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Dynamic Bayesian Networks: Representation, Inference and Learning
, 2002
"... Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have bee ..."
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Cited by 726 (3 self)
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Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and biosequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs
and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linearGaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data.
In particular, the main novel technical contributions of this thesis are as follows: a way of representing
Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of
applying RaoBlackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization
and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.
On Bayesian analysis of mixtures with an unknown number of components
 INSTITUTE OF INTERNATIONAL ECONOMICS PROJECT ON INTERNATIONAL COMPETITION POLICY,&QUOT; COM/DAFFE/CLP/TD(94)42
, 1997
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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 288 (47 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.
Image Segmentation by Data Driven Markov Chain Monte Carlo
, 2001
"... This paper presents a computational paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to exp ..."
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Cited by 274 (32 self)
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This paper presents a computational paradigm called Data Driven Markov Chain Monte Carlo (DDMCMC) for image segmentation in the Bayesian statistical framework. The paper contributes to image segmentation in three aspects. Firstly, it designs effective and well balanced Markov Chain dynamics to explore the solution space and makes the split and merge process reversible at a middle level vision formulation. Thus it achieves globally optimal solution independent of initial segmentations. Secondly, instead of computing a single maximum a posteriori solution, it proposes a mathematical principle for computing multiple distinct solutions to incorporates intrinsic ambiguities in image segmentation. A kadventurers algorithm is proposed for extracting distinct multiple solutions from the Markov chain sequence. Thirdly, it utilizes datadriven (bottomup) techniques, such as clustering and edge detection, to compute importance proposal probabilities, which eectively drive the Markov chain dynamics and achieve tremendous speedup in comparison to traditional jumpdiffusion method[4]. Thus DDMCMC paradigm provides a unifying framework where the role of existing segmentation algorithms, such as, edge detection, clustering, region growing, splitmerge, SNAKEs, region competition, are revealed as either realizing Markov chain dynamics or computing importance proposal probabilities. We report some results on color and grey level image segmentation in this paper and refer to a detailed report and a web site for extensive discussion.
Being Bayesian about network structure
 Machine Learning
, 2000
"... Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model sel ..."
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Cited by 270 (4 self)
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Abstract. In many multivariate domains, we are interested in analyzing the dependency structure of the underlying distribution, e.g., whether two variables are in direct interaction. We can represent dependency structures using Bayesian network models. To analyze a given data set, Bayesian model selection attempts to find the most likely (MAP) model, and uses its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have nonnegligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables. This allows us to compute, for a given order, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orders rather than over network structures. The space of orders is smaller and more regular than the space of structures, and has much a smoother posterior “landscape”. We present empirical results on synthetic and reallife datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a nonBayesian bootstrap approach.
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 lang ..."
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Cited by 227 (21 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.
The Unscented Particle Filter
, 2000
"... In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available info ..."
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Cited by 202 (9 self)
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In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.
Approaches for Bayesian variable selection
 Statistica Sinica
, 1997
"... Abstract: This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow for analytic ..."
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Cited by 202 (6 self)
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Abstract: This paper describes and compares various hierarchical mixture prior formulations of variable selection uncertainty in normal linear regression models. These include the nonconjugate SSVS formulation of George and McCulloch (1993), as well as conjugate formulations which allow for analytical simplification. Hyperparameter settings which base selection on practical significance, and the implications of using mixtures with point priors are discussed. Computational methods for posterior evaluation and exploration are considered. Rapid updating methods are seen to provide feasible methods for exhaustive evaluation using Gray Code sequencing in moderately sized problems, and fast Markov Chain Monte Carlo exploration in large problems. Estimation of normalization constants is seen to provide improved posterior estimates of individual model probabilities and the total visited probability. Various procedures are illustrated on simulated sample problems and on a real problem concerning the construction of financial index tracking portfolios.
MCMCbased particle filtering for tracking a variable number of interacting targets
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... We describe a particle filter that effectively deals with interacting targets targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, s ..."
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Cited by 191 (6 self)
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We describe a particle filter that effectively deals with interacting targets targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance sampling step in the particle filter with a novel Markov chain Monte Carlo (MCMC) sampling step to obtain a more efficient MCMCbased multitarget filter. We also show how to extend this MCMCbased filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions.