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142
Image Parsing: Unifying Segmentation, Detection, and Recognition
, 2005
"... In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation in a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The ..."
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Cited by 160 (18 self)
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In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation in a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and reconfigures it dynamically using a set of reversible Markov chain jumps. This computational framework integrates two popular inference approaches  generative (topdown) methods and discriminative (bottomup) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottomup tests/filters.
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 141 (24 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear FeynmanKac ow in distribution space. One interpretation of the FeynmanKac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.
Autocontext and its Application to Highlevel Vision Tasks
 In Proc. CVPR
"... The notion of using context information for solving highlevel vision and medical image segmentation problems has been increasingly realized in the field. However, how to learn an effective and efficient context model, together with an image appearance model, remains mostly unknown. The current lite ..."
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Cited by 84 (4 self)
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The notion of using context information for solving highlevel vision and medical image segmentation problems has been increasingly realized in the field. However, how to learn an effective and efficient context model, together with an image appearance model, remains mostly unknown. The current literature using Markov Random Fields (MRFs) and Conditional Random Fields (CRFs) often involves specific algorithm design, in which the modeling and computing stages are studied in isolation. In this paper, we propose the autocontext algorithm. Given a set of training images and their corresponding label maps, we first learn a classifier on local image patches. The discriminative probability (or classification confidence) maps created by the learned classifier are then used as context information, in addition to the original image patches, to train a new classifier. The algorithm then iterates until convergence. Autocontext integrates lowlevel and context information by fusing a large number of lowlevel appearance features with context and implicit shape information. The resulting discriminative algorithm is general and easy to implement. Under nearly the same parameter settings in training, we apply the algorithm to three challenging vision applications: foreground/background segregation, human body configuration estimation, and scene region labeling. Moreover, context also plays a very important role in medical/brain images where the anatomical structures are mostly constrained to relatively fixed positions. With only some slight changes resulting from using 3D instead of 2D features, the autocontext algorithm applied to brain MRI image segmentation is shown to outperform stateoftheart algorithms specifically designed for this domain. Furthermore, the scope of the proposed algorithm goes beyond image analysis and it has the potential to be used for a wide variety of problems in multivariate labeling.
Marginalized particle filters for mixed linear/nonlinear statespace models
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and nonGaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with th ..."
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Cited by 62 (23 self)
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Abstract—The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and nonGaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear statespace model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete highdimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported. Index Terms—Kalman filter, marginalization, navigation systems, nonlinear systems, particle filter, state estimation. I.
Audiovisual probabilistic tracking of multiple speakers in meetings
 IEEE Transactions on Audio, Speech, and Language Processing
, 2007
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Symmetry analysis of reversible markov chains
 Internet Mathematics
, 2005
"... We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend to ..."
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Cited by 33 (11 self)
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We show how to use subgroups of the symmetry group of a reversible Markov chain to give useful bounds on eigenvalues and their multiplicity. We supplement classical representation theoretic tools involving a group commuting with a selfadjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a maxdegree construction by an arbitrary amount and that, in turn, the fastest mixing Markov chain can dominate the Metropolis construction by an arbitrary amount. 1
Markov chain Monte Carlo: Can we trust the third significant figure
 University of Minnesota, School of Statistics
, 2007
"... Abstract. Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this is ..."
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Cited by 32 (14 self)
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Abstract. Current reporting of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting estimates is rarely reported. Thus we have little ability to objectively assess the quality of the reported estimates. We address this issue in that we discuss why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples.
Efficient block sampling strategies for sequential Monte Carlo
 Journal of Computational and Graphical Statistics
, 2006
"... Sequential Monte Carlo (SMC) methods are a powerful set of simulationbased techniques for sampling sequentially from a sequence of complex probability distributions. These methods rely on a combination of importance sampling and resampling techniques. In a Markov chain Monte Carlo (MCMC) framework, ..."
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Cited by 23 (5 self)
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Sequential Monte Carlo (SMC) methods are a powerful set of simulationbased techniques for sampling sequentially from a sequence of complex probability distributions. These methods rely on a combination of importance sampling and resampling techniques. In a Markov chain Monte Carlo (MCMC) framework, block sampling strategies often perform much better than algorithms based on oneatatime sampling strategies if “good ” proposal distributions to update blocks of variables can be designed. In an SMC framework, standard algorithms sequentially sample the variables one at a time whereas, like MCMC, the efficiency of algorithms could be improved significantly by using block sampling strategies. Unfortunately, a direct implementation of such strategies is impossible as it requires the knowledge of integrals which do not admit closedform expressions. This article introduces a new methodology which bypasses this problem and is a natural extension of standard SMC methods. Applications to several sequential Bayesian inference problems demonstrate these methods.
Stochastic Approximation in Monte Carlo Computation
, 2006
"... The WangLandau algorithm is an adaptive Markov chain Monte Carlo algorithm to calculate the spectral density for a physical system. A remarkable feature of the algorithm is that it is not trapped by local energy minima, which is very important for systems with rugged energy landscapes. This feature ..."
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Cited by 23 (13 self)
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The WangLandau algorithm is an adaptive Markov chain Monte Carlo algorithm to calculate the spectral density for a physical system. A remarkable feature of the algorithm is that it is not trapped by local energy minima, which is very important for systems with rugged energy landscapes. This feature has led to many successful applications of the algorithm in statistical physics and biophysics. However, there does not exist rigorous theory to support its convergence, and the estimates produced by the algorithm can only reach a limited statistical accuracy. In this paper, we propose the stochastic approximation Monte Carlo (SAMC) algorithm, which overcomes the shortcomings of the WangLandau algorithm. We establish a theorem concerning its convergence. The estimates produced by SAMC can be improved continuously as the simulation goes on. SAMC also extends applications of the WangLandau algorithm to continuum systems. The potential uses of SAMC in statistics are discussed through two classes of applications, importance sampling and model selection. The results show that SAMC can work as a general importance