{"id":"https://openalex.org/W2130590509","doi":"https://doi.org/10.1145/2608628.2608659","title":"Maximum likelihood geometry in the presence of data zeros","display_name":"Maximum likelihood geometry in the presence of data zeros","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W2130590509","doi":"https://doi.org/10.1145/2608628.2608659","mag":"2130590509"},"language":"en","primary_location":{"id":"doi:10.1145/2608628.2608659","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","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/A5070854426","display_name":"Elizabeth Gross","orcid":"https://orcid.org/0000-0003-4305-065X"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elizabeth Gross","raw_affiliation_strings":["North Carolina State University, Raleigh, NC","North Carolina State University, Raleigh, NC;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"North Carolina State University, Raleigh, NC;","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039894662","display_name":"Jose Israel Rodriguez","orcid":"https://orcid.org/0000-0003-3140-9944"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jose Israel Rodriguez","raw_affiliation_strings":["University of California at Berkeley, Berkeley, CA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at Berkeley, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8153,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.83592018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"232","last_page":"239"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/likelihood-function","display_name":"Likelihood function","score":0.719573974609375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7012739181518555},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6868219375610352},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6273683905601501},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.570648193359375},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.5076116323471069},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5070111751556396},{"id":"https://openalex.org/keywords/maximum-likelihood-sequence-estimation","display_name":"Maximum likelihood sequence estimation","score":0.5041052103042603},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.49386483430862427},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4866786599159241},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4660891890525818},{"id":"https://openalex.org/keywords/estimating-equations","display_name":"Estimating equations","score":0.4108423888683319},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3962303698062897},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36151421070098877},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34767380356788635},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17235174775123596},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14789244532585144}],"concepts":[{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.719573974609375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7012739181518555},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6868219375610352},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6273683905601501},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.570648193359375},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.5076116323471069},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5070111751556396},{"id":"https://openalex.org/C191462741","wikidata":"https://www.wikidata.org/wiki/Q6795902","display_name":"Maximum likelihood sequence estimation","level":3,"score":0.5041052103042603},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.49386483430862427},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4866786599159241},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4660891890525818},{"id":"https://openalex.org/C204016326","wikidata":"https://www.wikidata.org/wiki/Q5401384","display_name":"Estimating equations","level":3,"score":0.4108423888683319},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3962303698062897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36151421070098877},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34767380356788635},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17235174775123596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14789244532585144},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2608628.2608659","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608659","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W647818151","https://openalex.org/W1570420806","https://openalex.org/W1614570815","https://openalex.org/W1965520434","https://openalex.org/W2001588532","https://openalex.org/W2011972873","https://openalex.org/W2028576930","https://openalex.org/W2040177378","https://openalex.org/W2063677935","https://openalex.org/W2063979566","https://openalex.org/W2069641044","https://openalex.org/W2074673068","https://openalex.org/W2090551280","https://openalex.org/W2125561810","https://openalex.org/W2144327163","https://openalex.org/W2158639671","https://openalex.org/W2167360454","https://openalex.org/W2168359188","https://openalex.org/W2951446265","https://openalex.org/W3038124051","https://openalex.org/W3099419086","https://openalex.org/W3155460447"],"related_works":["https://openalex.org/W2019724159","https://openalex.org/W2371672232","https://openalex.org/W2120595071","https://openalex.org/W2103185490","https://openalex.org/W1512911331","https://openalex.org/W2110390278","https://openalex.org/W2118272055","https://openalex.org/W2148113631","https://openalex.org/W2010149275","https://openalex.org/W4250794892"],"abstract_inverted_index":{"Given":[0],"a":[1,66,79,117],"statistical":[2,25],"model,":[3],"the":[4,9,15,29,32,36,57,60,70,83,87,94,121,154,162],"maximum":[5],"likelihood":[6,16,33,61,71,95],"degree":[7,123,164],"is":[8],"number":[10,74],"of":[11,75,89,133,143,158],"complex":[12],"solutions":[13,30,58,77],"to":[14,31,59,93,115],"equations":[17,34,62],"for":[18,124,147,160],"generic":[19],"data.":[20],"We":[21,111],"consider":[22],"discrete":[23],"algebraic":[24],"models":[26],"and":[27,40,48,86,102,108,138],"study":[28],"when":[35],"data":[37],"contain":[38],"zeros":[39],"are":[41,63],"no":[42],"longer":[43],"generic.":[44],"Focusing":[45],"on":[46,82,120],"sampling":[47,107],"model":[49,109],"zeros,":[50],"we":[51],"show":[52],"that,":[53],"in":[54,65],"these":[55,76],"cases,":[56],"contained":[64],"previously":[67,166],"studied":[68],"variety,":[69],"correspondence.":[72],"The":[73],"give":[78],"lower":[80,118],"bound":[81,119],"ML":[84,122,163],"degree,":[85],"problem":[88],"finding":[90],"critical":[91],"points":[92],"function":[96],"can":[97],"be":[98],"partitioned":[99],"into":[100],"smaller":[101],"computationally":[103],"easier":[104],"problems":[105],"involving":[106],"zeros.":[110],"use":[112],"this":[113],"technique":[114],"compute":[116],"2":[125,127,129,131,137,146],"x":[126,128,130,140],"tensors":[132],"border":[134],"rank":[135,144],"\u2264":[136,145],"3":[139],"n":[141,148,159],"tables":[142],"=":[149],"11,":[150],"12,":[151],"13,":[152],"14,":[153],"first":[155],"four":[156],"values":[157],"which":[161],"was":[165],"unknown.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":2}],"updated_date":"2026-07-10T07:45:09.275182","created_date":"2025-10-10T00:00:00"}
