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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.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
FUTURE PATHS FOR INTEGER PROGRAMMING AND LINKS TO Artificial Intelligence
, 1986
"... Scope and PurposeA summary is provided of some of the recent (and a few notsorecent) developments that otTer promise for enhancing our ability to solve combinatorial optimization problems. These developments may be usefully viewed as a synthesis of the perspectives of operations research and arti ..."
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Cited by 356 (8 self)
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Scope and PurposeA summary is provided of some of the recent (and a few notsorecent) developments that otTer promise for enhancing our ability to solve combinatorial optimization problems. These developments may be usefully viewed as a synthesis of the perspectives of operations research and artificial intelligence. Although compatible with the use of algorithmic subroutines, the frameworks examined are primarily heuristic, based on the supposition that etTective solution of complex combinatorial structures in some cases may require a level of flexibility beyond that attainable by methods with formally demonstrable convergence properties. AbstractInteger programming has benefited from many innovations in models and methods. Some of the promising directions for elaborating these innovations in the future may be viewed from a framework that links the perspectives of artificial intelligence and operations research. To demonstrate this, four key areas are examined: (1) controlled randomization, (2) learning strategies, (3) induced decomposition and (4) tabu search. Each of these is shown to have characteristics that appear usefully relevant to developments on the horizon.
Lectures on matroids and oriented matroids
, 2005
"... These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005. ..."
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Cited by 1 (0 self)
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These lecture notes were prepared for the Algebraic Combinatorics; in Europe (ACE) Summer School in Vienna, July 2005.
On tangles and matroids
 J. Knot Theory Ramifications
"... Given matroids M and N there are two operations M ⊕2 N and M ⊗ N. When M and N are the cycle matroids of planar graphs these operations have interesting interpretations on the corresponding link diagrams. In fact, given a planar graph there are two wellestablished methods of generating an alternati ..."
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Cited by 7 (1 self)
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Given matroids M and N there are two operations M ⊕2 N and M ⊗ N. When M and N are the cycle matroids of planar graphs these operations have interesting interpretations on the corresponding link diagrams. In fact, given a planar graph there are two wellestablished methods of generating
Matroid bundles
 IN NEW PERSPECTIVES IN ALGEBRAIC COMBINATORICS, MSRI BOOK SERIES
, 1999
"... Combinatorial vector bundles, or matroid bundles, are a combinatorial analog to real vector bundles. Combinatorial objects called oriented matroids play the role of real vector spaces. This combinatorial analogy is remarkably strong, and has led to combinatorial results in topology and bundletheore ..."
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Cited by 4 (1 self)
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Combinatorial vector bundles, or matroid bundles, are a combinatorial analog to real vector bundles. Combinatorial objects called oriented matroids play the role of real vector spaces. This combinatorial analogy is remarkably strong, and has led to combinatorial results in topology and bundle
Matroid Homology
"... We construct chain complexes of matroids and Lagrangian symplectic matroids analogous to Kontsevich graph homology. ..."
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We construct chain complexes of matroids and Lagrangian symplectic matroids analogous to Kontsevich graph homology.
On The Generation Of Oriented Matroids
 DISCRETE COMPUT. GEOM
, 2000
"... We provide a multiple purpose algorithm for generating oriented matroids. An application disproves a conjecture of B. Grünbaum that every closed triangulated orientable 2manifold can be embedded geometrically in R³ i.e. with flat triangles and without self intersections. We can show in particular t ..."
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Cited by 47 (7 self)
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We provide a multiple purpose algorithm for generating oriented matroids. An application disproves a conjecture of B. Grünbaum that every closed triangulated orientable 2manifold can be embedded geometrically in R³ i.e. with flat triangles and without self intersections. We can show in particular
Matroid automorphisms of . . .
, 2010
"... We study the rank4 linear matroid M(H4) associated with the 4dimensional root system H4. This root system coincides with the vertices of the 600cell, a 4dimensional regular solid. We determine the automorphism group of this matroid, showing half of the 14,400 automorphisms are geometric and ha ..."
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We study the rank4 linear matroid M(H4) associated with the 4dimensional root system H4. This root system coincides with the vertices of the 600cell, a 4dimensional regular solid. We determine the automorphism group of this matroid, showing half of the 14,400 automorphisms are geometric
Results 1  10
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