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137
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple computational rule, the sumproduct algorithm operates in factor graphs to computeeither exactly or approximatelyvarious marginal functions by distributed messagepassing in the graph. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sumproduct algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative "turbo" decoding algorithm, Pearl's belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform algorithms.
Loopy Belief Propagation for Approximate Inference: An Empirical Study
 In Proceedings of Uncertainty in AI
, 1999
"... Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performa ..."
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Cited by 680 (18 self)
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Recently, researchers have demonstrated that "loopy belief propagation"  the use of Pearl's polytree algorithm in a Bayesian network with loops  can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performance of "Turbo Codes"  codes whose decoding algorithm is equivalent to loopy belief propagation in a chainstructured Bayesian network. In this paper we ask: is there something special about the errorcorrecting code context, or does loopy propagation work as an approximate inference scheme in a more general setting? We compare the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two realworld networks: ALARM and QMR. We find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals. However, on the QMR network, the loopy beliefs oscillated and had no obvious relationship ...
Learning lowlevel vision
 International Journal of Computer Vision
, 2000
"... We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently prop ..."
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Cited by 586 (31 self)
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We show a learningbased method for lowlevel vision problems. We setup a Markov network of patches of the image and the underlying scene. A factorization approximation allows us to easily learn the parameters of the Markov network from synthetic examples of image/scene pairs, and to e ciently propagate image information. Monte Carlo simulations justify this approximation. We apply this to the \superresolution &quot; problem (estimating high frequency details from a lowresolution image), showing good results. For the motion estimation problem, we show resolution of the aperture problem and llingin arising from application of the same probabilistic machinery.
Turbo decoding as an instance of Pearl’s belief propagation algorithm
 IEEE Journal on Selected Areas in Communications
, 1998
"... Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pear ..."
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Cited by 420 (16 self)
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Abstract—In this paper, we will describe the close connection between the now celebrated iterative turbo decoding algorithm of Berrou et al. and an algorithm that has been well known in the artificial intelligence community for a decade, but which is relatively unknown to information theorists: Pearl’s belief propagation algorithm. We shall see that if Pearl’s algorithm is applied to the “belief network ” of a parallel concatenation of two or more codes, the turbo decoding algorithm immediately results. Unfortunately, however, this belief diagram has loops, and Pearl only proved that his algorithm works when there are no loops, so an explanation of the excellent experimental performance of turbo decoding is still lacking. However, we shall also show that Pearl’s algorithm can be used to routinely derive previously known iterative, but suboptimal, decoding algorithms for a number of other errorcontrol systems, including Gallager’s
The generalized distributive law
 Information Theory, IEEE Transactions on
"... Abstract—In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence ..."
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Cited by 364 (2 self)
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Abstract—In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. It includes as special cases the Baum–Welch algorithm, the fast Fourier transform (FFT) on any finite Abelian group, the Gallager–Tanner–Wiberg decoding algorithm, Viterbi’s algorithm, the BCJR algorithm, Pearl’s “belief propagation ” algorithm, the Shafer–Shenoy probability propagation algorithm, and the turbo decoding algorithm. Although this algorithm is guaranteed to give exact answers only in certain cases (the “junction tree ” condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting that it often works approximately even when it is not supposed to. Index Terms—Belief propagation, distributive law, graphical models, junction trees, turbo codes. I.
Correctness of Local Probability Propagation in Graphical Models with Loops
, 2000
"... This article analyzes the behavior of local propagation rules in graphical models with a loop. ..."
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Cited by 231 (9 self)
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This article analyzes the behavior of local propagation rules in graphical models with a loop.
Regular and Irregular Progressive EdgeGrowth Tanner Graphs
 IEEE TRANS. INFORM. THEORY
, 2003
"... We propose a general method for constructing Tanner graphs having a large girth by progressively establishing edges or connections between symbol and check nodes in an edgebyedge manner, called progressive edgegrowth (PEG) construction. Lower bounds on the girth of PEG Tanner graphs and on the mi ..."
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Cited by 192 (0 self)
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We propose a general method for constructing Tanner graphs having a large girth by progressively establishing edges or connections between symbol and check nodes in an edgebyedge manner, called progressive edgegrowth (PEG) construction. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting lowdensity paritycheck (LDPC) codes are derived in terms of parameters of the graphs. The PEG construction attains essentially the same girth as Gallager's explicit construction for regular graphs, both of which meet or exceed the ErdosSachs bound. Asymptotic analysis of a relaxed version of the PEG construction is presented. We describe an empirical approach using a variant of the "downhill simplex" search algorithm to design irregular PEG graphs for short codes with fewer than a thousand of bits, complementing the design approach of "density evolution" for larger codes. Encoding of LDPC codes based on the PEG construction is also investigated. We show how to exploit the PEG principle to obtain LDPC codes that allow linear time encoding. We also investigate regular and irregular LDPC codes using PEG Tanner graphs but allowing the symbol nodes to take values over GF(q), q > 2. Analysis and simulation demonstrate that one can obtain better performance with increasing field size, which contrasts with previous observations.
Lowdensity paritycheck codes based on finite geometries: A rediscovery and new results
 IEEE Trans. Inform. Theory
, 2001
"... This paper presents a geometric approach to the construction of lowdensity paritycheck (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and thei ..."
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Cited by 182 (7 self)
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This paper presents a geometric approach to the construction of lowdensity paritycheck (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner graphs have girth T. Finitegeometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasicyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finitegeometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finitegeometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Collective classification in network data
, 2008
"... Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification te ..."
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Cited by 174 (33 self)
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Numerous realworld applications produce networked data such as web data (hypertext documents connected via hyperlinks) and communication networks (people connected via communication links). A recent focus in machine learning research has been to extend traditional machine learning classification techniques to classify nodes in such data. In this report, we attempt to provide a brief introduction to this area of research and how it has progressed during the past decade. We introduce four of the most widely used inference algorithms for classifying networked data and empirically compare them on both synthetic and realworld data.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 154 (19 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden