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 re-configures it dynamically using a set of reversible Markov chain jumps. This computational framework integrates two popular inference approaches -- generative (top-down) methods and discriminative (bottom-up) 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 bottom-up tests/filters.

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 Feynman-Kac ow in distribution space. One interpretation of the Feynman-Kac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard Metropolis-Hastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.

The notion of using context information for solving high-level 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 auto-context 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. Auto-context integrates low-level and context information by fusing a large number of low-level 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 auto-context algorithm applied to brain MRI image segmentation is shown to outperform state-of-the-art 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 multi-variate labeling.

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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 self-adjoint operator with criteria for an eigenvector to descend to an orbit graph. As examples, we show that the Metropolis construction can dominate a max-degree construction by an arbitrary amount and that, in turn, the fastest mixing Markov chain can dominate the Metropolis construction by an arbitrary amount. 1

The Wang-Landau 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 algo-rithm 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 Wang-Landau 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 Wang-Landau 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 sampling algorithm and a

Sequential Monte Carlo (SMC) methods are a powerful set of simulation-based 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 one-at-a-time 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 closed-form 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.

We study the problem of counting and randomly sampling binary contingency tables. For given row and column sums, we are interested in approximately counting (or sampling) 0/1 n×m matrices with the specified row/column sums. We present a simulated annealing algorithm with running time O((nm) 2 D 3 dmax log 5 (n + m)) for any row/column sums where D is the number of non-zero entries and dmax is the maximum row/column sum. In the worst case, the running time of the algorithm is O(n 11 log 5 n) for an n × n matrix. This is the first algorithm to directly solve binary contingency tables for all row/column sums. Previous work reduced the problem to the permanent, or restricted attention to row/column sums that are close to regular. The interesting aspect of our simulated annealing algorithm is that it starts at a non-trivial instance, whose solution relies on the existence of short alternating paths in the graph constructed by a particular Greedy algorithm. 1

Tracking speakers in multiparty conversations constitutes a fundamental task for automatic meeting analysis. In this paper, we present a probabilistic approach to jointly track the location and speaking activity of multiple speakers in a multisensor meeting room, equipped with a small microphone array and multiple uncalibrated cameras. Our framework is based on a mixed-state dynamic graphical model defined on a multiperson state-space, which includes the explicit definition of a proximity-based interaction model. The model integrates audio-visual (AV) data through a novel observation model. Audio observations are derived from a source localization algorithm. Visual observations are based on models of the shape and spatial structure of human heads. Approximate inference in our model, needed given its complexity, is performed with a Markov Chain Monte Carlo particle filter (MCMC-PF), which results in high sampling efficiency. We present results-based on an objective evaluation procedurethat show that our framework (1) is capable of locating and tracking the position and speaking activity of multiple meeting participants engaged in real conversations with good accuracy; (2) can deal with cases of visual clutter and partial occlusion; and (3) significantly outperforms a traditional sampling-based approach.