Results 1  10
of
32
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 ..."
Abstract

Cited by 122 (11 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 107 (11 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 102 (22 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 55 (5 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 51 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 31 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
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 e#cient 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. ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
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.
Robust distributed estimation using the embedded subgraphs algorithm
 IEEE Trans. Signal Process
, 2006
"... Abstract—We propose a new iterative, distributed approach for linear minimum meansquareerror (LMMSE) estimation in graphical models with cycles. The embedded subgraphs algorithm (ESA) decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel b ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
Abstract—We propose a new iterative, distributed approach for linear minimum meansquareerror (LMMSE) estimation in graphical models with cycles. The embedded subgraphs algorithm (ESA) decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block Jacobi iteration comprising local LMMSE estimation in each subgraph (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and subgraphs. Our primary application is sensor networks, where the model encodes the correlation structure of the sensor measurements, which are assumed to be Gaussian. The resulting LMMSE estimation problem involves a large matrix inverse, which must be solved innetwork with distributed computation and minimal intersensor communication. By invoking the theory of asynchronous iterations, we prove that ESA is robust to temporary communication faults such as failing links and sleeping nodes, and enjoys guaranteed convergence under relatively mild conditions. Simulation studies demonstrate that ESA compares favorably with other recently proposed algorithms for distributed estimation. Simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, sensor network energy conservation strategies such as lowpowered transmission and aggressive sleep schedules could actually prove counterproductive. Our results can be replicated using MATLAB code from www.dsp.rice.edu/software. Index Terms—Asynchronous iterations, distributed estimation, graphical models, matrix splitting, sensor networks, Wiener filter. I.