{"id":"https://openalex.org/W4384933297","doi":"https://doi.org/10.1137/22m1515690","title":"Toric and Non-toric Bayesian Networks","display_name":"Toric and Non-toric Bayesian Networks","publication_year":2023,"publication_date":"2023-07-20","ids":{"openalex":"https://openalex.org/W4384933297","doi":"https://doi.org/10.1137/22m1515690"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1515690","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/pdf/2208.06294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063098457","display_name":"Lisa Nicklasson","orcid":"https://orcid.org/0000-0003-3244-4100"},"institutions":[{"id":"https://openalex.org/I83816512","display_name":"University of Genoa","ror":"https://ror.org/0107c5v14","country_code":"IT","type":"education","lineage":["https://openalex.org/I83816512"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Lisa Nicklasson","raw_affiliation_strings":["Dipartimanto di Matematica, Universit\u00e0 di Genova, 16146 Genova, Italy."],"affiliations":[{"raw_affiliation_string":"Dipartimanto di Matematica, Universit\u00e0 di Genova, 16146 Genova, Italy.","institution_ids":["https://openalex.org/I83816512"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5063098457"],"corresponding_institution_ids":["https://openalex.org/I83816512"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":67},"biblio":{"volume":"7","issue":"3","first_page":"549","last_page":"566"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.997,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.997,"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":0.9939,"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"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9877,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5861682},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.5460392},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5449083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.536962},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5264115},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44072548},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37826642},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35316324},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24803635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15906224},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.061146468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1515690","pdf_url":null,"source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.06294","pdf_url":"http://arxiv.org/pdf/2208.06294","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2208.06294","pdf_url":"https://arxiv.org/pdf/2208.06294","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.06294","pdf_url":"http://arxiv.org/pdf/2208.06294","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse","award_id":"KAW 2019.0512"}],"datasets":[],"versions":[],"referenced_works_count":14,"referenced_works":["https://openalex.org/W1984853417","https://openalex.org/W1989061133","https://openalex.org/W1990576250","https://openalex.org/W2037181643","https://openalex.org/W2085926380","https://openalex.org/W2118870114","https://openalex.org/W2171712069","https://openalex.org/W217710249","https://openalex.org/W2786193720","https://openalex.org/W3154751644","https://openalex.org/W3161754242","https://openalex.org/W3179869510","https://openalex.org/W4256619042","https://openalex.org/W4388323202"],"related_works":["https://openalex.org/W4375956809","https://openalex.org/W4297950433","https://openalex.org/W4292635168","https://openalex.org/W4288279572","https://openalex.org/W4287023968","https://openalex.org/W4286909116","https://openalex.org/W3194471551","https://openalex.org/W2784911598","https://openalex.org/W1973978937","https://openalex.org/W1581373162"],"abstract_inverted_index":{"In":[0],"this":[1,60],"paper":[2],"we":[3,44,63],"study":[4,45],"Bayesian":[5,17,26,42],"networks":[6],"from":[7],"a":[8,13,25,51,65],"commutative":[9],"algebra":[10],"perspective.We":[11],"characterize":[12],"class":[14,39],"of":[15,24,36,40],"toric":[16,41],"nets,":[18,43],"and":[19,49,56],"provide":[20],"the":[21,38,69],"first":[22],"example":[23],"net":[27],"which":[28],"is":[29],"provably":[30],"non-toric":[31],"under":[32],"any":[33],"linear":[34],"change":[35],"variables.Concerning":[37],"their":[46],"quadratic":[47],"relations":[48,77],"prove":[50],"conjecture":[52],"by":[53],"Garcia,":[54],"Stillman,":[55],"Sturmfels":[57],"[9]":[58],"for":[59,74],"class.In":[61],"addition,":[62],"give":[64],"necessary":[66],"condition":[67],"on":[68],"underlying":[70],"directed":[71],"acyclic":[72],"graph":[73],"when":[75],"all":[76],"are":[78],"quadratic.":[79]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4384933297","counts_by_year":[],"updated_date":"2025-01-07T22:55:50.824251","created_date":"2023-07-22"}