{"id":"https://openalex.org/W2120416539","doi":"https://doi.org/10.1109/tsp.2009.2036042","title":"Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure","display_name":"Gaussian Multiresolution Models: Exploiting Sparse Markov and Covariance Structure","publication_year":2009,"publication_date":"2009-11-13","ids":{"openalex":"https://openalex.org/W2120416539","doi":"https://doi.org/10.1109/tsp.2009.2036042","mag":"2120416539"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2036042","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2036042","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://resolver.caltech.edu/CaltechAUTHORS:20121008-094406124","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101677030","display_name":"Myung-Jin Choi","orcid":"https://orcid.org/0000-0002-2761-7161"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Myung Jin Choi","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110218299","display_name":"V. Chandrasekaran","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"V. Chandrasekaran","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107833743","display_name":"Alan S. Willsky","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.S. Willsky","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2649,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.89766381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"3","first_page":"1012","last_page":"1024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9941999912261963,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9941999912261963,"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/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9861000180244446,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9857000112533569,"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/covariance","display_name":"Covariance","score":0.7226461172103882},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.5161762833595276},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5126046538352966},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.48864227533340454},{"id":"https://openalex.org/keywords/graphical-model","display_name":"Graphical model","score":0.48667269945144653},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4685206115245819},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4482109248638153},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4447258710861206},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.4413701295852661},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.4393395185470581},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.423054575920105},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4166381061077118},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.4159150719642639},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3778318464756012},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17320173978805542},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.08443331718444824}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7226461172103882},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.5161762833595276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5126046538352966},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.48864227533340454},{"id":"https://openalex.org/C155846161","wikidata":"https://www.wikidata.org/wiki/Q1143367","display_name":"Graphical model","level":2,"score":0.48667269945144653},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4685206115245819},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4482109248638153},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4447258710861206},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.4413701295852661},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.4393395185470581},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.423054575920105},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4166381061077118},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.4159150719642639},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3778318464756012},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17320173978805542},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.08443331718444824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tsp.2009.2036042","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2036042","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:34744","is_oa":true,"landing_page_url":null,"pdf_url":"https://resolver.caltech.edu/CaltechAUTHORS:20121008-094406124","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.208.2935","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.2935","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mit.edu/%7Emyungjin/publications/ieeesp10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.208.875","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.875","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ssg.mit.edu/%7Ewillsky/publ_pdfs/197_pub_IEEE.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.213.133","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.213.133","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ssg.mit.edu/~venkatc/ccw_sim_preprint09.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/58956","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/58956","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:authors.library.caltech.edu:34744","is_oa":true,"landing_page_url":null,"pdf_url":"https://resolver.caltech.edu/CaltechAUTHORS:20121008-094406124","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3910096803","display_name":null,"funder_award_id":"FA9550-08-1-1080","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7093029411","display_name":null,"funder_award_id":"FA9550-06-1-0324","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320332195","display_name":"Samsung","ror":"https://ror.org/04w3jy968"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320337253","display_name":"Instituto de Ciencias del Mar y Limnolog\u00eda, Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":null},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2120416539.pdf","grobid_xml":"https://content.openalex.org/works/W2120416539.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W102368363","https://openalex.org/W1506806321","https://openalex.org/W1530872699","https://openalex.org/W1552180419","https://openalex.org/W1663973292","https://openalex.org/W1746680969","https://openalex.org/W1903968474","https://openalex.org/W1973083622","https://openalex.org/W1997542937","https://openalex.org/W2031753087","https://openalex.org/W2067529521","https://openalex.org/W2070461923","https://openalex.org/W2083206954","https://openalex.org/W2088088467","https://openalex.org/W2100236179","https://openalex.org/W2101897555","https://openalex.org/W2105986965","https://openalex.org/W2114915914","https://openalex.org/W2122327008","https://openalex.org/W2130009812","https://openalex.org/W2132555912","https://openalex.org/W2134653808","https://openalex.org/W2134929491","https://openalex.org/W2135788072","https://openalex.org/W2139549194","https://openalex.org/W2147640502","https://openalex.org/W2151590071","https://openalex.org/W2153102839","https://openalex.org/W2155543892","https://openalex.org/W2166567662","https://openalex.org/W2166866346","https://openalex.org/W2170744156","https://openalex.org/W2182510773","https://openalex.org/W2296319761","https://openalex.org/W2536620281","https://openalex.org/W2567948266","https://openalex.org/W2578040947","https://openalex.org/W2616052791","https://openalex.org/W2798909945","https://openalex.org/W2978329087","https://openalex.org/W4212863985","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W4388323202","https://openalex.org/W6604202627","https://openalex.org/W6681688880"],"related_works":["https://openalex.org/W2106257677","https://openalex.org/W2964321162","https://openalex.org/W4322716735","https://openalex.org/W1971337326","https://openalex.org/W3096432517","https://openalex.org/W2963885072","https://openalex.org/W2375962503","https://openalex.org/W4391020316","https://openalex.org/W2060696366","https://openalex.org/W2908170832"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"consider":[4],"the":[5,20,24,103,110,143],"problem":[6],"of":[7,62,148],"learning":[8,106],"Gaussian":[9,63],"multiresolution":[10],"(MR)":[11],"models":[12,35,65,157],"in":[13,66,98,138],"which":[14,67],"data":[15],"are":[16,45],"only":[17],"available":[18],"at":[19,42,69,102],"finest":[21],"scale,":[22],"and":[23,145,158],"coarser,":[25],"hidden":[26,166],"variables":[27,41,68,91],"serve":[28],"to":[29,47,84,126,135],"capture":[30],"long-distance":[31],"dependencies.":[32],"Tree-structured":[33],"MR":[34,64,155],"have":[36,72],"limited":[37],"modeling":[38,144],"capabilities,":[39],"as":[40],"one":[43],"scale":[44,71,118],"forced":[46],"be":[48],"uncorrelated":[49],"with":[50],"each":[51,70,117],"other":[52,55,79,121],"conditioned":[53,77,119],"on":[54,78,120],"scales.":[56,80,122],"We":[57,141],"propose":[58],"a":[59,86],"new":[60,129],"class":[61],"sparse":[73,107],"conditional":[74,111],"covariance":[75,112],"structure":[76,108],"Our":[81],"goal":[82],"is":[83,133],"learn":[85],"tree-structured":[87],"graphical":[88],"model":[89,124],"connecting":[90],"across":[92],"scales":[93],"(which":[94],"translates":[95],"into":[96],"sparsity":[97],"inverse":[99],"covariance),":[100],"while":[101],"same":[104],"time":[105],"for":[109],"(not":[113],"its":[114],"inverse)":[115],"within":[116],"This":[123],"leads":[125],"an":[127],"efficient,":[128],"inference":[130,146],"algorithm":[131],"that":[132,153,162],"similar":[134],"multipole":[136],"methods":[137,152,161],"computational":[139],"physics.":[140],"demonstrate":[142],"advantages":[147],"our":[149],"approach":[150],"over":[151],"use":[154,165],"tree":[156],"single-scale":[159],"approximation":[160],"do":[163],"not":[164],"variables.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}