{"id":"https://openalex.org/W2397544591","doi":"https://doi.org/10.48550/arxiv.1605.08188","title":"Learning Multivariate Log-concave Distributions","display_name":"Learning Multivariate Log-concave Distributions","publication_year":2016,"publication_date":"2016-05-26","ids":{"openalex":"https://openalex.org/W2397544591","doi":"https://doi.org/10.48550/arxiv.1605.08188","mag":"2397544591"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1605.08188","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.08188","pdf_url":"https://arxiv.org/pdf/1605.08188","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,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.08188","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054966819","display_name":"Ilias Diakonikolas","orcid":"https://orcid.org/0000-0002-5486-1856","observed_orcids":["https://orcid.org/0000-0002-5486-1856"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diakonikolas, Ilias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035962853","display_name":"Daniel M. Kane","orcid":"https://orcid.org/0009-0007-9647-2609","observed_orcids":["https://orcid.org/0009-0007-9647-2609","https://orcid.org/0000-0002-0220-9962","https://orcid.org/0000-0002-5884-3487"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kane, Daniel M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5106184727","display_name":"Alistair Stewart","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stewart, Alistair","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":21,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"711","last_page":"727"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.6478999853134155,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.6478999853134155,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.10679999738931656,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.0284000001847744,"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/log-concave-density-estimation","display_name":"log-concave density estimation","score":0.8159999847412109},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"sample complexity","score":0.7739999890327454},{"id":"https://openalex.org/keywords/multivariate-probability-density-function","display_name":"multivariate probability density function","score":0.7910000085830688},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.7739999890327454},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"upper and lower bounds","score":0.6610000133514404}],"concepts":[{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.8531346321105957},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.826095461845398},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7083696126937866},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6889677047729492},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6619292497634888},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6372424364089966},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.43979835510253906},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.42070674896240234},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4176061451435089},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.41161686182022095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3691502809524536},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2668340802192688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16309669613838196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1446855664253235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10051965713500977},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0633726716041565},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1605.08188","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.08188","pdf_url":"https://arxiv.org/pdf/1605.08188","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,"listed_in":[],"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":"doi:10.48550/arxiv.1605.08188","doi":"https://doi.org/10.48550/arxiv.1605.08188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.08188","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,"listed_in":[],"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"},{"id":"mag:2962734918","doi":null,"is_oa":false,"landing_page_url":"http://proceedings.mlr.press/v65/diakonikolas17a/diakonikolas17a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306418075","display_name":"Conference on Learning Theory","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Conference on Learning Theory","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1605.08188","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.08188","pdf_url":"https://arxiv.org/pdf/1605.08188","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,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W119189535","https://openalex.org/W185751186","https://openalex.org/W611472129","https://openalex.org/W1494001604","https://openalex.org/W1511694993","https://openalex.org/W1520252399","https://openalex.org/W1528801940","https://openalex.org/W1585566614","https://openalex.org/W1763164889","https://openalex.org/W1940092327","https://openalex.org/W1966698631","https://openalex.org/W1975116882","https://openalex.org/W1979267397","https://openalex.org/W1979593580","https://openalex.org/W1979663407","https://openalex.org/W1995892550","https://openalex.org/W2006109604","https://openalex.org/W2014255551","https://openalex.org/W2014569888","https://openalex.org/W2029538739","https://openalex.org/W2033062730","https://openalex.org/W2046033161","https://openalex.org/W2047450510","https://openalex.org/W2065284301","https://openalex.org/W2068045918","https://openalex.org/W2068269714","https://openalex.org/W2072227363","https://openalex.org/W2085861256","https://openalex.org/W2104452301","https://openalex.org/W2107808918","https://openalex.org/W2122170585","https://openalex.org/W2136499803","https://openalex.org/W2146433171","https://openalex.org/W2146852149","https://openalex.org/W2154952480","https://openalex.org/W2156307401","https://openalex.org/W2163288162","https://openalex.org/W2186645727","https://openalex.org/W2227726937","https://openalex.org/W2344831783","https://openalex.org/W2419099043","https://openalex.org/W2928496982","https://openalex.org/W2962765673","https://openalex.org/W2963537613","https://openalex.org/W2963742519","https://openalex.org/W2963920131","https://openalex.org/W2963937023","https://openalex.org/W2964317125","https://openalex.org/W3099746525","https://openalex.org/W3100270455","https://openalex.org/W3105994413"],"related_works":["https://openalex.org/W2220190985","https://openalex.org/W2346846619","https://openalex.org/W2417295580","https://openalex.org/W1840639769","https://openalex.org/W4250921637","https://openalex.org/W2033612661","https://openalex.org/W4237200122","https://openalex.org/W2055354074","https://openalex.org/W198767307","https://openalex.org/W2014701453"],"abstract_inverted_index":{"We":[0,11],"study":[1],"the":[2,13,38,48,92,102,108],"problem":[3,44],"of":[4,41,50,112],"estimating":[5],"multivariate":[6],"log-concave":[7,21,77],"probability":[8],"density":[9,78],"functions.":[10],"prove":[12],"first":[14],"sample":[15,39,103],"complexity":[16,40,104],"upper":[17,35,99],"bound":[18,36,100,111],"for":[19,25,47,60,117],"learning":[20,43],"densities":[22],"on":[23,37,79,101],"$\\mathbb{R}^d$,":[24,80],"all":[26],"$d":[27,62],"\\geq":[28],"1$.":[29],"Prior":[30],"to":[31,91,107],"our":[32],"work,":[33],"no":[34],"this":[42,118],"was":[45],"known":[46,109],"case":[49],"$d>3$.":[51],"In":[52],"more":[53],"detail,":[54],"we":[55],"give":[56],"an":[57,74],"estimator":[58],"that,":[59],"any":[61],"\\ge":[63],"1$":[64],"and":[65,81],"$\u03b5>0$,":[66],"draws":[67],"$\\tilde{O}_d":[68],"\\left(":[69,114],"(1/\u03b5)^{(d+5)/2}":[70],"\\right)$":[71,116],"samples":[72],"from":[73],"unknown":[75],"target":[76],"outputs":[82],"a":[83],"hypothesis":[84],"that":[85],"(with":[86],"high":[87],"probability)":[88],"is":[89],"$\u03b5$-close":[90],"target,":[93],"in":[94],"total":[95],"variation":[96],"distance.":[97],"Our":[98],"comes":[105],"close":[106],"lower":[110],"$\u03a9_d":[113],"(1/\u03b5)^{(d+1)/2}":[115],"problem.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
