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833
An Improved Particle Filter for Nonlinear Problems
, 2004
"... The Kalman filter provides an effective solution to the linearGaussian filtering problem. However, where there is nonlinearity, either in the model specification or the observation process, other methods are required. We consider methods known generically as particle filters, which include the c ..."
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Cited by 268 (10 self)
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The Kalman filter provides an effective solution to the linearGaussian filtering problem. However, where there is nonlinearity, either in the model specification or the observation process, other methods are required. We consider methods known generically as particle filters, which include the condensation algorithm and the Bayesian bootstrap or sampling importance resampling (SIR) filter. These filters
Annealed importance sampling
 In Statistics and Computing
, 2001
"... Abstract. Simulated annealing — moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions — has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain t ..."
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Cited by 262 (5 self)
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Abstract. Simulated annealing — moving from a tractable distribution to a distribution of interest via a sequence of intermediate distributions — has traditionally been used as an inexact method of handling isolated modes in Markov chain samplers. Here, it is shown how one can use the Markov chain transitions for such an annealing sequence to define an importance sampler. The Markov chain aspect allows this method to perform acceptably even for highdimensional problems, where finding good importance sampling distributions would otherwise be very difficult, while the use of importance weights ensures that the estimates found converge to the correct values as the number of annealing runs increases. This annealed importance sampling procedure resembles the second half of the previouslystudied tempered transitions, and can be seen as a generalization of a recentlyproposed variant of sequential importance sampling. It is also related to thermodynamic integration methods for estimating ratios of normalizing constants. Annealed importance sampling is most attractive when isolated modes are present, or when estimates of normalizing constants are required, but it may also be more generally useful, since its independent sampling allows one to bypass some of the problems of assessing convergence and autocorrelation in Markov chain samplers. 1
The Bayes Net Toolbox for MATLAB
 Computing Science and Statistics
, 2001
"... The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the ..."
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Cited by 243 (1 self)
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The Bayes Net Toolbox (BNT) is an opensource Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a highlevel, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.
Particle Filters for Positioning, Navigation and Tracking
, 2002
"... A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the part ..."
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Cited by 212 (23 self)
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A framework for positioning, navigation and tracking problems using particle filters (sequential Monte Carlo methods) is developed. It consists of a class of motion models and a general nonlinear measurement equation in position. A general algorithm is presented, which is parsimonious with the particle dimension. It is based on marginalization, enabling a Kalman filter to estimate all position derivatives, and the particle filter becomes lowdimensional. This is of utmost importance for highperformance realtime applications. Automotive and airborne applications illustrate numerically the advantage over classical Kalman filter based algorithms. Here the use of nonlinear models and nonGaussian noise is the main explanation for the improvement in accuracy. More specifically, we describe how the technique of map matching is used to match an aircraft's elevation profile to a digital elevation map, and a car's horizontal driven path to a street map. In both cases, realtime implementations are available, and tests have shown that the accuracy in both cases is comparable to satellite navigation (as GPS), but with higher integrity. Based on simulations, we also argue how the particle filter can be used for positioning based on cellular phone measurements, for integrated navigation in aircraft, and for target tracking in aircraft and cars. Finally, the particle filter enables a promising solution to the combined task of navigation and tracking, with possible application to airborne hunting and collision avoidance systems in cars.
Dependency networks for inference, collaborative filtering, and data visualization
 Journal of Machine Learning Research
"... We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of ..."
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Cited by 207 (11 self)
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We describe a graphical model for probabilistic relationshipsan alternative tothe Bayesian networkcalled a dependency network. The graph of a dependency network, unlike aBayesian network, is potentially cyclic. The probability component of a dependency network, like aBayesian network, is a set of conditional distributions, one for each nodegiven its parents. We identify several basic properties of this representation and describe a computationally e cient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative ltering (the task of predicting preferences), and the visualization of acausal predictive relationships.
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 204 (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.
Statistical algorithms for models in state space using SsfPack 2.2
 Econometrics Journal
, 1999
"... Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download an ..."
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Cited by 200 (35 self)
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Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download and print one copy of any publication from the public portal for the purpose of private study or research? You may not further distribute the material or use it for any profitmaking activity or commercial gain? You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 12. mei. 2016 Econometrics Journal (1998), volume 1, pp. 1{55. Statistical algorithms for models in state space
Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables
 Machine Learning
, 1997
"... We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MD ..."
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Cited by 195 (12 self)
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We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naiveBayes models having a hidden root node, we find that (1) the BIC/MDL measure is the least accurate, having a bias in favor of simple models, and (2) the Draper and CS measures are the most accurate. 1
General state space Markov chains and MCMC algorithm
 PROBABILITY SURVEYS
, 2004
"... This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform e ..."
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Cited by 190 (38 self)
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This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for MetropolisHastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.
RNA secondary structure prediction using stochastic contextfree grammars and evolutionary history
, 1999
"... Motivation: Many computerized methods for RNA secondary structure prediction have been developed. Few of these methods, however, employ an evolutionary model, thus relevant information is often left out from the structure determination. This paper introduces a method which incorporates evolutionary ..."
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Cited by 179 (15 self)
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Motivation: Many computerized methods for RNA secondary structure prediction have been developed. Few of these methods, however, employ an evolutionary model, thus relevant information is often left out from the structure determination. This paper introduces a method which incorporates evolutionary history into RNA secondary structure prediction. The method reported here is based on stochastic contextfree grammars (SCFGs) to give a prior probability distribution of structures.