{"id":"https://openalex.org/W7153045225","doi":"https://doi.org/10.48550/arxiv.2604.07796","title":"Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes","display_name":"Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W7153045225","doi":"https://doi.org/10.48550/arxiv.2604.07796"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07796","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.07796","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040200112","display_name":"Ivan Lau","orcid":"https://orcid.org/0000-0002-9596-6726"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lau, Ivan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133353714","display_name":"Jonathan Scarlett","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scarlett, Jonathan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.21199999749660492,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.21199999749660492,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.1842000037431717,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10317","display_name":"Advanced Database Systems and Queries","score":0.1046999990940094,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7276999950408936},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6923999786376953},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6229000091552734},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5547000169754028},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.47200000286102295},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.45989999175071716},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4056999981403351},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.40130001306533813},{"id":"https://openalex.org/keywords/bias-of-an-estimator","display_name":"Bias of an estimator","score":0.39239999651908875},{"id":"https://openalex.org/keywords/sequential-estimation","display_name":"Sequential estimation","score":0.3806000053882599}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7764999866485596},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7276999950408936},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6923999786376953},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6229000091552734},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5547000169754028},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46149998903274536},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C191393472","wikidata":"https://www.wikidata.org/wiki/Q15222032","display_name":"Bias of an estimator","level":4,"score":0.39239999651908875},{"id":"https://openalex.org/C86426650","wikidata":"https://www.wikidata.org/wiki/Q7452504","display_name":"Sequential estimation","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3686000108718872},{"id":"https://openalex.org/C164172150","wikidata":"https://www.wikidata.org/wiki/Q1782585","display_name":"Consistent estimator","level":4,"score":0.3610999882221222},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C35594927","wikidata":"https://www.wikidata.org/wiki/Q2265984","display_name":"Efficient estimator","level":4,"score":0.3544999957084656},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C100279318","wikidata":"https://www.wikidata.org/wiki/Q467440","display_name":"Sample space","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3424000144004822},{"id":"https://openalex.org/C2780617739","wikidata":"https://www.wikidata.org/wiki/Q4680738","display_name":"Adaptive estimator","level":3,"score":0.33869999647140503},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C133939421","wikidata":"https://www.wikidata.org/wiki/Q6865379","display_name":"Minimax estimator","level":4,"score":0.2976999878883362},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C91716921","wikidata":"https://www.wikidata.org/wiki/Q1289366","display_name":"Scale parameter","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C181243257","wikidata":"https://www.wikidata.org/wiki/Q1693522","display_name":"Sample mean and sample covariance","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.26919999718666077},{"id":"https://openalex.org/C2781395549","wikidata":"https://www.wikidata.org/wiki/Q4680762","display_name":"Adaptive sampling","level":3,"score":0.26080000400543213},{"id":"https://openalex.org/C205167067","wikidata":"https://www.wikidata.org/wiki/Q3300636","display_name":"Interval estimation","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07796","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.07796","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07796","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,133],"paper,":[2],"we":[3,124,185],"study":[4],"the":[5,97,109,158,169,221],"problem":[6],"of":[7,139,161,213,223],"mean":[8,19,52],"estimation":[9],"under":[10],"1-bit":[11,29,140,226,235],"communication":[12,240],"constraints.":[13],"We":[14,142],"propose":[15],"a":[16,33,37,50,57,126,136,145],"novel":[17,127],"adaptive":[18,182],"estimator":[20,42,164],"based":[21],"solely":[22],"on":[23],"randomized":[24],"threshold":[25,151],"queries,":[26,157,227],"where":[27],"each":[28],"outcome":[30],"indicates":[31],"whether":[32],"given":[34,204],"sample":[35,73,94,115,159,178,218],"exceeds":[36],"sequentially":[38],"chosen":[39],"threshold.":[40],"Our":[41],"is":[43,75,135],"$(\u03b5,":[44],"\u03b4)$-PAC":[45],"for":[46,65,83,149],"any":[47,66,162],"distribution":[48],"with":[49,168],"bounded":[51,58],"$\u03bc\\in":[53],"[-\u03bb,":[54],"\u03bb]$":[55],"and":[56,123,153,228],"$k$-th":[59],"central":[60],"moment":[61],"$\\mathbb{E}[|X-\u03bc|^k]":[62],"\\le":[63],"\u03c3^k$":[64],"fixed":[67],"$k":[68,89],"&gt;":[69],"1$.":[70],"Moreover,":[71],"our":[72,92,113,181],"complexity":[74,95,116,160,219],"order-optimal":[76,217],"in":[77],"all":[78],"such":[79,85],"tail":[80],"regimes,":[81],"i.e.,":[82],"every":[84],"$k$":[86],"value.":[87],"For":[88,108],"\\neq":[90],"2$,":[91],"estimator's":[93,114],"matches":[96],"unquantized":[98],"minimax":[99],"lower":[100,129],"bounds":[101],"plus":[102],"an":[103,118,192,199],"unavoidable":[104],"$O(\\log(\u03bb/\u03c3))$":[105],"localization":[106],"cost.":[107],"finite-variance":[110],"case":[111],"($k=2$),":[112],"has":[117],"extra":[119],"multiplicative":[120],"$O(\\log(\u03c3/\u03b5))$":[121],"penalty,":[122],"establish":[125,144],"information-theoretic":[128],"bound":[130],"showing":[131],"that":[132,189],"penalty":[134],"fundamental":[137],"limit":[138],"quantization.":[141],"also":[143],"significant":[146],"adaptivity":[147,214],"gap:":[148],"both":[150],"queries":[152],"more":[154,224],"general":[155,225],"interval":[156],"non-adaptive":[163],"must":[165],"scale":[166,201],"linearly":[167],"search":[170],"space":[171],"parameter":[172,202],"$\u03bb/\u03c3$,":[173],"rendering":[174],"it":[175],"vastly":[176],"less":[177],"efficient":[179],"than":[180],"approach.":[183],"Finally,":[184],"present":[186],"algorithmic":[187],"variants":[188],"(i)":[190],"handle":[191],"unknown":[193,200],"sampling":[194],"budget,":[195],"(ii)":[196],"adapt":[197],"to":[198,215,237],"$\u03c3$":[203],"(possibly":[205],"loose)":[206],"bounds,":[207],"(iii)":[208],"require":[209],"only":[210],"two":[211],"stages":[212],"achieve":[216],"at":[220],"expense":[222],"(iv)":[229],"leverage":[230],"multiple":[231],"local":[232],"samples":[233],"per":[234],"query":[236],"proportionally":[238],"reduce":[239],"costs.":[241]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-11T00:00:00"}
