{"id":"https://openalex.org/W2294675398","doi":"https://doi.org/10.1109/tpami.2016.2618381","title":"On the Latent Variable Interpretation in Sum-Product Networks","display_name":"On the Latent Variable Interpretation in Sum-Product Networks","publication_year":2016,"publication_date":"2016-11-18","ids":{"openalex":"https://openalex.org/W2294675398","doi":"https://doi.org/10.1109/tpami.2016.2618381","mag":"2294675398","pmid":"https://pubmed.ncbi.nlm.nih.gov/27875213"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2016.2618381","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2016.2618381","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/8024097/07748514.pdf","source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/34/8024097/07748514.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057485787","display_name":"Robert Peharz","orcid":"https://orcid.org/0000-0002-8644-9655"},"institutions":[{"id":"https://openalex.org/I202276237","display_name":"Medical University of Graz","ror":"https://ror.org/02n0bts35","country_code":"AT","type":"education","lineage":["https://openalex.org/I202276237"]},{"id":"https://openalex.org/I4210117258","display_name":"BioTechMed-Graz","ror":"https://ror.org/02jfbm483","country_code":"AT","type":"facility","lineage":["https://openalex.org/I4210117258"]},{"id":"https://openalex.org/I4210166371","display_name":"Czech Academy of Sciences, Institute of Physiology","ror":"https://ror.org/05xw0ep96","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210166371"]}],"countries":["AT","CZ"],"is_corresponding":true,"raw_author_name":"Robert Peharz","raw_affiliation_strings":["BioTechMed\u2014Graz, Graz, Austria","Institute of Physiology (iDN), Medical University of Graz","Institute of Physiology (iDN)Medical University of Graz"],"affiliations":[{"raw_affiliation_string":"BioTechMed\u2014Graz, Graz, Austria","institution_ids":["https://openalex.org/I4210117258"]},{"raw_affiliation_string":"Institute of Physiology (iDN), Medical University of Graz","institution_ids":["https://openalex.org/I202276237","https://openalex.org/I4210166371"]},{"raw_affiliation_string":"Institute of Physiology (iDN)Medical University of Graz","institution_ids":["https://openalex.org/I202276237","https://openalex.org/I4210166371"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015336962","display_name":"Robert Gens","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Gens","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Washington, Seattle, WA","Department of Computer Science and Engineering, University of Washington, Seattle WA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Washington, Seattle, WA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Washington, Seattle WA","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015798259","display_name":"Franz Pernkopf","orcid":"https://orcid.org/0000-0002-6356-3367"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Franz Pernkopf","raw_affiliation_strings":["Signal Processing and Speech Communication Lab, Graz University of Technology, Graz, Austria"],"affiliations":[{"raw_affiliation_string":"Signal Processing and Speech Communication Lab, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018711331","display_name":"Pedro Domingos","orcid":"https://orcid.org/0000-0003-4523-5631"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pedro Domingos","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Washington, Seattle, WA","Department of Computer Science and Engineering, University of Washington, Seattle WA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Washington, Seattle, WA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Washington, Seattle WA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5057485787"],"corresponding_institution_ids":["https://openalex.org/I202276237","https://openalex.org/I4210117258","https://openalex.org/I4210166371"],"apc_list":null,"apc_paid":null,"fwci":5.3209,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.95750668,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"39","issue":"10","first_page":"2030","last_page":"2044"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9988999962806702,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9988999962806702,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9811999797821045,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9571999907493591,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.8060252070426941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.609272837638855},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.5721334218978882},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5697203278541565},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5514612197875977},{"id":"https://openalex.org/keywords/bayesian-network","display_name":"Bayesian network","score":0.5119472742080688},{"id":"https://openalex.org/keywords/probabilistic-latent-semantic-analysis","display_name":"Probabilistic latent semantic analysis","score":0.48865774273872375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.45320677757263184},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42895203828811646},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4223124384880066},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3249443769454956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3115575909614563}],"concepts":[{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.8060252070426941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.609272837638855},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.5721334218978882},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5697203278541565},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5514612197875977},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.5119472742080688},{"id":"https://openalex.org/C112933361","wikidata":"https://www.wikidata.org/wiki/Q2845258","display_name":"Probabilistic latent semantic analysis","level":2,"score":0.48865774273872375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.45320677757263184},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42895203828811646},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4223124384880066},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3249443769454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3115575909614563},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":6,"locations":[{"id":"doi:10.1109/tpami.2016.2618381","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2016.2618381","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/8024097/07748514.pdf","source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:27875213","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/27875213","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:arXiv.org:1601.06180","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.06180","pdf_url":"https://arxiv.org/pdf/1601.06180","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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2294675398","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.06180.pdf","pdf_url":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:generic.eprints.org:890619","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/890619/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1601.06180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.06180","pdf_url":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/tpami.2016.2618381","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tpami.2016.2618381","pdf_url":"https://ieeexplore.ieee.org/ielx7/34/8024097/07748514.pdf","source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6299999952316284,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1540304609","display_name":null,"funder_award_id":"P25244-N15","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2067986655","display_name":null,"funder_award_id":"FA8750-13-2-0019","funder_id":"https://openalex.org/F4320338294","funder_display_name":"Air Force Research Laboratory"},{"id":"https://openalex.org/G3430869213","display_name":null,"funder_award_id":"N00014-16-1-2697","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4953263825","display_name":null,"funder_award_id":"N00014-16-1-26","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G5501761068","display_name":null,"funder_award_id":"4-16-1-","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G7381131158","display_name":null,"funder_award_id":"P27803-N15","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338294","display_name":"Air Force Research Laboratory","ror":"https://ror.org/02e2egq70"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2294675398.pdf","grobid_xml":"https://content.openalex.org/works/W2294675398.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W181231970","https://openalex.org/W1535430927","https://openalex.org/W1562643156","https://openalex.org/W1635564296","https://openalex.org/W1748004346","https://openalex.org/W1760941220","https://openalex.org/W1832793528","https://openalex.org/W1835282959","https://openalex.org/W1862639047","https://openalex.org/W1864566053","https://openalex.org/W1986660301","https://openalex.org/W1991567646","https://openalex.org/W2040370888","https://openalex.org/W2049633694","https://openalex.org/W2064052975","https://openalex.org/W2070450685","https://openalex.org/W2101968469","https://openalex.org/W2103560185","https://openalex.org/W2105197197","https://openalex.org/W2110715012","https://openalex.org/W2119900738","https://openalex.org/W2128221272","https://openalex.org/W2141473882","https://openalex.org/W2153074847","https://openalex.org/W2159080219","https://openalex.org/W2159687189","https://openalex.org/W2166049352","https://openalex.org/W2171016142","https://openalex.org/W2196348858","https://openalex.org/W2395740735","https://openalex.org/W2399803916","https://openalex.org/W2403625461","https://openalex.org/W2952995550","https://openalex.org/W2956476286","https://openalex.org/W3099451540","https://openalex.org/W6600061378","https://openalex.org/W6632384879","https://openalex.org/W6633765838","https://openalex.org/W6637828697","https://openalex.org/W6638728745","https://openalex.org/W6639306265","https://openalex.org/W6677915450","https://openalex.org/W6679233511","https://openalex.org/W6679317373","https://openalex.org/W6680850120","https://openalex.org/W6683309385","https://openalex.org/W6684905728","https://openalex.org/W6685090696","https://openalex.org/W6686016265","https://openalex.org/W6693692838","https://openalex.org/W6711982178","https://openalex.org/W6713063833","https://openalex.org/W6718063875","https://openalex.org/W6763122330","https://openalex.org/W6765212771","https://openalex.org/W6965162379"],"related_works":["https://openalex.org/W2159687189","https://openalex.org/W2399803916","https://openalex.org/W2119900738","https://openalex.org/W2746410435","https://openalex.org/W2945431146","https://openalex.org/W2956476286","https://openalex.org/W2128744540","https://openalex.org/W3206555886","https://openalex.org/W2890896922","https://openalex.org/W2997985764","https://openalex.org/W2891425677","https://openalex.org/W2105480138","https://openalex.org/W1953055146","https://openalex.org/W2181191726","https://openalex.org/W2801058001","https://openalex.org/W2100927999","https://openalex.org/W3200863653","https://openalex.org/W2099900459","https://openalex.org/W2099808310","https://openalex.org/W2609763701"],"abstract_inverted_index":{"One":[0],"of":[1,12,32,119,126,141],"the":[2,10,30,33,44,52,57,73,83,95,100,116,120,142,148],"central":[3],"themes":[4],"in":[5,64,70,76,111,154,177,189],"Sum-Product":[6],"networks":[7],"(SPNs)":[8],"is":[9,69,166],"interpretation":[11,21,46,118,125],"sum":[13],"nodes":[14],"as":[15,61,129],"marginalized":[16],"latent":[17],"variables":[18,54],"(LVs).":[19],"This":[20],"yields":[22],"an":[23,124],"increased":[24],"syntactic":[25],"or":[26],"semantic":[27],"structure,":[28],"allows":[29],"application":[31],"EM":[34,143],"algorithm":[35,144,150],"and":[36,78,122,176,194],"to":[37,56,159,173,181],"efficiently":[38],"perform":[39],"MPE":[40,152],"inference.":[41],"In":[42],"literature,":[43],"LV":[45],"was":[47,156],"justified":[48],"by":[49,93],"explicitly":[50],"introducing":[51,99],"indicator":[53],"corresponding":[55],"LVs'":[58],"states.":[59],"However,":[60],"pointed":[62],"out":[63],"this":[65,67,91,165],"paper,":[66],"approach":[68,97],"conflict":[71],"with":[72],"completeness":[74],"condition":[75],"SPNs":[77,128],"does":[79],"not":[80],"fully":[81],"specify":[82],"probabilistic":[84,117],"model.":[85],"We":[86,107,162],"propose":[87],"a":[88,138,168],"remedy":[89],"for":[90,98,145,151],"problem":[92],"modifying":[94],"original":[96],"LVs,":[101],"which":[102],"we":[103,136],"call":[104],"SPN":[105],"augmentation.":[106],"discuss":[108],"conditional":[109],"independencies":[110],"augmented":[112,127,182],"SPNs,":[113,175],"formally":[114],"establish":[115],"sum-weights":[121],"give":[123],"Bayesian":[130],"networks.":[131],"Based":[132],"on":[133,191],"these":[134],"results,":[135],"find":[137],"sound":[139],"derivation":[140],"SPNs.":[146,183],"Furthermore,":[147],"Viterbi-style":[149],"proposed":[153],"literature":[155],"never":[157],"proven":[158],"be":[160],"correct.":[161],"show":[163],"that":[164],"indeed":[167],"correct":[169],"algorithm,":[170],"when":[171,179],"applied":[172,180],"selective":[174],"particular":[178],"Our":[184],"theoretical":[185],"results":[186],"are":[187],"confirmed":[188],"experiments":[190],"synthetic":[192],"data":[193],"103":[195],"real-world":[196],"datasets.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}