Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis
Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class...
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Veröffentlicht in: | IEEE transactions on signal processing 2008-05, Vol.56 (5), p.1916-1930 |
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creator | Chandrasekaran, V. Johnson, J.K. Willsky, A.S. |
description | Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations. |
doi_str_mv | 10.1109/TSP.2007.912280 |
format | Article |
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Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2007.912280</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Application software ; Applied sciences ; Artificial intelligence ; Computer science; control theory; systems ; Computer vision ; Convergence ; Distributed estimation ; Exact sciences and technology ; Gauss-Markov random fields ; Gaussian ; Gaussian processes ; Graphical models ; Image processing ; Image sensors ; Inference ; Inference algorithms ; Information, signal and communications theory ; Iterative methods ; Mathematical analysis ; Mathematical models ; maximum walk-sum block ; maximum walk-sum tree ; Miscellaneous ; Networks ; Pattern recognition. Digital image processing. Computational geometry ; Sensors ; Signal processing ; Signal processing algorithms ; Studies ; subgraph preconditioners ; Telecommunications and information theory ; Tree graphs ; Trees ; walk-sum diagrams ; walk-sums</subject><ispartof>IEEE transactions on signal processing, 2008-05, Vol.56 (5), p.1916-1930</ispartof><rights>2008 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2008</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c422t-72535711316910fed0957e9a0f0b7932dbd65e9b616158a54057ed22a4f849bd3</citedby><cites>FETCH-LOGICAL-c422t-72535711316910fed0957e9a0f0b7932dbd65e9b616158a54057ed22a4f849bd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4490096$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4490096$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20294742$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Chandrasekaran, V.</creatorcontrib><creatorcontrib>Johnson, J.K.</creatorcontrib><creatorcontrib>Willsky, A.S.</creatorcontrib><title>Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations.</description><subject>Algorithms</subject><subject>Application software</subject><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Computer science; control theory; systems</subject><subject>Computer vision</subject><subject>Convergence</subject><subject>Distributed estimation</subject><subject>Exact sciences and technology</subject><subject>Gauss-Markov random fields</subject><subject>Gaussian</subject><subject>Gaussian processes</subject><subject>Graphical models</subject><subject>Image processing</subject><subject>Image sensors</subject><subject>Inference</subject><subject>Inference algorithms</subject><subject>Information, signal and communications theory</subject><subject>Iterative methods</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>maximum walk-sum block</subject><subject>maximum walk-sum tree</subject><subject>Miscellaneous</subject><subject>Networks</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Sensors</subject><subject>Signal processing</subject><subject>Signal processing algorithms</subject><subject>Studies</subject><subject>subgraph preconditioners</subject><subject>Telecommunications and information theory</subject><subject>Tree graphs</subject><subject>Trees</subject><subject>walk-sum diagrams</subject><subject>walk-sums</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kbtLxEAQh4Mo-KwtbBZBrXI3-8yu3SF6CorCnY8ubJKNruaScycp_O_d48TCwmoG5psfzHxJckhhRCmY8Xz2MGIA2chQxjRsJDvUCJqCyNRm7EHyVOrsZTvZRXwHoEIYtZM8XWLvF7b3XUt8S6Z2QPQ2NsEu33xpG3LXVa5B8oi-fSXzYMveFo0js6F4XTF4Tibk2TYf6WxYkElrmy_0uJ9s1bZBd_BT95LHq8v5xXV6ez-9uZjcpqVgrE8zJrnMKOVUGQq1q8DIzBkLNRSZ4awqKiWdKRRVVGorBcRxxZgVtRamqPhecrbOXYbuc3DY5wuPpWsa27puwFxrUEJLJiJ5-i_JhWFagIng8R_wvRtCvCumKc6U4HoFjddQGTrE4Op8GeIbw1dOIV_pyKOOfKUjX-uIGyc_sRbjW-tg29Lj7xoDZkQmWOSO1px3zv2OoywAo_g3TJCQsA</recordid><startdate>20080501</startdate><enddate>20080501</enddate><creator>Chandrasekaran, V.</creator><creator>Johnson, J.K.</creator><creator>Willsky, A.S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</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>20080501</creationdate><title>Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis</title><author>Chandrasekaran, V. ; Johnson, J.K. ; Willsky, A.S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c422t-72535711316910fed0957e9a0f0b7932dbd65e9b616158a54057ed22a4f849bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Algorithms</topic><topic>Application software</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Computer vision</topic><topic>Convergence</topic><topic>Distributed estimation</topic><topic>Exact sciences and technology</topic><topic>Gauss-Markov random fields</topic><topic>Gaussian</topic><topic>Gaussian processes</topic><topic>Graphical models</topic><topic>Image processing</topic><topic>Image sensors</topic><topic>Inference</topic><topic>Inference algorithms</topic><topic>Information, signal and communications theory</topic><topic>Iterative methods</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>maximum walk-sum block</topic><topic>maximum walk-sum tree</topic><topic>Miscellaneous</topic><topic>Networks</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Sensors</topic><topic>Signal processing</topic><topic>Signal processing algorithms</topic><topic>Studies</topic><topic>subgraph preconditioners</topic><topic>Telecommunications and information theory</topic><topic>Tree graphs</topic><topic>Trees</topic><topic>walk-sum diagrams</topic><topic>walk-sums</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chandrasekaran, V.</creatorcontrib><creatorcontrib>Johnson, J.K.</creatorcontrib><creatorcontrib>Willsky, A.S.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</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 signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chandrasekaran, V.</au><au>Johnson, J.K.</au><au>Willsky, A.S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2008-05-01</date><risdate>2008</risdate><volume>56</volume><issue>5</issue><spage>1916</spage><epage>1930</epage><pages>1916-1930</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as embedded trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks ldquocomputedrdquo by the algorithms using walk-sum diagrams, and show that for iterations based on a very large and flexible set of sequences of subgraphs, convergence is guaranteed in walk-summable models. Consequently, we are free to choose spanning trees and subsets of variables adaptively at each iteration. This leads to efficient methods for optimizing the next iteration step to achieve maximum reduction in error. Simulation results demonstrate that these nonstationary algorithms provide a significant speedup in convergence over traditional one-tree and two-tree iterations.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2007.912280</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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subjects | Algorithms Application software Applied sciences Artificial intelligence Computer science control theory systems Computer vision Convergence Distributed estimation Exact sciences and technology Gauss-Markov random fields Gaussian Gaussian processes Graphical models Image processing Image sensors Inference Inference algorithms Information, signal and communications theory Iterative methods Mathematical analysis Mathematical models maximum walk-sum block maximum walk-sum tree Miscellaneous Networks Pattern recognition. Digital image processing. Computational geometry Sensors Signal processing Signal processing algorithms Studies subgraph preconditioners Telecommunications and information theory Tree graphs Trees walk-sum diagrams walk-sums |
title | Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis |
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