{"id":"https://openalex.org/W7095304666","doi":null,"title":"Exploring Compositional High Order Pattern Potentials for Structured Output Learning Supplementary Material","display_name":"Exploring Compositional High Order Pattern Potentials for Structured Output Learning Supplementary Material","publication_year":2013,"publication_date":"2013-07-15","ids":{"openalex":"https://openalex.org/W7095304666"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.295.7069","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.7069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~yujiali/papers/cvpr13_sup.pdf","raw_type":"text"},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Yujia Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yujia Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081231468","display_name":"Daniel Tarlow","orcid":"https://orcid.org/0009-0009-4304-6395","observed_orcids":["https://orcid.org/0009-0009-4304-6395"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Tarlow","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026085036","display_name":"Rich Zemel","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Zemel","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43704132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.4975999891757965,"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":0.4975999891757965,"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/T10320","display_name":"Neural Networks and Applications","score":0.1656000018119812,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.07620000094175339,"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":[{"id":"https://openalex.org/keywords/restricted-boltzmann-machine","display_name":"restricted Boltzmann machine","score":0.9520000219345093},{"id":"https://openalex.org/keywords/structured-prediction","display_name":"structured prediction","score":0.8849999904632568},{"id":"https://openalex.org/keywords/equivalence-proof","display_name":"equivalence proof","score":0.49799999594688416},{"id":"https://openalex.org/keywords/variable-transformation","display_name":"change of variables","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6121000051498413},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5562999844551086},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.520799994468689},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.4943000078201294},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.4641000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45829999446868896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43529999256134033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42419999837875366},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4056999981403351},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C2985264313","wikidata":"https://www.wikidata.org/wiki/Q378859","display_name":"Pattern analysis","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.295.7069","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.7069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/~yujiali/papers/cvpr13_sup.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7095514212","https://openalex.org/W7099725367","https://openalex.org/W3170560415","https://openalex.org/W4391942287","https://openalex.org/W2803350078","https://openalex.org/W7095852869","https://openalex.org/W2294157169","https://openalex.org/W1526146785","https://openalex.org/W2972210078","https://openalex.org/W2018168021"],"abstract_inverted_index":{"This":[0],"section":[1],"provides":[2],"the":[3,7,19,37,73,106,123],"detailed":[4],"proof":[5,20],"of":[6,18,39,52],"equivalence":[8],"between":[9],"pattern":[10,40,75,94,110,127],"potentials":[11,41,76],"and":[12,55,68],"RBMs.":[13,78],"The":[14],"high":[15,63],"level":[16],"idea":[17],"is":[21,114],"to":[22,59,77,93],"treat":[23],"each":[24],"hidden":[25,87,102,119],"variable":[26,53],"in":[27,46,81,89],"an":[28],"RBM":[29],"as":[30],"encoding":[31],"a":[32,48,115],"pattern.":[33],"We":[34,79],"first":[35],"introduce":[36],"definition":[38],"by":[42],"Rother":[43],"et":[44],"al.":[45],"[2],":[47],"few":[49],"necessary":[50],"change":[51],"tricks,":[54],"two":[56],"different":[57],"ways":[58],"compose":[60],"more":[61],"general":[62],"order":[64],"potentials,":[65],"\u201csum":[66,107],"\u201d":[67,108,125],"\u201cmin\u201d.":[69],"Then":[70],"we":[71,104,121,132],"relates":[72],"composite":[74,109,126],"show":[80],"Section":[82,130],"1.2":[83],"that":[84],"minimizing":[85],"out":[86],"variables":[88],"RBMs":[90],"are":[91,98],"equivalent":[92],"potentials.":[95,128],"When":[96],"there":[97,113],"no":[99],"constraints":[100],"on":[101,118],"variables,":[103,120],"recover":[105,122],"potentials;":[111],"when":[112],"1-of-J":[116],"constraint":[117],"\u201cmin":[124],"In":[129],"1.3,":[131]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-27T00:00:00"}
