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168
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 598 (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.
A Unifying Review of Linear Gaussian Models
, 1999
"... Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observa ..."
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Cited by 277 (18 self)
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Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model. We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models.
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 148 (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.
Learning Dynamic Bayesian Networks
 In Adaptive Processing of Sequences and Data Structures, Lecture Notes in Artificial Intelligence
, 1998
"... Suppose we wish to build a model of data from a finite sequence of ordered observations, {Y1, Y2,..., Yt}. In most realistic scenarios, from modeling stock prices to physiological data, the observations are not related deterministically. Furthermore, there is added uncertainty resulting from the li ..."
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Cited by 142 (0 self)
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Suppose we wish to build a model of data from a finite sequence of ordered observations, {Y1, Y2,..., Yt}. In most realistic scenarios, from modeling stock prices to physiological data, the observations are not related deterministically. Furthermore, there is added uncertainty resulting from the limited size of our data set and any mismatch between our model and the true process. Probability theory provides a powerful tool for expressing both randomness and uncertainty in our model [23]. We can express the uncertainty in our prediction of the future outcome Yt+l via a probability density P(Yt+llY1,..., Yt). Such a probability density can then be used to make point predictions, define error bars, or make decisions that are expected to minimize some loss function. This chapter presents a probabilistic framework for learning models of temporal data. We express these models using the Bayesian network formalism (a.k.a. probabilistic graphical models or belief networks)a marriage of probability theory and graph theory in which dependencies between variables are expressed graphically. The graph not only allows the user to understand which variables
Machine recognition of human activities: A survey
, 2008
"... The past decade has witnessed a rapid proliferation of video cameras in all walks of life and has resulted in a tremendous explosion of video content. Several applications such as contentbased video annotation and retrieval, highlight extraction and video summarization require recognition of the a ..."
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Cited by 116 (0 self)
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The past decade has witnessed a rapid proliferation of video cameras in all walks of life and has resulted in a tremendous explosion of video content. Several applications such as contentbased video annotation and retrieval, highlight extraction and video summarization require recognition of the activities occurring in the video. The analysis of human activities in videos is an area with increasingly important consequences from security and surveillance to entertainment and personal archiving. Several challenges at various levels of processing—robustness against errors in lowlevel processing, view and rateinvariant representations at midlevel processing and semantic representation of human activities at higher level processing—make this problem hard to solve. In this review paper, we present a comprehensive survey of efforts in the past couple of decades to address the problems of representation, recognition, and learning of human activities from video and related applications. We discuss the problem at two major levels of complexity: 1) “actions ” and 2) “activities. ” “Actions ” are characterized by simple motion patterns typically executed by a single human. “Activities ” are more complex and involve coordinated actions among a small number of humans. We will discuss several approaches and classify them according to their ability to handle varying degrees of complexity as interpreted above. We begin with a discussion of approaches to model the simplest of action classes known as atomic or primitive actions that do not require sophisticated dynamical modeling. Then, methods to model actions with more complex dynamics are discussed. The discussion then leads naturally to methods for higher level representation of complex activities.
Gaussian process dynamical models for human motion
 IEEE Trans. Pattern Anal. Machine Intell
, 2007
"... Abstract—We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from highdimensional motion capture data. A GPDM is a latent variable model. It comprises a lowdimensional latent space with associated d ..."
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Cited by 103 (5 self)
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Abstract—We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from highdimensional motion capture data. A GPDM is a latent variable model. It comprises a lowdimensional latent space with associated dynamics, as well as a map from the latent space to an observation space. We marginalize out the model parameters in closed form by using Gaussian process priors for both the dynamical and the observation mappings. This results in a nonparametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach and compare four learning algorithms on human motion capture data, in which each pose is 50dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces. Index Terms—Machine learning, motion, tracking, animation, stochastic processes, time series analysis. 1
Markovian Models for Sequential Data
, 1996
"... Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We firs ..."
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Cited by 94 (2 self)
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Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many machine learning applications, especially for speech recognition. Furthermore, in the last few years, many new and promising probabilistic models related to HMMs have been proposed. We first summarize the basics of HMMs, and then review several recent related learning algorithms and extensions of HMMs, including in particular hybrids of HMMs with artificial neural networks, InputOutput HMMs (which are conditional HMMs using neural networks to compute probabilities), weighted transducers, variablelength Markov models and Markov switching statespace models. Finally, we discuss some of the challenges of future research in this very active area. 1 Introduction Hidden Markov Models (HMMs) are statistical models of sequential data that have been used successfully in many applications in artificial intelligence, pattern recognition, speech recognition, and modeling of biological ...
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 82 (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.
Switching Kalman Filters
, 1998
"... We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results ..."
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Cited by 61 (2 self)
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We show how many different variants of Switching Kalman Filter models can be represented in a unified way, leading to a single, generalpurpose inference algorithm. We then show how to find approximate Maximum Likelihood Estimates of the parameters using the EM algorithm, extending previous results on learning using EM in the nonswitching case [DRO93, GH96a] and in the switching, but fully observed, case [Ham90]. 1 Introduction Dynamical systems are often assumed to be linear and subject to Gaussian noise. This model, called the Linear Dynamical System (LDS) model, can be defined as x t = A t x t\Gamma1 + v t y t = C t x t +w t where x t is the hidden state variable at time t, y t is the observation at time t, and v t ¸ N(0; Q t ) and w t ¸ N(0; R t ) are independent Gaussian noise sources. Typically the parameters of the model \Theta = f(A t ; C t ; Q t ; R t )g are assumed to be timeinvariant, so that they can be estimated from data using e.g., EM [GH96a]. One of the main adva...