Bayesian nonparametric priors for hidden Markov random fields

One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate numbe...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Statistics and computing 2020-07, Vol.30 (4), p.1015-1035
Hauptverfasser: Lü, Hongliang, Arbel, Julyan, Forbes, Florence
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 1035
container_issue 4
container_start_page 1015
container_title Statistics and computing
container_volume 30
creator Lü, Hongliang
Arbel, Julyan
Forbes, Florence
description One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modeling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP–MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modeling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.
doi_str_mv 10.1007/s11222-020-09935-9
format Article
fullrecord <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02163046v3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2409875125</sourcerecordid><originalsourceid>FETCH-LOGICAL-c397t-af3b6685136f242d753f8f7bf67adc50040461bfa95ffd8ef9edc8d265e36153</originalsourceid><addsrcrecordid>eNp9kE1PAyEQhonRxFr9A55IPHlAB1hgOXiojV9JjZfeCV3Abm2XCm2T_nupa_TmaZLJ8z6ZeRG6pHBDAdRtppQxRoABAa25IPoIDahQnFCuxDEagJZAOFXVKTrLeQFAqeTVAN3d273Pre1wF7u1TXblN6lt8Dq1MWUcYsLz1jnf4VebPuIOJ9u5uMKh9UuXz9FJsMvsL37mEE0fH6bjZzJ5e3oZjyak4VptiA18JmUtKJeBVcwpwUMd1CxIZV0jACqoJJ0Fq0UIrvZBe9fUjknhuaSCD9F1r53bpSmXrWzam2hb8zyamMMOWPmmOHa8sFc9u07xc-vzxiziNnXlOsMq0LUSlB2MrKeaFHNOPvxqKZhDo6ZvtJjBfDdqdAnxPpQL3L379Kf-J_UFHtp3vQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2409875125</pqid></control><display><type>article</type><title>Bayesian nonparametric priors for hidden Markov random fields</title><source>SpringerLink Journals - AutoHoldings</source><creator>Lü, Hongliang ; Arbel, Julyan ; Forbes, Florence</creator><creatorcontrib>Lü, Hongliang ; Arbel, Julyan ; Forbes, Florence</creatorcontrib><description>One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modeling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP–MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modeling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.</description><identifier>ISSN: 0960-3174</identifier><identifier>EISSN: 1573-1375</identifier><identifier>DOI: 10.1007/s11222-020-09935-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Artificial Intelligence ; Bayesian analysis ; Clustering ; Dependence ; Fields (mathematics) ; Image segmentation ; Machine learning ; Markov analysis ; Mathematics ; Mathematics and Statistics ; Modelling ; Nonparametric statistics ; Probability and Statistics in Computer Science ; Statistical Theory and Methods ; Statistics ; Statistics and Computing/Statistics Programs</subject><ispartof>Statistics and computing, 2020-07, Vol.30 (4), p.1015-1035</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c397t-af3b6685136f242d753f8f7bf67adc50040461bfa95ffd8ef9edc8d265e36153</citedby><cites>FETCH-LOGICAL-c397t-af3b6685136f242d753f8f7bf67adc50040461bfa95ffd8ef9edc8d265e36153</cites><orcidid>0000-0002-2525-4416 ; 0000-0003-3639-0226</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11222-020-09935-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11222-020-09935-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27923,27924,41487,42556,51318</link.rule.ids><backlink>$$Uhttps://hal.science/hal-02163046$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Lü, Hongliang</creatorcontrib><creatorcontrib>Arbel, Julyan</creatorcontrib><creatorcontrib>Forbes, Florence</creatorcontrib><title>Bayesian nonparametric priors for hidden Markov random fields</title><title>Statistics and computing</title><addtitle>Stat Comput</addtitle><description>One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modeling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP–MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modeling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.</description><subject>Algorithms</subject><subject>Artificial Intelligence</subject><subject>Bayesian analysis</subject><subject>Clustering</subject><subject>Dependence</subject><subject>Fields (mathematics)</subject><subject>Image segmentation</subject><subject>Machine learning</subject><subject>Markov analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Modelling</subject><subject>Nonparametric statistics</subject><subject>Probability and Statistics in Computer Science</subject><subject>Statistical Theory and Methods</subject><subject>Statistics</subject><subject>Statistics and Computing/Statistics Programs</subject><issn>0960-3174</issn><issn>1573-1375</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1PAyEQhonRxFr9A55IPHlAB1hgOXiojV9JjZfeCV3Abm2XCm2T_nupa_TmaZLJ8z6ZeRG6pHBDAdRtppQxRoABAa25IPoIDahQnFCuxDEagJZAOFXVKTrLeQFAqeTVAN3d273Pre1wF7u1TXblN6lt8Dq1MWUcYsLz1jnf4VebPuIOJ9u5uMKh9UuXz9FJsMvsL37mEE0fH6bjZzJ5e3oZjyak4VptiA18JmUtKJeBVcwpwUMd1CxIZV0jACqoJJ0Fq0UIrvZBe9fUjknhuaSCD9F1r53bpSmXrWzam2hb8zyamMMOWPmmOHa8sFc9u07xc-vzxiziNnXlOsMq0LUSlB2MrKeaFHNOPvxqKZhDo6ZvtJjBfDdqdAnxPpQL3L379Kf-J_UFHtp3vQ</recordid><startdate>20200701</startdate><enddate>20200701</enddate><creator>Lü, Hongliang</creator><creator>Arbel, Julyan</creator><creator>Forbes, Florence</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag (Germany)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-2525-4416</orcidid><orcidid>https://orcid.org/0000-0003-3639-0226</orcidid></search><sort><creationdate>20200701</creationdate><title>Bayesian nonparametric priors for hidden Markov random fields</title><author>Lü, Hongliang ; Arbel, Julyan ; Forbes, Florence</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c397t-af3b6685136f242d753f8f7bf67adc50040461bfa95ffd8ef9edc8d265e36153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algorithms</topic><topic>Artificial Intelligence</topic><topic>Bayesian analysis</topic><topic>Clustering</topic><topic>Dependence</topic><topic>Fields (mathematics)</topic><topic>Image segmentation</topic><topic>Machine learning</topic><topic>Markov analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Modelling</topic><topic>Nonparametric statistics</topic><topic>Probability and Statistics in Computer Science</topic><topic>Statistical Theory and Methods</topic><topic>Statistics</topic><topic>Statistics and Computing/Statistics Programs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lü, Hongliang</creatorcontrib><creatorcontrib>Arbel, Julyan</creatorcontrib><creatorcontrib>Forbes, Florence</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Statistics and computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lü, Hongliang</au><au>Arbel, Julyan</au><au>Forbes, Florence</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bayesian nonparametric priors for hidden Markov random fields</atitle><jtitle>Statistics and computing</jtitle><stitle>Stat Comput</stitle><date>2020-07-01</date><risdate>2020</risdate><volume>30</volume><issue>4</issue><spage>1015</spage><epage>1035</epage><pages>1015-1035</pages><issn>0960-3174</issn><eissn>1573-1375</eissn><abstract>One of the central issues in statistics and machine learning is how to select an adequate model that can automatically adapt its complexity to the observed data. In the present paper, we focus on the issue of determining the structure of clustered data, both in terms of finding the appropriate number of clusters and of modeling the right dependence structure between the observations. Bayesian nonparametric (BNP) models, which do not impose an upper limit on the number of clusters, are appropriate to avoid the required guess on the number of clusters but have been mainly developed for independent data. In contrast, Markov random fields (MRF) have been extensively used to model dependencies in a tractable manner but usually reduce to finite cluster numbers when clustering tasks are addressed. Our main contribution is to propose a general scheme to design tractable BNP–MRF priors that combine both features: no commitment to an arbitrary number of clusters and a dependence modeling. A key ingredient in this construction is the availability of a stick-breaking representation which has the threefold advantage to allowing us to extend standard discrete MRFs to infinite state space, to design a tractable estimation algorithm using variational approximation and to derive theoretical properties on the predictive distribution and the number of clusters of the proposed model. This approach is illustrated on a challenging natural image segmentation task for which it shows good performance with respect to the literature.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11222-020-09935-9</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0002-2525-4416</orcidid><orcidid>https://orcid.org/0000-0003-3639-0226</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0960-3174
ispartof Statistics and computing, 2020-07, Vol.30 (4), p.1015-1035
issn 0960-3174
1573-1375
language eng
recordid cdi_hal_primary_oai_HAL_hal_02163046v3
source SpringerLink Journals - AutoHoldings
subjects Algorithms
Artificial Intelligence
Bayesian analysis
Clustering
Dependence
Fields (mathematics)
Image segmentation
Machine learning
Markov analysis
Mathematics
Mathematics and Statistics
Modelling
Nonparametric statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
title Bayesian nonparametric priors for hidden Markov random fields
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T22%3A33%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bayesian%20nonparametric%20priors%20for%20hidden%20Markov%20random%20fields&rft.jtitle=Statistics%20and%20computing&rft.au=L%C3%BC,%20Hongliang&rft.date=2020-07-01&rft.volume=30&rft.issue=4&rft.spage=1015&rft.epage=1035&rft.pages=1015-1035&rft.issn=0960-3174&rft.eissn=1573-1375&rft_id=info:doi/10.1007/s11222-020-09935-9&rft_dat=%3Cproquest_hal_p%3E2409875125%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2409875125&rft_id=info:pmid/&rfr_iscdi=true