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29
A New Class of Upper Bounds on the Log Partition Function
 In Uncertainty in Artificial Intelligence
, 2002
"... Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis [11, 5, 4]. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distribution ..."
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Cited by 154 (27 self)
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Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis [11, 5, 4]. We introduce a new class of upper bounds on the log partition function, based on convex combinations of distributions in the exponential domain, that is applicable to an arbitrary undirected graphical model. In the special case of convex combinations of treestructured distributions, we obtain a family of variational problems, similar to the Bethe free energy, but distinguished by the following desirable properties: (i) they are convex, and have a unique global minimum; and (ii) the global minimum gives an upper bound on the log partition function. The global minimum is defined by stationary conditions very similar to those defining xed points of belief propagation (BP) or treebased reparameterization [see 13, 14]. As with BP fixed points, the elements of the minimizing argument can be used as approximations to the marginals of the original model. The analysis described here can be extended to structures of higher treewidth (e.g., hypertrees), thereby making connections with more advanced approximations (e.g., Kikuchi and variants [15, 10]).
Dynamic Conditional Random Fields: Factorized Probabilistic Models for Labeling and Segmenting Sequence Data
 IN ICML
, 2004
"... In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain cond ..."
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Cited by 121 (11 self)
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In sequence modeling, we often wish to represent complex interaction between labels, such as when performing multiple, cascaded labeling tasks on the same sequence, or when longrange dependencies exist. We present dynamic conditional random fields (DCRFs), a generalization of linearchain conditional random fields (CRFs) in which each time slice contains a set of state variables and edgesa distributed state representation as in dynamic Bayesian networks (DBNs)and parameters are tied across slices. Since exact
MAP estimation via agreement on (hyper)trees: Messagepassing and linear programming approaches
 IEEE Transactions on Information Theory
, 2002
"... We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original ..."
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Cited by 106 (11 self)
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We develop an approach for computing provably exact maximum a posteriori (MAP) configurations for a subclass of problems on graphs with cycles. By decomposing the original problem into a convex combination of treestructured problems, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is met with equality if and only if the tree problems share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original problem. Next we present and analyze two methods for attempting to obtain tight upper bounds: (a) a treereweighted messagepassing algorithm that is related to but distinct from the maxproduct (minsum) algorithm; and (b) a treerelaxed linear program (LP), which is derived from the Lagrangian dual of the upper bounds. Finally, we discuss the conditions that govern when the relaxation is tight, in which case the MAP configuration can be obtained. The analysis described here generalizes naturally to convex combinations of hypertreestructured distributions.
TreeBased Reparameterization Framework for Analysis of Belief Propagation and Related Algorithms
, 2001
"... We present a treebased reparameterization framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This class includes the belief propagation or sumproduct algorithm [39, 36], as well as a rich set of variations and ext ..."
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Cited by 101 (21 self)
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We present a treebased reparameterization framework that provides a new conceptual view of a large class of algorithms for computing approximate marginals in graphs with cycles. This class includes the belief propagation or sumproduct algorithm [39, 36], as well as a rich set of variations and extensions of belief propagation. Algorithms in this class can be formulated as a sequence of reparameterization updates, each of which entails refactorizing a portion of the distribution corresponding to an acyclic subgraph (i.e., a tree). The ultimate goal is to obtain an alternative but equivalent factorization using functions that represent (exact or approximate) marginal distributions on cliques of the graph. Our framework highlights an important property of BP and the entire class of reparameterization algorithms: the distribution on the full graph is not changed. The perspective of treebased updates gives rise to a simple and intuitive characterization of the fixed points in terms of tree consistency. We develop interpretations of these results in terms of information geometry. The invariance of the distribution, in conjunction with the fixed point characterization, enables us to derive an exact relation between the exact marginals on an arbitrary graph with cycles, and the approximations provided by belief propagation, and more broadly, any algorithm that minimizes the Bethe free energy. We also develop bounds on this approximation error, which illuminate the conditions that govern their accuracy. Finally, we show how the reparameterization perspective extends naturally to more structured approximations (e.g., Kikuchi and variants [52, 37]) that operate over higher order cliques.
Tree Consistency and Bounds on the Performance of the MaxProduct Algorithm and Its Generalizations
, 2002
"... Finding the maximum a posteriori (MAP) assignment of a discretestate distribution specified by a graphical model requires solving an integer program. The maxproduct algorithm, also known as the maxplus or minsum algorithm, is an iterative method for (approximately) solving such a problem on gr ..."
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Cited by 55 (5 self)
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Finding the maximum a posteriori (MAP) assignment of a discretestate distribution specified by a graphical model requires solving an integer program. The maxproduct algorithm, also known as the maxplus or minsum algorithm, is an iterative method for (approximately) solving such a problem on graphs with cycles.
Treereweighted belief propagation algorithms and approximate ML estimation by pseudomoment matching
 In AISTATS
, 2003
"... In previous work [10], we presented a class of upper bounds on the log partition function of an arbitrary undirected graphical model based on solving a convex variational problem. Here we develop a class of local messagepassing algorithms, which we call treereweighted belief propagation, for ..."
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Cited by 51 (4 self)
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In previous work [10], we presented a class of upper bounds on the log partition function of an arbitrary undirected graphical model based on solving a convex variational problem. Here we develop a class of local messagepassing algorithms, which we call treereweighted belief propagation, for ef ciently computing the value of these upper bounds, as well as the associated pseudomarginals.
Graphical models and point pattern matching
 IEEE Trans. PAMI
, 2006
"... Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless c ..."
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Cited by 30 (5 self)
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Abstract—This paper describes a novel solution to the rigid point pattern matching problem in Euclidean spaces of any dimension. Although we assume rigid motion, jitter is allowed. We present a noniterative, polynomial time algorithm that is guaranteed to find an optimal solution for the noiseless case. First, we model point pattern matching as a weighted graph matching problem, where weights correspond to Euclidean distances between nodes. We then formulate graph matching as a problem of finding a maximum probability configuration in a graphical model. By using graph rigidity arguments, we prove that a sparse graphical model yields equivalent results to the fully connected model in the noiseless case. This allows us to obtain an algorithm that runs in polynomial time and is provably optimal for exact matching between noiseless point sets. For inexact matching, we can still apply the same algorithm to find approximately optimal solutions. Experimental results obtained by our approach show improvements in accuracy over current methods, particularly when matching patterns of different sizes. Index Terms—Point pattern matching, graph matching, graphical models, Markov random fields, junction tree algorithm. 1
Semidefinite Relaxations for Approximate Inference on Graphs With Cycles
, 2003
"... We present a new method for calculating approximate marginals for probability distributions defined by graphs with cycles, based on a Gaussian entropy bound combined with a semidefinite outer bound on the marginal polytope. This combination leads to a logdeterminant maximization problem that can ..."
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Cited by 14 (3 self)
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We present a new method for calculating approximate marginals for probability distributions defined by graphs with cycles, based on a Gaussian entropy bound combined with a semidefinite outer bound on the marginal polytope. This combination leads to a logdeterminant maximization problem that can be solved by efficient interior point methods [13]. As with the Bethe approximation and its generalizations [18], the optimizing arguments of this problem can be taken as approximations to the exact marginals. In contrast to Bethe/Kikuchi approaches, our variational problem is strictly convex and so has a unique global optimum. An additional desirable feature is that the value of the optimal solution is guaranteed to provide an upper bound on the log partition function. Such upper bounds are of interest in their own right (e.g., for parameter estimation, large deviations exponents, combinatorial enumeration). Finally, we show that taking the zerotemperature limit of our logdeterminant relaxation recovers a class of wellknown semidefinite relaxations for integer programming [e.g., 6].
Autonomous exploration and mapping of abandoned mines
 IEEE ROBOTICS AND AUTOMATION MAGAZINE
, 2004
"... Abandoned mines pose significant threats to society, yet a large fraction of them lack accurate maps. This article discusses the software architecture of an autonomous robotic system designed to explore and map abandoned mines. We have built a robot capable of autonomously exploring abandoned mines. ..."
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Cited by 13 (0 self)
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Abandoned mines pose significant threats to society, yet a large fraction of them lack accurate maps. This article discusses the software architecture of an autonomous robotic system designed to explore and map abandoned mines. We have built a robot capable of autonomously exploring abandoned mines. A new set of software tools is presented, enabling robots to acquire maps of unprecedented size and accuracy. On May 30, 2003, our robot “Groundhog” successfully explored and mapped a main corridor of the abandoned Mathies mine near Courtney, PA. The article also discusses some of the challenges that arise in the subterraneans environments, and some the difficulties of building truly autonomous robots.
An Autonomous Robotic System for Mapping Abandoned Mines
 Proceedings of Conference on Neural Information Processing Systems (NIPS
, 2003
"... We present the software architecture of a robotic system for mapping abandoned mines. The software is capable of acquiring consistent 2D maps of large mines with many cycles, represented as Markov random fields. 3D Cspace maps are acquired from local 3D range scans, which are used to identify n ..."
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Cited by 12 (6 self)
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We present the software architecture of a robotic system for mapping abandoned mines. The software is capable of acquiring consistent 2D maps of large mines with many cycles, represented as Markov random fields. 3D Cspace maps are acquired from local 3D range scans, which are used to identify navigable paths using A* search. Our system has been deployed in three abandoned mines, two of which inaccessible to people, where it has acquired maps of unprecedented detail and accuracy.