High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization Article Swipe
Wanrong Zhu
,
Zhipeng Lou
,
Ziyang Wei
,
Wei Biao Wu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.09346
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.09346
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with efficient computation and fast convergence to the nominal level. Specifically, we propose to use a small number of independent multi-runs to acquire distribution information and construct a t-based confidence interval. Our method requires minimal additional computation and memory beyond the standard updating of estimates, making the inference process almost cost-free. We provide a rigorous theoretical guarantee for the confidence interval, demonstrating that the coverage is approximately exact with an explicit convergence rate and allowing for high confidence level inference. In particular, a new Gaussian approximation result is developed for the online estimators to characterize the coverage properties of our confidence intervals in terms of relative errors. Additionally, our method also allows for leveraging parallel computing to further accelerate calculations using multiple cores. It is easy to implement and can be integrated with existing stochastic algorithms without the need for complicated modifications.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.09346
- https://arxiv.org/pdf/2401.09346
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4391013580
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4391013580Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2401.09346Digital Object Identifier
- Title
-
High Confidence Level Inference is Almost Free using Parallel Stochastic OptimizationWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-01-17Full publication date if available
- Authors
-
Wanrong Zhu, Zhipeng Lou, Ziyang Wei, Wei Biao WuList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.09346Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2401.09346Direct 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/2401.09346Direct OA link when available
- Concepts
-
Inference, Computer science, Estimator, Computation, Confidence interval, Coverage probability, Convergence (economics), Algorithm, Mathematical optimization, Gaussian process, Gaussian, Mathematics, Artificial intelligence, Statistics, Physics, Economic growth, Economics, Quantum mechanicsTop 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/W4391013580 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2401.09346 |
| ids.doi | https://doi.org/10.48550/arxiv.2401.09346 |
| ids.openalex | https://openalex.org/W4391013580 |
| fwci | |
| type | preprint |
| title | High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T12535 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9958000183105469 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1702 |
| topics[0].subfield.display_name | Artificial Intelligence |
| topics[0].display_name | Machine Learning and Data Classification |
| topics[1].id | https://openalex.org/T12814 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.995199978351593 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1702 |
| topics[1].subfield.display_name | Artificial Intelligence |
| topics[1].display_name | Gaussian Processes and Bayesian Inference |
| topics[2].id | https://openalex.org/T12101 |
| topics[2].field.id | https://openalex.org/fields/18 |
| topics[2].field.display_name | Decision Sciences |
| topics[2].score | 0.9947999715805054 |
| topics[2].domain.id | https://openalex.org/domains/2 |
| topics[2].domain.display_name | Social Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1803 |
| topics[2].subfield.display_name | Management Science and Operations Research |
| topics[2].display_name | Advanced Bandit Algorithms Research |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C2776214188 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7749581336975098 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q408386 |
| concepts[0].display_name | Inference |
| concepts[1].id | https://openalex.org/C41008148 |
| concepts[1].level | 0 |
| concepts[1].score | 0.6979087591171265 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[1].display_name | Computer science |
| concepts[2].id | https://openalex.org/C185429906 |
| concepts[2].level | 2 |
| concepts[2].score | 0.650154709815979 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q1130160 |
| concepts[2].display_name | Estimator |
| concepts[3].id | https://openalex.org/C45374587 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5772060751914978 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q12525525 |
| concepts[3].display_name | Computation |
| concepts[4].id | https://openalex.org/C44249647 |
| concepts[4].level | 2 |
| concepts[4].score | 0.557736873626709 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q208498 |
| concepts[4].display_name | Confidence interval |
| concepts[5].id | https://openalex.org/C2776292839 |
| concepts[5].level | 3 |
| concepts[5].score | 0.5018882751464844 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q5179217 |
| concepts[5].display_name | Coverage probability |
| concepts[6].id | https://openalex.org/C2777303404 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4957786500453949 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q759757 |
| concepts[6].display_name | Convergence (economics) |
| concepts[7].id | https://openalex.org/C11413529 |
| concepts[7].level | 1 |
| concepts[7].score | 0.46854886412620544 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q8366 |
| concepts[7].display_name | Algorithm |
| concepts[8].id | https://openalex.org/C126255220 |
| concepts[8].level | 1 |
| concepts[8].score | 0.448560506105423 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[8].display_name | Mathematical optimization |
| concepts[9].id | https://openalex.org/C61326573 |
| concepts[9].level | 3 |
| concepts[9].score | 0.4297899603843689 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q1496376 |
| concepts[9].display_name | Gaussian process |
| concepts[10].id | https://openalex.org/C163716315 |
| concepts[10].level | 2 |
| concepts[10].score | 0.27859267592430115 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q901177 |
| concepts[10].display_name | Gaussian |
| concepts[11].id | https://openalex.org/C33923547 |
| concepts[11].level | 0 |
| concepts[11].score | 0.22502374649047852 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[11].display_name | Mathematics |
| concepts[12].id | https://openalex.org/C154945302 |
| concepts[12].level | 1 |
| concepts[12].score | 0.16907188296318054 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[12].display_name | Artificial intelligence |
| concepts[13].id | https://openalex.org/C105795698 |
| concepts[13].level | 1 |
| concepts[13].score | 0.14150658249855042 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[13].display_name | Statistics |
| concepts[14].id | https://openalex.org/C121332964 |
| concepts[14].level | 0 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[14].display_name | Physics |
| concepts[15].id | https://openalex.org/C50522688 |
| concepts[15].level | 1 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q189833 |
| concepts[15].display_name | Economic growth |
| concepts[16].id | https://openalex.org/C162324750 |
| concepts[16].level | 0 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q8134 |
| concepts[16].display_name | Economics |
| concepts[17].id | https://openalex.org/C62520636 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[17].display_name | Quantum mechanics |
| keywords[0].id | https://openalex.org/keywords/inference |
| keywords[0].score | 0.7749581336975098 |
| keywords[0].display_name | Inference |
| keywords[1].id | https://openalex.org/keywords/computer-science |
| keywords[1].score | 0.6979087591171265 |
| keywords[1].display_name | Computer science |
| keywords[2].id | https://openalex.org/keywords/estimator |
| keywords[2].score | 0.650154709815979 |
| keywords[2].display_name | Estimator |
| keywords[3].id | https://openalex.org/keywords/computation |
| keywords[3].score | 0.5772060751914978 |
| keywords[3].display_name | Computation |
| keywords[4].id | https://openalex.org/keywords/confidence-interval |
| keywords[4].score | 0.557736873626709 |
| keywords[4].display_name | Confidence interval |
| keywords[5].id | https://openalex.org/keywords/coverage-probability |
| keywords[5].score | 0.5018882751464844 |
| keywords[5].display_name | Coverage probability |
| keywords[6].id | https://openalex.org/keywords/convergence |
| keywords[6].score | 0.4957786500453949 |
| keywords[6].display_name | Convergence (economics) |
| keywords[7].id | https://openalex.org/keywords/algorithm |
| keywords[7].score | 0.46854886412620544 |
| keywords[7].display_name | Algorithm |
| keywords[8].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[8].score | 0.448560506105423 |
| keywords[8].display_name | Mathematical optimization |
| keywords[9].id | https://openalex.org/keywords/gaussian-process |
| keywords[9].score | 0.4297899603843689 |
| keywords[9].display_name | Gaussian process |
| keywords[10].id | https://openalex.org/keywords/gaussian |
| keywords[10].score | 0.27859267592430115 |
| keywords[10].display_name | Gaussian |
| keywords[11].id | https://openalex.org/keywords/mathematics |
| keywords[11].score | 0.22502374649047852 |
| keywords[11].display_name | Mathematics |
| keywords[12].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[12].score | 0.16907188296318054 |
| keywords[12].display_name | Artificial intelligence |
| keywords[13].id | https://openalex.org/keywords/statistics |
| keywords[13].score | 0.14150658249855042 |
| keywords[13].display_name | Statistics |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2401.09346 |
| 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/2401.09346 |
| 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/2401.09346 |
| locations[1].id | doi:10.48550/arxiv.2401.09346 |
| 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 | |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | |
| 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.2401.09346 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5023400154 |
| authorships[0].author.orcid | https://orcid.org/0009-0005-3448-0078 |
| authorships[0].author.display_name | Wanrong Zhu |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Zhu, Wanrong |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5013258402 |
| authorships[1].author.orcid | https://orcid.org/0009-0008-0421-9313 |
| authorships[1].author.display_name | Zhipeng Lou |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Lou, Zhipeng |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5101303021 |
| authorships[2].author.orcid | |
| authorships[2].author.display_name | Ziyang Wei |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Wei, Ziyang |
| authorships[2].is_corresponding | False |
| authorships[3].author.id | https://openalex.org/A5036683934 |
| authorships[3].author.orcid | https://orcid.org/0000-0003-4310-9965 |
| authorships[3].author.display_name | Wei Biao Wu |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Wu, Wei Biao |
| authorships[3].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/2401.09346 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2024-01-19T00:00:00 |
| display_name | High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T12535 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9958000183105469 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1702 |
| primary_topic.subfield.display_name | Artificial Intelligence |
| primary_topic.display_name | Machine Learning and Data Classification |
| related_works | https://openalex.org/W4287880334, https://openalex.org/W4366700029, https://openalex.org/W4285230481, https://openalex.org/W4385769873, https://openalex.org/W2015759683, https://openalex.org/W4281634296, https://openalex.org/W4319161863, https://openalex.org/W2371687270, https://openalex.org/W4307819175, https://openalex.org/W4311888330 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2401.09346 |
| 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/2401.09346 |
| 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/2401.09346 |
| primary_location.id | pmh:oai:arXiv.org:2401.09346 |
| 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/2401.09346 |
| 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/2401.09346 |
| publication_date | 2024-01-17 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 19, 43, 55, 81, 110 |
| abstract_inverted_index.In | 108 |
| abstract_inverted_index.It | 151 |
| abstract_inverted_index.We | 79 |
| abstract_inverted_index.an | 9, 97 |
| abstract_inverted_index.be | 158 |
| abstract_inverted_index.in | 8, 130 |
| abstract_inverted_index.is | 93, 115, 152 |
| abstract_inverted_index.of | 46, 71, 126, 132 |
| abstract_inverted_index.on | 24 |
| abstract_inverted_index.to | 34, 41, 49, 121, 144, 154 |
| abstract_inverted_index.we | 39 |
| abstract_inverted_index.Our | 59 |
| abstract_inverted_index.and | 31, 53, 65, 101, 156 |
| abstract_inverted_index.can | 157 |
| abstract_inverted_index.for | 2, 85, 103, 117, 140, 167 |
| abstract_inverted_index.has | 12 |
| abstract_inverted_index.new | 111 |
| abstract_inverted_index.our | 127, 136 |
| abstract_inverted_index.the | 35, 68, 74, 86, 91, 118, 123, 165 |
| abstract_inverted_index.use | 42 |
| abstract_inverted_index.This | 16 |
| abstract_inverted_index.also | 138 |
| abstract_inverted_index.easy | 153 |
| abstract_inverted_index.fast | 32 |
| abstract_inverted_index.high | 104 |
| abstract_inverted_index.need | 166 |
| abstract_inverted_index.rate | 100 |
| abstract_inverted_index.that | 90 |
| abstract_inverted_index.with | 28, 96, 160 |
| abstract_inverted_index.exact | 95 |
| abstract_inverted_index.level | 106 |
| abstract_inverted_index.novel | 20 |
| abstract_inverted_index.paper | 17 |
| abstract_inverted_index.small | 44 |
| abstract_inverted_index.terms | 131 |
| abstract_inverted_index.using | 148 |
| abstract_inverted_index.allows | 139 |
| abstract_inverted_index.almost | 77 |
| abstract_inverted_index.beyond | 67 |
| abstract_inverted_index.cores. | 150 |
| abstract_inverted_index.gained | 13 |
| abstract_inverted_index.level. | 37 |
| abstract_inverted_index.making | 73 |
| abstract_inverted_index.memory | 66 |
| abstract_inverted_index.method | 22, 60, 137 |
| abstract_inverted_index.number | 45 |
| abstract_inverted_index.online | 10, 119 |
| abstract_inverted_index.result | 114 |
| abstract_inverted_index.acquire | 50 |
| abstract_inverted_index.errors. | 134 |
| abstract_inverted_index.focused | 23 |
| abstract_inverted_index.further | 145 |
| abstract_inverted_index.minimal | 62 |
| abstract_inverted_index.nominal | 36 |
| abstract_inverted_index.process | 76 |
| abstract_inverted_index.propose | 40 |
| abstract_inverted_index.provide | 80 |
| abstract_inverted_index.setting | 11 |
| abstract_inverted_index.t-based | 56 |
| abstract_inverted_index.through | 4 |
| abstract_inverted_index.without | 164 |
| abstract_inverted_index.Gaussian | 112 |
| abstract_inverted_index.allowing | 102 |
| abstract_inverted_index.coverage | 92, 124 |
| abstract_inverted_index.existing | 161 |
| abstract_inverted_index.explicit | 98 |
| abstract_inverted_index.multiple | 149 |
| abstract_inverted_index.parallel | 142 |
| abstract_inverted_index.relative | 133 |
| abstract_inverted_index.requires | 61 |
| abstract_inverted_index.rigorous | 82 |
| abstract_inverted_index.standard | 69 |
| abstract_inverted_index.updating | 70 |
| abstract_inverted_index.computing | 143 |
| abstract_inverted_index.construct | 54 |
| abstract_inverted_index.developed | 116 |
| abstract_inverted_index.efficient | 29 |
| abstract_inverted_index.guarantee | 84 |
| abstract_inverted_index.implement | 155 |
| abstract_inverted_index.inference | 21, 75 |
| abstract_inverted_index.interval, | 88 |
| abstract_inverted_index.interval. | 58 |
| abstract_inverted_index.intervals | 27, 129 |
| abstract_inverted_index.recently. | 15 |
| abstract_inverted_index.solutions | 7 |
| abstract_inverted_index.accelerate | 146 |
| abstract_inverted_index.additional | 63 |
| abstract_inverted_index.algorithms | 163 |
| abstract_inverted_index.confidence | 26, 57, 87, 105, 128 |
| abstract_inverted_index.cost-free. | 78 |
| abstract_inverted_index.estimates, | 72 |
| abstract_inverted_index.estimation | 3 |
| abstract_inverted_index.estimators | 120 |
| abstract_inverted_index.inference. | 107 |
| abstract_inverted_index.integrated | 159 |
| abstract_inverted_index.introduces | 18 |
| abstract_inverted_index.leveraging | 141 |
| abstract_inverted_index.multi-runs | 48 |
| abstract_inverted_index.popularity | 14 |
| abstract_inverted_index.properties | 125 |
| abstract_inverted_index.stochastic | 5, 162 |
| abstract_inverted_index.Uncertainty | 0 |
| abstract_inverted_index.complicated | 168 |
| abstract_inverted_index.computation | 30, 64 |
| abstract_inverted_index.convergence | 33, 99 |
| abstract_inverted_index.independent | 47 |
| abstract_inverted_index.information | 52 |
| abstract_inverted_index.particular, | 109 |
| abstract_inverted_index.theoretical | 83 |
| abstract_inverted_index.calculations | 147 |
| abstract_inverted_index.characterize | 122 |
| abstract_inverted_index.constructing | 25 |
| abstract_inverted_index.distribution | 51 |
| abstract_inverted_index.optimization | 6 |
| abstract_inverted_index.Additionally, | 135 |
| abstract_inverted_index.Specifically, | 38 |
| abstract_inverted_index.approximately | 94 |
| abstract_inverted_index.approximation | 113 |
| abstract_inverted_index.demonstrating | 89 |
| abstract_inverted_index.modifications. | 169 |
| abstract_inverted_index.quantification | 1 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile |