Results 1  10
of
302
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 ..."
Abstract

Cited by 800 (26 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 1108 (51 self)
 Add to MetaCart
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.
The Matroid Median Problem
"... In the classical kmedian problem, we are given a metric space and would like to openk centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper, we consider the following generalization of the problem: instead of opening at mo ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
is in fact integral; the integrality proof is based on a connection to matroid intersection. We also consider the penalty version (alternately, the socalled prize collecting version) of the matroid median problem and obtain a constant factor approximation algorithm for it. Finally, we look at the Knapsack
What is a matroid?
, 2007
"... Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which th ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which
Visibility Graphs and Oriented Matroids
, 2002
"... We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon whos ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon
CIRCUIT AND COCIRCUIT PARTITIONS OF BINARY MATROIDS
, 2003
"... This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DMLCZ: The Czech Digital ..."
Abstract
 Add to MetaCart
This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DMLCZ: The Czech Digital
Linear Programming: Foundations and Extensions
, 1996
"... under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. ISBN 0000000000 The text for this book was formated in Time ..."
Abstract

Cited by 196 (0 self)
 Add to MetaCart
under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. ISBN 0000000000 The text for this book was formated in TimesRoman and the mathematics was formated in Michael Spivak’s Mathtimes using AMSL ATEX(which is a macro package for Leslie Lamport’s L ATEX, which itself is a macro package for Donald Knuth’s TEXtext formatting system) and converted from deviceindependent to postscript format using DVIPS. The figures were produced using SHOWCASE on a Silicon Graphics, Inc. workstation and were incorporated into the text as encapsulated postscript files with the macro package called PSFIG.TEX. To my parents, Howard and Marilyn, my dear wife, Krisadee, and the babes, Marisa and Diana Contents
Combinatorial Commutative Algebra
, 2004
"... The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geo ..."
Abstract

Cited by 125 (5 self)
 Add to MetaCart
The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic
Results 1  10
of
302