Factor graphs and the sum-product algorithm
Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph th...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory 2001-02, Vol.47 (2), p.498-519 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 519 |
|---|---|
| container_issue | 2 |
| container_start_page | 498 |
| container_title | IEEE transactions on information theory |
| container_volume | 47 |
| creator | Kschischang, F.R. Frey, B.J. Loeliger, H.-A. |
| description | Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms. |
| doi_str_mv | 10.1109/18.910572 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_proquest_journals_195872864</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>910572</ieee_id><sourcerecordid>70393279</sourcerecordid><originalsourceid>FETCH-LOGICAL-c403t-dfeedcb9a3aa5eb9ac689e2aa4d2c98959db7181c77dcd1ae3f51b06f24aa5a73</originalsourceid><addsrcrecordid>eNp90DtPwzAQAGALgUQpDKxMEQMCoRSfY8f2iCpeUiUWmC3XvrSpkqbYycC_x1UqBgam0-m-O90dIZdAZwBUP4CaaaBCsiMyASFkrkvBj8mEUlC55lydkrMYNynlAtiE3D9b13chWwW7W8fMbn3WrzGLQ5vvQucH12e2WXWh7tftOTmpbBPx4hCn5PP56WP-mi_eX97mj4vccVr0ua8QvVtqW1grMEVXKo3MWu6Z00oL7ZcSFDgpvfNgsagELGlZMZ4arCym5Gacmzb4GjD2pq2jw6axW-yGaJhiutCCJXj7L4RSAhOcyT29_kM33RC26QwDWijJVMkTuhuRC12MASuzC3Vrw7cBavbvNaDM-N5kr0ZbI-KvOxR_AID0c-I</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>195872864</pqid></control><display><type>article</type><title>Factor graphs and the sum-product algorithm</title><source>IEEE Electronic Library (IEL)</source><creator>Kschischang, F.R. ; Frey, B.J. ; Loeliger, H.-A.</creator><creatorcontrib>Kschischang, F.R. ; Frey, B.J. ; Loeliger, H.-A.</creatorcontrib><description>Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/18.910572</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithms ; Artificial intelligence ; Fourier transforms ; Graph theory ; Graphs ; Information theory ; Markov analysis ; Mathematical analysis ; Mathematical models ; Networks</subject><ispartof>IEEE transactions on information theory, 2001-02, Vol.47 (2), p.498-519</ispartof><rights>Copyright Institute of Electrical and Electronics Engineers, Inc. (IEEE) Feb 2001</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-dfeedcb9a3aa5eb9ac689e2aa4d2c98959db7181c77dcd1ae3f51b06f24aa5a73</citedby><cites>FETCH-LOGICAL-c403t-dfeedcb9a3aa5eb9ac689e2aa4d2c98959db7181c77dcd1ae3f51b06f24aa5a73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/910572$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/910572$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Kschischang, F.R.</creatorcontrib><creatorcontrib>Frey, B.J.</creatorcontrib><creatorcontrib>Loeliger, H.-A.</creatorcontrib><title>Factor graphs and the sum-product algorithm</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.</description><subject>Algorithms</subject><subject>Artificial intelligence</subject><subject>Fourier transforms</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Information theory</subject><subject>Markov analysis</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Networks</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp90DtPwzAQAGALgUQpDKxMEQMCoRSfY8f2iCpeUiUWmC3XvrSpkqbYycC_x1UqBgam0-m-O90dIZdAZwBUP4CaaaBCsiMyASFkrkvBj8mEUlC55lydkrMYNynlAtiE3D9b13chWwW7W8fMbn3WrzGLQ5vvQucH12e2WXWh7tftOTmpbBPx4hCn5PP56WP-mi_eX97mj4vccVr0ua8QvVtqW1grMEVXKo3MWu6Z00oL7ZcSFDgpvfNgsagELGlZMZ4arCym5Gacmzb4GjD2pq2jw6axW-yGaJhiutCCJXj7L4RSAhOcyT29_kM33RC26QwDWijJVMkTuhuRC12MASuzC3Vrw7cBavbvNaDM-N5kr0ZbI-KvOxR_AID0c-I</recordid><startdate>20010201</startdate><enddate>20010201</enddate><creator>Kschischang, F.R.</creator><creator>Frey, B.J.</creator><creator>Loeliger, H.-A.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20010201</creationdate><title>Factor graphs and the sum-product algorithm</title><author>Kschischang, F.R. ; Frey, B.J. ; Loeliger, H.-A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-dfeedcb9a3aa5eb9ac689e2aa4d2c98959db7181c77dcd1ae3f51b06f24aa5a73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Algorithms</topic><topic>Artificial intelligence</topic><topic>Fourier transforms</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Information theory</topic><topic>Markov analysis</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Networks</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kschischang, F.R.</creatorcontrib><creatorcontrib>Frey, B.J.</creatorcontrib><creatorcontrib>Loeliger, H.-A.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kschischang, F.R.</au><au>Frey, B.J.</au><au>Loeliger, H.-A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Factor graphs and the sum-product algorithm</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2001-02-01</date><risdate>2001</risdate><volume>47</volume><issue>2</issue><spage>498</spage><epage>519</epage><pages>498-519</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of "local" functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/18.910572</doi><tpages>22</tpages></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 2001-02, Vol.47 (2), p.498-519 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_proquest_journals_195872864 |
| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Artificial intelligence Fourier transforms Graph theory Graphs Information theory Markov analysis Mathematical analysis Mathematical models Networks |
| title | Factor graphs and the sum-product algorithm |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T04%3A17%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Factor%20graphs%20and%20the%20sum-product%20algorithm&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Kschischang,%20F.R.&rft.date=2001-02-01&rft.volume=47&rft.issue=2&rft.spage=498&rft.epage=519&rft.pages=498-519&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/18.910572&rft_dat=%3Cproquest_RIE%3E70393279%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=195872864&rft_id=info:pmid/&rft_ieee_id=910572&rfr_iscdi=true |