{"id":"https://openalex.org/W2004957736","doi":"https://doi.org/10.1145/2582112.2582131","title":"Sub-linear Time Hybrid Approximations for Least Trimmed Squares Estimator and Related Problems","display_name":"Sub-linear Time Hybrid Approximations for Least Trimmed Squares Estimator and Related Problems","publication_year":2014,"publication_date":"2014-05-02","ids":{"openalex":"https://openalex.org/W2004957736","doi":"https://doi.org/10.1145/2582112.2582131","mag":"2004957736"},"language":"en","primary_location":{"id":"doi:10.1145/2582112.2582131","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100725915","display_name":"Hu Ding","orcid":"https://orcid.org/0000-0002-1307-6077"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hu Ding","raw_affiliation_strings":["Department of Computer Science and Engineering, State University of New York at Buffalo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, State University of New York at Buffalo","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006945148","display_name":"Jinhui Xu","orcid":"https://orcid.org/0000-0001-5730-9429"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jinhui Xu","raw_affiliation_strings":["Department of Computer Science and Engineering, State University of New York at Buffalo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, State University of New York at Buffalo","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63190737"],"apc_list":null,"apc_paid":null,"fwci":0.9255,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.75367289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"110","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6865030527114868},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6386856436729431},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6305834054946899},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5452339053153992},{"id":"https://openalex.org/keywords/quantile","display_name":"Quantile","score":0.5423340201377869},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4828625023365021},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.45944344997406006},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4371546506881714},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.4242684841156006},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3674454092979431},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35645586252212524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28352540731430054},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2598445415496826},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17765045166015625},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12410959601402283}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6865030527114868},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6386856436729431},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6305834054946899},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5452339053153992},{"id":"https://openalex.org/C118671147","wikidata":"https://www.wikidata.org/wiki/Q578714","display_name":"Quantile","level":2,"score":0.5423340201377869},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4828625023365021},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.45944344997406006},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4371546506881714},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.4242684841156006},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3674454092979431},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35645586252212524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28352540731430054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2598445415496826},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17765045166015625},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12410959601402283},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2582112.2582131","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2582112.2582131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirtieth annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W581837698","https://openalex.org/W1488526968","https://openalex.org/W1578468649","https://openalex.org/W1684309424","https://openalex.org/W1704895987","https://openalex.org/W1972925770","https://openalex.org/W1982475381","https://openalex.org/W1986520777","https://openalex.org/W1986948589","https://openalex.org/W1988374166","https://openalex.org/W2004931706","https://openalex.org/W2016267457","https://openalex.org/W2054995322","https://openalex.org/W2083131242","https://openalex.org/W2091283109","https://openalex.org/W2096287911","https://openalex.org/W2096830858","https://openalex.org/W2110553125","https://openalex.org/W2112442678","https://openalex.org/W2117499877","https://openalex.org/W2129249398","https://openalex.org/W2134746140","https://openalex.org/W2139959487","https://openalex.org/W2147026670","https://openalex.org/W2152285609","https://openalex.org/W2155229861","https://openalex.org/W2167816765","https://openalex.org/W2172030265","https://openalex.org/W2202186557","https://openalex.org/W2618362965","https://openalex.org/W4234407907","https://openalex.org/W4285719527","https://openalex.org/W6616888767","https://openalex.org/W6671215827"],"related_works":["https://openalex.org/W2369655046","https://openalex.org/W2019467317","https://openalex.org/W1488761988","https://openalex.org/W1585519779","https://openalex.org/W2044551864","https://openalex.org/W1965515989","https://openalex.org/W1572557500","https://openalex.org/W2088737283","https://openalex.org/W1999587863","https://openalex.org/W1929902734"],"abstract_inverted_index":{"Least":[0,279],"Trimmed":[1,280],"Squares":[2,281],"(LTS)":[3],"estimator":[4],"is":[5,70,99,112,155,166,174,197,219,285],"a":[6,13,18,21,34,43,51,100,106,113,193],"statistical":[7],"tool":[8],"for":[9,254,262],"estimating":[10],"how":[11],"well":[12],"set":[14,35],"of":[15,37,59,109,143,176],"points":[16,39],"fits":[17],"hyperplane.":[19],"As":[20],"robust":[22],"alternative":[23],"to":[24,68,93,186,224,248,293],"the":[25,57,60,156,167,177,225,277],"classical":[26],"least":[27],"squares":[28],"estimator,":[29],"LTS":[30,79,144,263,270],"takes":[31,203],"as":[32,232,259],"input":[33,178],"P":[36,67],"n":[38],"in":[40,124,127,148,264],"Rd":[41],"and":[42,49,118,160,208,227,239,273,276],"fitting":[44,296],"parameter":[45],"m":[46,61,182],"\u2264":[47],"n,":[48,180],"computes":[50],"non-vertical":[52],"hyperplane":[53],"H":[54,69],"so":[55],"that":[56,76,138,287],"sum":[58],"smallest":[62],"squared":[63],"vertical":[64],"distances":[65],"from":[66],"minimized.":[71],"Previous":[72],"research":[73],"has":[74,191,200],"indicated":[75],"although":[77],"solving":[78],"(exactly":[80],"or":[81],"approximately)":[82],"could":[83],"be":[84,122,146,246,291],"quite":[85,192],"costly":[86],"(i.e.,":[87],"it":[88,96],"may":[89],"take":[90],"\u03a9(nd\u22121)":[91],"time":[92,126,173,251],"even":[94],"approximate":[95],"when":[97,181],"m/n":[98],"positive":[101],"constant":[102,205],"c":[103],"<":[104,162,164],"1),":[105],"hybrid":[107,252],"version":[108],"approximation,":[110,120],"which":[111],"bi-criteria":[114],"on":[115,221,271],"residual":[116,157],"approximation":[117,142,158,169],"quantile":[119,168],"can":[121,145,209,244],"obtained":[123],"linear":[125],"any":[128],"fixed":[129],"dimensional":[130],"space.":[131],"In":[132],"this":[133],"paper,":[134],"we":[135],"further":[136],"show":[137],"an":[139],"(\u03f5r,":[140],"\u03f5q)-hybrid":[141],"computed":[147],"sub-linear":[149,250],"time,":[150],"where":[151],"\u03f5r":[152],">":[153],"0":[154,161],"ratio":[159],"\u03f5q":[163],"1":[165],"ratio.":[170],"The":[171],"running":[172],"independent":[175],"size":[179],"=":[183],"\u229d(n).":[184],"Comparing":[185],"existing":[187],"result,":[188],"our":[189,288],"approach":[190],"few":[194],"advantages,":[195],"e.g.,":[196],"much":[198],"simpler,":[199],"better":[201],"robustness,":[202],"only":[204],"additional":[206],"space,":[207],"deal":[210],"with":[211],"big":[212],"data":[213],"(e.g.,":[214],"streaming":[215],"data).":[216],"Our":[217,242],"result":[218],"based":[220],"new":[222],"insights":[223],"problem":[226],"several":[228,255],"novel":[229],"techniques,":[230],"such":[231,258],"recursive":[233],"slab":[234],"partition,":[235],"sequential":[236],"orthogonal":[237],"rotation,":[238],"symmetric":[240],"sampling.":[241],"technique":[243,289],"also":[245],"extended":[247],"achieve":[249],"approximations":[253],"related":[256],"problems,":[257],"data-oblivious":[260],"computation":[261],"Secure":[265],"Multi-party":[266],"Computation":[267],"(SMC)":[268],"protocol,":[269],"uncertain":[272],"range":[274],"data,":[275],"Orthogonal":[278],"(OLTS)":[282],"problem.":[283],"It":[284],"likely":[286],"will":[290],"applicable":[292],"other":[294],"shape":[295],"problems.":[297]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}