Results 1  10
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268
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 579 (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.
Independent Factor Analysis
 Neural Computation
, 1999
"... We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square no ..."
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Cited by 225 (9 self)
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We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing, but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a twostep procedure. In the first step, the source densities, mixing matrix and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectationmaximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of Gaussians, thus all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear ...
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 179 (2 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.
Variational Inference for Bayesian Mixtures of Factor Analysers
 In Advances in Neural Information Processing Systems 12
, 2000
"... We present an algorithm that infers the model structure of a mixture of factor analysers using an ecient and deterministic variational approximation to full Bayesian integration over model parameters. This procedure can automatically determine the optimal number of components and the local dimension ..."
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Cited by 151 (16 self)
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We present an algorithm that infers the model structure of a mixture of factor analysers using an ecient and deterministic variational approximation to full Bayesian integration over model parameters. This procedure can automatically determine the optimal number of components and the local dimensionality of each component (i.e. the number of factors in each factor analyser). Alternatively it can be used to infer posterior distributions over number of components and dimensionalities. Since all parameters are integrated out the method is not prone to over tting. Using a stochastic procedure for adding components it is possible to perform the variational optimisation incrementally and to avoid local maxima. Results show that the method works very well in practice and correctly infers the number and dimensionality of nontrivial synthetic examples. By importance sampling from the variational approximation we show how to obtain unbiased estimates of the true evidence, the exa...
Variational learning for switching statespace models
 Neural Computation
, 1998
"... We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Ma ..."
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Cited by 145 (6 self)
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We introduce a new statistical model for time series which iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time series models  hidden Markov models and linear dynamical systems  and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs et al., 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact Expectation Maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log likelihood and makes use of both the forwardbackward recursions for hidden Markov models and the Kalman lter recursions for linear dynamical systems. We tested the algorithm both on artificial data sets and on a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching statespace models.
On Tempo Tracking: Tempogram Representation and Kalman Filtering
, 2000
"... We formulate tempo tracking in a Bayesian framework where a tempo tracker is modeled as a stochastic dynamical system. The tempo is modeled as a hidden state variable of the system and is estimated by a Kalman filter. The Kalman filter operates on a Tempogram, a waveletlike multiscale expansion ..."
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Cited by 79 (8 self)
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We formulate tempo tracking in a Bayesian framework where a tempo tracker is modeled as a stochastic dynamical system. The tempo is modeled as a hidden state variable of the system and is estimated by a Kalman filter. The Kalman filter operates on a Tempogram, a waveletlike multiscale expansion of a real performance. An important advantage of our approach is that it is possible to formulate both offline or realtime algorithms. The simulation results on a systematically collected set of MIDI piano performances of Yesterday and Michelle by the Beatles shows accurate tracking of approximately %90 of the beats.
Variational principal components
 In Proceedings Ninth International Conference on Artificial Neural Networks, ICANN’99
, 1999
"... One of the central issues in the use of principal component analysis (PCA) for data modelling is that of choosing the appropriate number of retained components. This problem was recently addressed through the formulation of a Bayesian treatment of PCA (Bishop, 1999a) in terms of a probabilistic late ..."
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Cited by 76 (5 self)
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One of the central issues in the use of principal component analysis (PCA) for data modelling is that of choosing the appropriate number of retained components. This problem was recently addressed through the formulation of a Bayesian treatment of PCA (Bishop, 1999a) in terms of a probabilistic latent variable model. A central feature of this approach is that the effective dimensionality of the latent space (equivalent to the number of retained principal components) is determined automatically as part of the Bayesian inference procedure. In common with most nontrivial Bayesian models, however, the required marginalizations are analytically intractable, and so an approximation scheme based on a local Gaussian representation of the posterior distribution was employed. In this paper we develop an alternative, variational formulation of Bayesian PCA, based on a factorial representation of the posterior distribution. This approach is computationally efficient, and unlike other approximation schemes, it maximizes a rigorous lower bound on the marginal log probability of the observed data. 1
Graphical models and automatic speech recognition
 Mathematical Foundations of Speech and Language Processing
, 2003
"... Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recog ..."
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Cited by 68 (13 self)
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Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recognition techniques commonly used as part of a speech recognition system can be described by a graph – this includes Gaussian distributions, mixture models, decision trees, factor analysis, principle component analysis, linear discriminant analysis, and hidden Markov models. Moreover, this paper shows that many advanced models for speech recognition and language processing can also be simply described by a graph, including many at the acoustic, pronunciation, and languagemodeling levels. A number of speech recognition techniques born directly out of the graphicalmodels paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov modelbased speech recognition by improving structural discriminability. It also includes an example where a graph can be used to represent language model smoothing constraints. As will be seen, the space of models describable by a graph is quite large. A thorough exploration of this space should yield techniques that ultimately will supersede the hidden Markov model.
Clustering binary data streams with Kmeans
 in Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery (DMKD ’03
, 2003
"... ..."
Modeling, clustering, and segmenting video with mixtures of dynamic textures
 PAMI
, 2008
"... A dynamic texture is a spatiotemporal generative model for video, which represents video sequences as observations from a linear dynamical system. This work studies the mixture of dynamic textures, a statistical model for an ensemble of video sequences that is sampled from a finite collection of v ..."
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Cited by 45 (13 self)
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A dynamic texture is a spatiotemporal generative model for video, which represents video sequences as observations from a linear dynamical system. This work studies the mixture of dynamic textures, a statistical model for an ensemble of video sequences that is sampled from a finite collection of visual processes, each of which is a dynamic texture. An expectationmaximization (EM) algorithm is derived for learning the parameters of the model, and the model is related to previous works in linear systems, machine learning, timeseries clustering, control theory, and computer vision. Through experimentation, it is shown that the mixture of dynamic textures is a suitable representation for both the appearance and dynamics of a variety of visual processes that have traditionally been challenging for computer vision (for example, fire, steam, water, vehicle and pedestrian traffic, and so forth). When compared with stateoftheart methods in motion segmentation, including both temporal texture methods and traditional representations (for example, optical flow or other localized motion representations), the mixture of dynamic textures achieves superior performance in the problems of clustering and segmenting video of such processes.