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
Hauptverfasser: Chandrasekaran, V., Johnson, J.K., Willsky, A.S.
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container_end_page 1930
container_issue 5
container_start_page 1916
container_title IEEE transactions on signal processing
container_volume 56
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
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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. 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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><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. 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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 &amp; 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 &amp; 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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ispartof IEEE transactions on signal processing, 2008-05, Vol.56 (5), p.1916-1930
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1941-0476
language eng
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source IEEE Electronic Library (IEL)
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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