fundername: National Science Foundation grantid: 1254204; 1564278 funderid: 10.13039/100000001 – fundername: National Science Foundation grantid: 1527162; 1716388 funderid: 10.13039/100000001 – fundername: Office of Naval Research grantid: N00014-15-1-2677 funderid: 10.13039/100000006 – fundername: National Science Foundation grantid: 1302336; 1564142; 1547332 funderid: 10.13039/100000001
GroupedDBID	-~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACGOD ACIWK AENEX AETEA AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNS RXW TAE TN5 VH1 VJK AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D RIG
ID	FETCH-LOGICAL-c291t-5d25d1ecf03c50e7dc4219c02f1bda964a5f76c4a7cd8448258ee01359054c123
IEDL.DBID	RIE
ISICitedReferencesCount	281
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000487041200039&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0018-9448
IngestDate	Sun Jun 29 15:44:55 EDT 2025 Tue Nov 18 22:30:38 EST 2025 Sat Nov 29 03:31:42 EST 2025 Wed Aug 27 02:42:10 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	10
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c291t-5d25d1ecf03c50e7dc4219c02f1bda964a5f76c4a7cd8448258ee01359054c123
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-0939-7545 0000-0002-0925-8169
PQID	2292979079
PQPubID	36024
PageCount	21
ParticipantIDs	ieee_primary_8713501 crossref_citationtrail_10_1109_TIT_2019_2916359 proquest_journals_2292979079 crossref_primary_10_1109_TIT_2019_2916359
PublicationCentury	2000
PublicationDate	2019-10-01
PublicationDateYYYYMMDD	2019-10-01
PublicationDate_xml	– month: 10 year: 2019 text: 2019-10-01 day: 01
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	IEEE transactions on information theory
PublicationTitleAbbrev	TIT
PublicationYear	2019
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref35 ref12 ref37 ref36 ref31 ref11 ref32 ref2 ref1 ref17 ref38 ref16 seeger (ref14) 2005 manoel (ref10) 2015 çakmak (ref19) 2015 ref24 ref23 pearl (ref29) 1988 ref26 ref25 ref20 ref22 yedidia (ref30) 2003 ref21 (ref33) 2019 opper (ref15) 2005; 1 ref28 minka (ref13) 2001 ref27 ref8 ref7 çakmak (ref18) 2014 ref9 ref4 ref3 ref6 ref5 fletcher (ref34) 2017
References_xml	– year: 1988 ident: ref29 publication-title: Probabilistic Reasoning in Intelligent Systems Networks of Plausible Inference – start-page: 239 year: 2003 ident: ref30 article-title: Understanding belief propagation and its generalizations publication-title: Exploring Artificial Intelligence in the New Millennium – year: 2019 ident: ref33 publication-title: Generalized Approximate Message Passing SourceForge net Project Gampmatlab – ident: ref17 doi: 10.1109/ISIT.2016.7541287 – ident: ref3 doi: 10.1109/ITWKSPS.2010.5503193 – ident: ref2 doi: 10.1073/pnas.0909892106 – ident: ref37 doi: 10.1109/ISIT.2016.7541382 – ident: ref27 doi: 10.1002/cpa.20042 – ident: ref9 doi: 10.1109/ICASSP.2015.7178325 – ident: ref36 doi: 10.1561/0100000001 – ident: ref25 doi: 10.1017/CBO9780511794308.010 – ident: ref4 doi: 10.1109/TIT.2010.2094817 – ident: ref24 doi: 10.1109/ISIT.2011.6033942 – year: 2001 ident: ref13 article-title: A family of algorithms for approximate Bayesian inference – start-page: 1123 year: 2015 ident: ref10 article-title: Swept approximate message passing for sparse estimation publication-title: Proc ICML – year: 2005 ident: ref14 article-title: Expectation propagation for exponential families – ident: ref38 doi: 10.1109/ALLERTON.2016.7852290 – ident: ref21 doi: 10.1109/TIT.2013.2250578 – volume: 1 start-page: 2177 year: 2005 ident: ref15 article-title: Expectation consistent approximate inference publication-title: J Mach Learn Res – ident: ref22 doi: 10.1137/090771806 – start-page: 2807 year: 2015 ident: ref19 article-title: S-AMP for non-linear observation models publication-title: Proc IEEE ISIT – ident: ref6 doi: 10.1109/ISIT.2016.7541400 – start-page: 192 year: 2014 ident: ref18 article-title: S-AMP: Approximate message passing for general matrix ensembles publication-title: Proc IEEE Inf Theory Workshop (ITW) – ident: ref32 doi: 10.1109/ISIT.2014.6875083 – ident: ref31 doi: 10.1109/ISIT.2013.6620309 – ident: ref35 doi: 10.1007/978-3-642-55925-9_36 – ident: ref12 doi: 10.1103/PhysRevE.64.056131 – ident: ref11 doi: 10.1109/ISIT.2015.7282734 – ident: ref20 doi: 10.1109/ACCESS.2017.2653119 – ident: ref7 doi: 10.1109/ISIT.2014.6874830 – ident: ref26 doi: 10.1109/83.661182 – start-page: 2542 year: 2017 ident: ref34 article-title: Rigorous dynamics and consistent estimation in arbitrarily conditioned linear systems publication-title: Proc NIPS – ident: ref5 doi: 10.1214/14-AAP1010 – ident: ref28 doi: 10.1080/14786437708235992 – ident: ref1 doi: 10.1109/JSTSP.2015.2496908 – ident: ref23 doi: 10.1109/ISIT.2017.8006578 – ident: ref8 doi: 10.1109/ISIT.2014.6875146 – ident: ref16 doi: 10.1109/ISIT.2014.6874828
SSID	ssj0014512
Score	2.6974144
Snippet	The standard linear regression (SLR) problem is to recover a vector <inline-formula> <tex-math notation="LaTeX">\mathrm {x}^{0} </tex-math></inline-formula>... The standard linear regression (SLR) problem is to recover a vector [Formula Omitted] from noisy linear observations [Formula Omitted]. The approximate message...
SourceID	proquest crossref ieee
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	6664
SubjectTerms	Algorithms Approximation algorithms Belief propagation compressive sensing Covariance matrices Evolution inference algorithms Iterative methods Linear regression Matrices (mathematics) Message passing Minimization random matrices Signal processing algorithms Singular value decomposition
Title	Vector Approximate Message Passing
URI	https://ieeexplore.ieee.org/document/8713501 https://www.proquest.com/docview/2292979079
Volume	65
WOSCitedRecordID	wos000487041200039&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1557-9654 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014512 issn: 0018-9448 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NS8NAEB1q8aAHq61itUoQL4Jps-luNnssYtGDpYcqvYVkM5GCtKUf4s93dvNBQRG85TAbkrfZzJud2XkAt1ogOVZMXGmK_XifB24cC-4KkQYZ9xlKnVqxCTkahdOpGtfgvjoLg4i2-Ay75tLm8tOF3pqtsl5o9OTMYa09KYP8rFaVMeCC5Z3BGS1gijnKlKSnepPnianhUl2fuFDfdCXdcUFWU-XHj9h6l2Hjf891DEcFi3QG-bSfQA3nTWiUCg1OsWCbcLjTbrAFN292i94ZmD7iXzPiqui8GAmUd3TGRKLJ6BReh4-Thye30EhwNb3NxhWpL1KGOvP6mjCXqSaAlfb8jCVprAIei0wGmseEeUiw-CJEJNonFHE1TW7rDOrzxRzPwREyZrFIEopRGEeVhUKTGSOGw7VpK9-GXglbpIsG4kbH4iOygYSnIgI6MkBHBdBtuKtGLPPmGX_YtgywlV2BaRs65cxExepaR75PpE5SWK8ufh91CQfm3nnRXQfqm9UWr2Bff25m69W1_XC-AdfuvQU
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fS8MwED7GFNQHp5vidGoRXwS7tV3SNo8ijg23sYcqewttmspANtkP8c_3kqZloAi-9eFC2y9N77vc5T6AW0ElOlaZ2IEq9iNd4ttxTIlNaepnxHNlIFItNhGMx-F0yiYVuC_PwkgpdfGZbKtLnctPF2Kjtso6odKTU4e1dpRyljmtVeYMCHXz3uAuLmGMOoqkpMM60SBSVVys7SEb6qq-pFtOSKuq_PgVa__Sq_3vyY7g0PBI6yGf-GOoyHkdaoVGg2WWbB0OthoONuDmVW_SWw-qk_jXDNmqtEZKBOVNWhOk0Wh0Ai-9p-ixbxuVBFvg26xtmno0daXInK5A1INUIMRMOF7mJmnMfBLTLPAFiRH1EGHxaCglEj_KkK0JdFynUJ0v5vIMLBrEbkyTBKMUl0iWhVSgmYschwjVWL4JnQI2LkwLcaVk8c51KOEwjkBzBTQ3QDfhrhzxkbfP-MO2oYAt7QymTWgVM8PN-lpxz0NaF2Bgz85_H3UNe_1oNOTDwfj5AvbVffISvBZU18uNvIRd8bmerZZX-iP6BuHKwE4
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Vector+Approximate+Message+Passing&rft.jtitle=IEEE+transactions+on+information+theory&rft.au=Rangan%2C+Sundeep&rft.au=Schniter%2C+Philip&rft.au=Fletcher%2C+Alyson+K&rft.date=2019-10-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=0018-9448&rft.eissn=1557-9654&rft.volume=65&rft.issue=10&rft.spage=6664&rft_id=info:doi/10.1109%2FTIT.2019.2916359&rft.externalDBID=NO_FULL_TEXT
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9448&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9448&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9448&client=summon