Result: MAP estimation via agreement on trees : Message-passing and linear programming

Title:
MAP estimation via agreement on trees : Message-passing and linear programming
Authors:
WAINWRIGHT, Martin J, JAAKKOLA, Tommi S, WILLSKY, Alan S
Source:
IEEE transactions on information theory. 51(11):3697-3717
Publisher Information:
New York, NY: Institute of Electrical and Electronics Engineers, 2005.
Publication Year:
2005
Physical Description:
print, 47 ref
Original Material:
INIST-CNRS
Subject Terms:
Telecommunications, Télécommunications, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Théorie de l'information, du signal et des communications, Information, signal and communications theory, Théorie du signal et des communications, Signal and communications theory, Codage, codes, Coding, codes, Algorithme, Algorithm, Algoritmo, Approche probabiliste, Probabilistic approach, Enfoque probabilista, Champ aléatoire, Random field, Campo aleatorio, Cycle graphe, Cycle(graph), Ciclo diagrama, Décodage itératif, Iterative decoding, Envoi message, Message passing, Estimation a posteriori, A posteriori estimation, Estimación a posteriori, Modèle Markov, Markov model, Modelo Markov, Méthode calcul, Computing method, Método cálculo, Méthode minimax, Minimax method, Método minimax, Polytope, Politope, Probabilité a posteriori, Posterior probability, Probabilidad a posteriori, Problème maximin, Maximin problem, Problema maximin, Programmation en nombres entiers, Integer programming, Programación entera, Programmation linéaire, Linear programming, Programación lineal, Relaxation, Relajación, Structure arborescente, Tree structure, Estructura arborescente, Approximate inference, Markov random fields, integer programming, iterative decoding, linear programming (LP) relaxation, marginal polytope, max-product algorithm, maximum a posteriori probability (MAP) estimation, message-passing algorithms, min-sum algorithm
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Electrical Engineering and Computer Science and the Department of Statistics, University of California, Berkeley, Berkeley, CA 94720, United States
Department of Electrical En gineering and Computer Science, the Massachusetts Institute of Technology, Cambridge, MA 02139, United States
ISSN:
0018-9448
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17238678
Rights:
Copyright 2005 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Telecommunications and information theory
Accession Number:
edscal.17238678
Database:
PASCAL Archive

Further Information

We develop and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: a) a tree-relaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds; and b) a tree-reweighted max-product message-passing algorithm that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the mode-finding problem and a reweighted form of the max-product (min-sum) message-passing algorithm.