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Local Algorithms for Approximate Inference in MinorExcluded Graphs
"... We present a new local approximation algorithm for computing MAP and logpartition function for arbitrary exponential family distribution represented by a finitevalued pairwise Markov random field (MRF), say G. Our algorithm is based on decomposing G into appropriately chosen small components; comp ..."
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Cited by 5 (3 self)
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are examples of such graphs. The running time of the algorithm is Θ(n) (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minorexcluded graphs uses the decomposition scheme
Local Algorithms for Approximate Inference in MinorExcluded Graphs Anonymous Author(s) Affiliation
"... Address email We present a new local approximation algorithm for computing MAP and logpartition function for arbitrary exponential family distribution represented by a finitevalued pairwise Markov random field (MRF), say G. Our algorithm is based on decomposing G into appropriately chosen small co ..."
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degree are examples of such graphs. The running time of the algorithm is Θ(n) (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minorexcluded graphs uses
Local Algorithms for Approximate Inference in MinorExcluded Graphs Anonymous Author(s) Affiliation
"... Address email We present a new local approximation algorithm for computing MAP and logpartition function for arbitrary exponential family distribution represented by a finitevalued pairwise Markov random field (MRF), say G. Our algorithm is based on decomposingG into appropriately chosen small com ..."
Abstract
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degree are examples of such graphs. The running time of the algorithm is Θ(n) (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minorexcluded graphs uses
Local Algorithms for Approximate Inference in MinorExcluded Graphs Anonymous Author(s) Affiliation
"... Address email We present a new local approximation algorithm for computing MAP and logpartition function for arbitrary exponential family distribution represented by a finitevalued pairwise Markov random field (MRF), say G. Our algorithm is based on decomposing G into appropriately chosen small co ..."
Abstract
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degree are examples of such graphs. The running time of the algorithm is Θ(n) (n is the number of nodes in G), with constant dependent on accuracy, degree of graph and size of the graph that is excluded as a minor (constant for Planar graphs). Our algorithm for minorexcluded graphs uses
The Thickness of a MinorExcluded Class of Graphs
 DISCRETE MATH
, 1998
"... The thickness problem on graphs is NPhard and only few results concerning this graph invariant are known. Using a decomposition theorem of Truemper, we show that the thickness of the class of graphs without G 12  minors is less than or equal to two (and therefore, the same is true for the more wel ..."
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Cited by 5 (0 self)
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The thickness problem on graphs is NPhard and only few results concerning this graph invariant are known. Using a decomposition theorem of Truemper, we show that the thickness of the class of graphs without G 12  minors is less than or equal to two (and therefore, the same is true for the more
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations
, 2005
"... How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include hea ..."
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Cited by 534 (48 self)
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How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include
A Survey of Program Slicing Techniques
 JOURNAL OF PROGRAMMING LANGUAGES
, 1995
"... A program slice consists of the parts of a program that (potentially) affect the values computed at some point of interest, referred to as a slicing criterion. The task of computing program slices is called program slicing. The original definition of a program slice was presented by Weiser in 197 ..."
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Cited by 777 (8 self)
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A program slice consists of the parts of a program that (potentially) affect the values computed at some point of interest, referred to as a slicing criterion. The task of computing program slices is called program slicing. The original definition of a program slice was presented by Weiser in 1979. Since then, various slightly different notions of program slices have been proposed, as well as a number of methods to compute them. An important distinction is that between a static and a dynamic slice. The former notion is computed without making assumptions regarding a program's input, whereas the latter relies on some specific test case. Procedures, arbitrary control flow, composite datatypes and pointers, and interprocess communication each require a specific solution. We classify static and dynamic slicing methods for each of these features, and compare their accuracy and efficiency. Moreover, the possibilities for combining solutions for different features are investigated....
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing likelihoods, marginal probabilities and most probable configurations. We describe how a wide varietyof algorithms — among them sumproduct, cluster variational methods, expectationpropagation, mean field methods, maxproduct and linear programming relaxation, as well as conic programming relaxations — can all be understood in terms of exact or approximate forms of these variational representations. The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in largescale statistical models.
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