{"id":"https://openalex.org/W3084360281","doi":"https://doi.org/10.1109/lwc.2020.3036588","title":"Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms","display_name":"Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms","publication_year":2020,"publication_date":"2020-11-06","ids":{"openalex":"https://openalex.org/W3084360281","doi":"https://doi.org/10.1109/lwc.2020.3036588","mag":"3084360281"},"language":"en","primary_location":{"id":"doi:10.1109/lwc.2020.3036588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lwc.2020.3036588","pdf_url":null,"source":{"id":"https://openalex.org/S2500830676","display_name":"IEEE Wireless Communications Letters","issn_l":"2162-2337","issn":["2162-2337","2162-2345"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Wireless Communications Letters","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2009.03677","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011406516","display_name":"Chaouki Ben Issaid","orcid":"https://orcid.org/0000-0002-4481-8168"},"institutions":[{"id":"https://openalex.org/I98381234","display_name":"University of Oulu","ror":"https://ror.org/03yj89h83","country_code":"FI","type":"education","lineage":["https://openalex.org/I98381234"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Chaouki Ben Issaid","raw_affiliation_strings":["Centre for Wireless Communications, University of Oulu, Oulu, Finland"],"affiliations":[{"raw_affiliation_string":"Centre for Wireless Communications, University of Oulu, Oulu, Finland","institution_ids":["https://openalex.org/I98381234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083193286","display_name":"Mohamed\u2010Slim Alouini","orcid":"https://orcid.org/0000-0003-4827-1793"},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohamed-Slim Alouini","raw_affiliation_strings":["King Abdullah University of Science and Technology, Thuwal, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080666143","display_name":"and Raul Tempone","orcid":null},"institutions":[{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE","SA"],"is_corresponding":false,"raw_author_name":"Raul Tempone","raw_affiliation_strings":["King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","RWTH Aachen University, Aachen, Germany","KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY"],"affiliations":[{"raw_affiliation_string":"King Abdullah University of Science and Technology, Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"KING ABDULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY","institution_ids":["https://openalex.org/I71920554"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011406516"],"corresponding_institution_ids":["https://openalex.org/I98381234"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16713222,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"10","issue":"3","first_page":"527","last_page":"531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11720","display_name":"Probability and Risk Models","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.805706262588501},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.6213728785514832},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6143002510070801},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6031299233436584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.583530843257904},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5833468437194824},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5769810080528259},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5326656103134155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5165685415267944},{"id":"https://openalex.org/keywords/importance-sampling","display_name":"Importance sampling","score":0.49326223134994507},{"id":"https://openalex.org/keywords/rejection-sampling","display_name":"Rejection sampling","score":0.4786749482154846},{"id":"https://openalex.org/keywords/probability-sampling","display_name":"Probability sampling","score":0.41226232051849365},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3892993628978729},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.37017226219177246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3689824044704437},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3534172773361206},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.14048495888710022},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12376201152801514},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.10363960266113281},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0897093117237091}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.805706262588501},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.6213728785514832},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6143002510070801},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6031299233436584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.583530843257904},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5833468437194824},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5769810080528259},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5326656103134155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5165685415267944},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.49326223134994507},{"id":"https://openalex.org/C187192777","wikidata":"https://www.wikidata.org/wiki/Q381699","display_name":"Rejection sampling","level":5,"score":0.4786749482154846},{"id":"https://openalex.org/C2993010571","wikidata":"https://www.wikidata.org/wiki/Q49908","display_name":"Probability sampling","level":3,"score":0.41226232051849365},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3892993628978729},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37017226219177246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3689824044704437},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3534172773361206},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.14048495888710022},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12376201152801514},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.10363960266113281},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0897093117237091},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/lwc.2020.3036588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lwc.2020.3036588","pdf_url":null,"source":{"id":"https://openalex.org/S2500830676","display_name":"IEEE Wireless Communications Letters","issn_l":"2162-2337","issn":["2162-2337","2162-2345"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Wireless Communications Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2009.03677","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.03677","pdf_url":"https://arxiv.org/pdf/2009.03677","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3084360281","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2009.03677.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:publications.rwth-aachen.de:816838","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/816838","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE wireless communications letters 10(3), 527-531 (2021). doi:10.1109/LWC.2020.3036588","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/665134","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/665134","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.2009.03677","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2009.03677","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2009.03677","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.03677","pdf_url":"https://arxiv.org/pdf/2009.03677","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W608889345","https://openalex.org/W1502620588","https://openalex.org/W2016886155","https://openalex.org/W2033935789","https://openalex.org/W2051338647","https://openalex.org/W2052236587","https://openalex.org/W2087747394","https://openalex.org/W2128393863","https://openalex.org/W2249111724","https://openalex.org/W2290804602","https://openalex.org/W2428781461","https://openalex.org/W2495268772","https://openalex.org/W2741318886","https://openalex.org/W2775698417","https://openalex.org/W2936038167","https://openalex.org/W2963433039","https://openalex.org/W2964344119","https://openalex.org/W3099338525","https://openalex.org/W4252418167"],"related_works":["https://openalex.org/W3133392554","https://openalex.org/W3149327226","https://openalex.org/W3033377337","https://openalex.org/W2022450888","https://openalex.org/W1637469959","https://openalex.org/W2996228413","https://openalex.org/W2918761813","https://openalex.org/W2888075180","https://openalex.org/W3103961368","https://openalex.org/W3156310190","https://openalex.org/W2964074174","https://openalex.org/W2765651750","https://openalex.org/W2945405745","https://openalex.org/W2998520009","https://openalex.org/W2745840381","https://openalex.org/W1983699743","https://openalex.org/W2740272948","https://openalex.org/W2460697741","https://openalex.org/W2989328214","https://openalex.org/W135374354"],"abstract_inverted_index":{"Estimating":[0],"the":[1,33,42,49,60,74,88],"left":[2],"tail":[3],"of":[4,12,44,62,76,87],"quadratic":[5],"forms":[6],"in":[7,16],"Gaussian":[8],"random":[9],"vectors":[10],"is":[11,30,64],"major":[13],"practical":[14],"importance":[15,26],"many":[17],"applications.":[18],"In":[19],"this":[20],"letter,":[21],"we":[22],"propose":[23],"an":[24],"efficient":[25],"sampling":[27],"estimator":[28,51,78],"that":[29],"endowed":[31],"with":[32],"bounded":[34],"relative":[35],"error":[36],"property.":[37],"This":[38],"property":[39],"significantly":[40],"reduces":[41],"number":[43],"simulation":[45,68],"runs":[46],"required":[47],"by":[48],"proposed":[50],"compared":[52,79],"to":[53,72,80],"naive":[54,81],"Monte":[55],"Carlo":[56],"(MC),":[57],"especially":[58],"when":[59],"probability":[61],"interest":[63],"very":[65],"small.":[66],"Selected":[67],"results":[69],"are":[70],"presented":[71],"illustrate":[73],"efficiency":[75],"our":[77],"MC":[82],"as":[83,85],"well":[84],"some":[86],"well-known":[89],"approximations.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
