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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
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
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combin ..."
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Cited by 423 (37 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Matroids
, 2009
"... One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses a ..."
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One of the primary goals of pure mathematics is to identify common patterns that occur in disparate circumstances, and to create unifying abstractions which identify commonalities and provide a useful framework for further theorems. For example the pattern of an associative operation with inverses
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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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
The excluded minors for nearregular matroids
, 2009
"... In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7, ..."
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Cited by 7 (6 self)
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In unpublished work, Geelen proved that a matroid is nearregular if and only if it has no minor isomorphic to U2,5, U3,5, F7, F ∗ 7,
Matchings, Matroids and Submodular Functions
, 2008
"... This thesis focuses on three fundamental problems in combinatorial optimization: nonbipartite matching, matroid intersection, and submodular function minimization. We develop simple, efficient, randomized algorithms for the first two problems, and prove new lower bounds for the last two problems. F ..."
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Cited by 1 (0 self)
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. For the matching problem, we give an algorithm for constructing perfect or maximum cardinality matchings in nonbipartite graphs. Our algorithm requires O(n ω) time in graphs with n vertices, where ω < 2.38 is the matrix multiplication exponent. This algorithm achieves the bestknown running time for dense
Connected rigidity matroids and unique realizations of graphs
, 2003
"... A ddimensional framework is a straight line embedding of a graph G in R d. We shall only consider generic frameworks, in which the coordinates of all the vertices of G are algebraically independent. Two frameworks for G are equivalent if corresponding edges in the two frameworks have the same le ..."
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Cited by 102 (13 self)
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graph as a 2dimensional generic framework is a unique realization. Our proof is based on a new inductive characterization of 3connected graphs whose rigidity matroid is connected.
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