A non-asymptotic distributional theory of approximate message passing for sparse and robust regression Article Swipe
Gen Li
,
Yuting Wei
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.03923
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.03923
Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension. This paper makes progress towards this by developing non-asymptotic distributional characterizations for approximate message passing (AMP) -- a family of iterative algorithms that prove effective as both fast estimators and powerful theoretical machinery -- for both sparse and robust regression. Prior AMP theory, which focused on high-dimensional asymptotics for the most part, failed to describe the behavior of AMP when the number of iterations exceeds $o\big({\log n}/{\log \log n}\big)$ (with $n$ the sample size). We establish the first finite-sample non-asymptotic distributional theory of AMP for both sparse and robust regression that accommodates a polynomial number of iterations. Our results derive approximate accuracy of Gaussian approximation of the AMP iterates, which improves upon all prior results and implies enhanced distributional characterizations for both optimally tuned Lasso and robust M-estimator.
Related Topics
Concepts
Estimator
Iterated function
Mathematics
Applied mathematics
Lasso (programming language)
Asymptotic analysis
Asymptotic distribution
Message passing
Gaussian
Regression
Dimension (graph theory)
Regression analysis
Robust regression
Sample size determination
Statistics
Computer science
Combinatorics
Mathematical analysis
World Wide Web
Quantum mechanics
Physics
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.03923
- https://arxiv.org/pdf/2401.03923
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4390723626
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4390723626Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2401.03923Digital Object Identifier
- Title
-
A non-asymptotic distributional theory of approximate message passing for sparse and robust regressionWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-01-08Full publication date if available
- Authors
-
Gen Li, Yuting WeiList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.03923Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2401.03923Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2401.03923Direct OA link when available
- Concepts
-
Estimator, Iterated function, Mathematics, Applied mathematics, Lasso (programming language), Asymptotic analysis, Asymptotic distribution, Message passing, Gaussian, Regression, Dimension (graph theory), Regression analysis, Robust regression, Sample size determination, Statistics, Computer science, Combinatorics, Mathematical analysis, World Wide Web, Quantum mechanics, Physics, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4390723626 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2401.03923 |
| ids.doi | https://doi.org/10.48550/arxiv.2401.03923 |
| ids.openalex | https://openalex.org/W4390723626 |
| fwci | |
| type | preprint |
| title | A non-asymptotic distributional theory of approximate message passing for sparse and robust regression |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10136 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9986000061035156 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2613 |
| topics[0].subfield.display_name | Statistics and Probability |
| topics[0].display_name | Statistical Methods and Inference |
| topics[1].id | https://openalex.org/T10243 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9761000275611877 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2613 |
| topics[1].subfield.display_name | Statistics and Probability |
| topics[1].display_name | Statistical Methods and Bayesian Inference |
| topics[2].id | https://openalex.org/T11901 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9722999930381775 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1702 |
| topics[2].subfield.display_name | Artificial Intelligence |
| topics[2].display_name | Bayesian Methods and Mixture Models |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C185429906 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7575453519821167 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1130160 |
| concepts[0].display_name | Estimator |
| concepts[1].id | https://openalex.org/C140479938 |
| concepts[1].level | 2 |
| concepts[1].score | 0.6931285858154297 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q5254619 |
| concepts[1].display_name | Iterated function |
| concepts[2].id | https://openalex.org/C33923547 |
| concepts[2].level | 0 |
| concepts[2].score | 0.6340506672859192 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[2].display_name | Mathematics |
| concepts[3].id | https://openalex.org/C28826006 |
| concepts[3].level | 1 |
| concepts[3].score | 0.6077468395233154 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[3].display_name | Applied mathematics |
| concepts[4].id | https://openalex.org/C37616216 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5978004932403564 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q3218363 |
| concepts[4].display_name | Lasso (programming language) |
| concepts[5].id | https://openalex.org/C119047807 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5552802681922913 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q752718 |
| concepts[5].display_name | Asymptotic analysis |
| concepts[6].id | https://openalex.org/C65778772 |
| concepts[6].level | 3 |
| concepts[6].score | 0.5466684103012085 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q12345341 |
| concepts[6].display_name | Asymptotic distribution |
| concepts[7].id | https://openalex.org/C854659 |
| concepts[7].level | 2 |
| concepts[7].score | 0.5435810089111328 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1859284 |
| concepts[7].display_name | Message passing |
| concepts[8].id | https://openalex.org/C163716315 |
| concepts[8].level | 2 |
| concepts[8].score | 0.5161575078964233 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q901177 |
| concepts[8].display_name | Gaussian |
| concepts[9].id | https://openalex.org/C83546350 |
| concepts[9].level | 2 |
| concepts[9].score | 0.4959288537502289 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q1139051 |
| concepts[9].display_name | Regression |
| concepts[10].id | https://openalex.org/C33676613 |
| concepts[10].level | 2 |
| concepts[10].score | 0.43463563919067383 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q13415176 |
| concepts[10].display_name | Dimension (graph theory) |
| concepts[11].id | https://openalex.org/C152877465 |
| concepts[11].level | 2 |
| concepts[11].score | 0.42757970094680786 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q208042 |
| concepts[11].display_name | Regression analysis |
| concepts[12].id | https://openalex.org/C70259352 |
| concepts[12].level | 3 |
| concepts[12].score | 0.42146414518356323 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q1847839 |
| concepts[12].display_name | Robust regression |
| concepts[13].id | https://openalex.org/C129848803 |
| concepts[13].level | 2 |
| concepts[13].score | 0.4171193838119507 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2564360 |
| concepts[13].display_name | Sample size determination |
| concepts[14].id | https://openalex.org/C105795698 |
| concepts[14].level | 1 |
| concepts[14].score | 0.22796592116355896 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[14].display_name | Statistics |
| concepts[15].id | https://openalex.org/C41008148 |
| concepts[15].level | 0 |
| concepts[15].score | 0.22246363759040833 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[15].display_name | Computer science |
| concepts[16].id | https://openalex.org/C114614502 |
| concepts[16].level | 1 |
| concepts[16].score | 0.16871419548988342 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[16].display_name | Combinatorics |
| concepts[17].id | https://openalex.org/C134306372 |
| concepts[17].level | 1 |
| concepts[17].score | 0.12786048650741577 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[17].display_name | Mathematical analysis |
| concepts[18].id | https://openalex.org/C136764020 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q466 |
| concepts[18].display_name | World Wide Web |
| concepts[19].id | https://openalex.org/C62520636 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[19].display_name | Quantum mechanics |
| concepts[20].id | https://openalex.org/C121332964 |
| concepts[20].level | 0 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[20].display_name | Physics |
| concepts[21].id | https://openalex.org/C199360897 |
| concepts[21].level | 1 |
| concepts[21].score | 0.0 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q9143 |
| concepts[21].display_name | Programming language |
| keywords[0].id | https://openalex.org/keywords/estimator |
| keywords[0].score | 0.7575453519821167 |
| keywords[0].display_name | Estimator |
| keywords[1].id | https://openalex.org/keywords/iterated-function |
| keywords[1].score | 0.6931285858154297 |
| keywords[1].display_name | Iterated function |
| keywords[2].id | https://openalex.org/keywords/mathematics |
| keywords[2].score | 0.6340506672859192 |
| keywords[2].display_name | Mathematics |
| keywords[3].id | https://openalex.org/keywords/applied-mathematics |
| keywords[3].score | 0.6077468395233154 |
| keywords[3].display_name | Applied mathematics |
| keywords[4].id | https://openalex.org/keywords/lasso |
| keywords[4].score | 0.5978004932403564 |
| keywords[4].display_name | Lasso (programming language) |
| keywords[5].id | https://openalex.org/keywords/asymptotic-analysis |
| keywords[5].score | 0.5552802681922913 |
| keywords[5].display_name | Asymptotic analysis |
| keywords[6].id | https://openalex.org/keywords/asymptotic-distribution |
| keywords[6].score | 0.5466684103012085 |
| keywords[6].display_name | Asymptotic distribution |
| keywords[7].id | https://openalex.org/keywords/message-passing |
| keywords[7].score | 0.5435810089111328 |
| keywords[7].display_name | Message passing |
| keywords[8].id | https://openalex.org/keywords/gaussian |
| keywords[8].score | 0.5161575078964233 |
| keywords[8].display_name | Gaussian |
| keywords[9].id | https://openalex.org/keywords/regression |
| keywords[9].score | 0.4959288537502289 |
| keywords[9].display_name | Regression |
| keywords[10].id | https://openalex.org/keywords/dimension |
| keywords[10].score | 0.43463563919067383 |
| keywords[10].display_name | Dimension (graph theory) |
| keywords[11].id | https://openalex.org/keywords/regression-analysis |
| keywords[11].score | 0.42757970094680786 |
| keywords[11].display_name | Regression analysis |
| keywords[12].id | https://openalex.org/keywords/robust-regression |
| keywords[12].score | 0.42146414518356323 |
| keywords[12].display_name | Robust regression |
| keywords[13].id | https://openalex.org/keywords/sample-size-determination |
| keywords[13].score | 0.4171193838119507 |
| keywords[13].display_name | Sample size determination |
| keywords[14].id | https://openalex.org/keywords/statistics |
| keywords[14].score | 0.22796592116355896 |
| keywords[14].display_name | Statistics |
| keywords[15].id | https://openalex.org/keywords/computer-science |
| keywords[15].score | 0.22246363759040833 |
| keywords[15].display_name | Computer science |
| keywords[16].id | https://openalex.org/keywords/combinatorics |
| keywords[16].score | 0.16871419548988342 |
| keywords[16].display_name | Combinatorics |
| keywords[17].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[17].score | 0.12786048650741577 |
| keywords[17].display_name | Mathematical analysis |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2401.03923 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2401.03923 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2401.03923 |
| locations[1].id | doi:10.48550/arxiv.2401.03923 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | cc-by |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2401.03923 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5100357040 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-7298-2141 |
| authorships[0].author.display_name | Gen Li |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Li, Gen |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5005015806 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-1488-4647 |
| authorships[1].author.display_name | Yuting Wei |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Wei, Yuting |
| authorships[1].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2401.03923 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2024-01-13T00:00:00 |
| display_name | A non-asymptotic distributional theory of approximate message passing for sparse and robust regression |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T10136 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9986000061035156 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2613 |
| primary_topic.subfield.display_name | Statistics and Probability |
| primary_topic.display_name | Statistical Methods and Inference |
| related_works | https://openalex.org/W2949789221, https://openalex.org/W4248126265, https://openalex.org/W1606335093, https://openalex.org/W3123593911, https://openalex.org/W4298371340, https://openalex.org/W2131095263, https://openalex.org/W2021866332, https://openalex.org/W2037214953, https://openalex.org/W3125855424, https://openalex.org/W3121988082 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2401.03923 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2401.03923 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2401.03923 |
| primary_location.id | pmh:oai:arXiv.org:2401.03923 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2401.03923 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2401.03923 |
| publication_date | 2024-01-08 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 8, 39, 114 |
| abstract_inverted_index.-- | 38, 55 |
| abstract_inverted_index.We | 96 |
| abstract_inverted_index.as | 47 |
| abstract_inverted_index.by | 28 |
| abstract_inverted_index.in | 19 |
| abstract_inverted_index.is | 7 |
| abstract_inverted_index.of | 3, 15, 41, 79, 84, 104, 117, 124, 127 |
| abstract_inverted_index.on | 67 |
| abstract_inverted_index.to | 12, 75 |
| abstract_inverted_index.$n$ | 92 |
| abstract_inverted_index.AMP | 63, 80, 105, 129 |
| abstract_inverted_index.Our | 119 |
| abstract_inverted_index.all | 134 |
| abstract_inverted_index.and | 51, 59, 109, 137, 147 |
| abstract_inverted_index.due | 11 |
| abstract_inverted_index.for | 33, 56, 70, 106, 142 |
| abstract_inverted_index.the | 1, 13, 71, 77, 82, 93, 98, 128 |
| abstract_inverted_index.This | 22 |
| abstract_inverted_index.\log | 89 |
| abstract_inverted_index.both | 48, 57, 107, 143 |
| abstract_inverted_index.fast | 49 |
| abstract_inverted_index.high | 20 |
| abstract_inverted_index.most | 72 |
| abstract_inverted_index.that | 44, 112 |
| abstract_inverted_index.this | 27 |
| abstract_inverted_index.upon | 133 |
| abstract_inverted_index.when | 81 |
| abstract_inverted_index.(AMP) | 37 |
| abstract_inverted_index.(with | 91 |
| abstract_inverted_index.Lasso | 146 |
| abstract_inverted_index.Prior | 62 |
| abstract_inverted_index.first | 99 |
| abstract_inverted_index.makes | 24 |
| abstract_inverted_index.paper | 23 |
| abstract_inverted_index.part, | 73 |
| abstract_inverted_index.prior | 135 |
| abstract_inverted_index.prove | 45 |
| abstract_inverted_index.task, | 10 |
| abstract_inverted_index.tuned | 145 |
| abstract_inverted_index.which | 65, 131 |
| abstract_inverted_index.derive | 121 |
| abstract_inverted_index.failed | 74 |
| abstract_inverted_index.family | 40 |
| abstract_inverted_index.number | 83, 116 |
| abstract_inverted_index.robust | 60, 110, 148 |
| abstract_inverted_index.sample | 94 |
| abstract_inverted_index.size). | 95 |
| abstract_inverted_index.sparse | 58, 108 |
| abstract_inverted_index.theory | 18, 103 |
| abstract_inverted_index.exceeds | 86 |
| abstract_inverted_index.focused | 66 |
| abstract_inverted_index.implies | 138 |
| abstract_inverted_index.message | 35 |
| abstract_inverted_index.passing | 36 |
| abstract_inverted_index.results | 120, 136 |
| abstract_inverted_index.theory, | 64 |
| abstract_inverted_index.towards | 26 |
| abstract_inverted_index.Gaussian | 125 |
| abstract_inverted_index.accuracy | 123 |
| abstract_inverted_index.behavior | 78 |
| abstract_inverted_index.describe | 76 |
| abstract_inverted_index.enhanced | 139 |
| abstract_inverted_index.improves | 132 |
| abstract_inverted_index.n}/{\log | 88 |
| abstract_inverted_index.n}\big)$ | 90 |
| abstract_inverted_index.powerful | 52 |
| abstract_inverted_index.progress | 25 |
| abstract_inverted_index.breakdown | 14 |
| abstract_inverted_index.classical | 16 |
| abstract_inverted_index.effective | 46 |
| abstract_inverted_index.establish | 97 |
| abstract_inverted_index.iterates, | 130 |
| abstract_inverted_index.iterative | 42 |
| abstract_inverted_index.machinery | 54 |
| abstract_inverted_index.optimally | 144 |
| abstract_inverted_index.algorithms | 43 |
| abstract_inverted_index.asymptotic | 17 |
| abstract_inverted_index.developing | 29 |
| abstract_inverted_index.dimension. | 21 |
| abstract_inverted_index.estimators | 6, 50 |
| abstract_inverted_index.iterations | 85 |
| abstract_inverted_index.polynomial | 115 |
| abstract_inverted_index.regression | 111 |
| abstract_inverted_index.approximate | 34, 122 |
| abstract_inverted_index.asymptotics | 69 |
| abstract_inverted_index.challenging | 9 |
| abstract_inverted_index.iterations. | 118 |
| abstract_inverted_index.regression. | 61 |
| abstract_inverted_index.statistical | 5 |
| abstract_inverted_index.theoretical | 53 |
| abstract_inverted_index.$o\big({\log | 87 |
| abstract_inverted_index.M-estimator. | 149 |
| abstract_inverted_index.accommodates | 113 |
| abstract_inverted_index.distribution | 2 |
| abstract_inverted_index.approximation | 126 |
| abstract_inverted_index.finite-sample | 100 |
| abstract_inverted_index.Characterizing | 0 |
| abstract_inverted_index.distributional | 31, 102, 140 |
| abstract_inverted_index.non-asymptotic | 30, 101 |
| abstract_inverted_index.high-dimensional | 4, 68 |
| abstract_inverted_index.characterizations | 32, 141 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |