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91
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 564 (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.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 122 (18 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
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 67 (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.
Unsupervised learning of human motion
 IEEE Trans. PAMI
, 2003
"... Abstract—An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful “foreground ” features as well as feat ..."
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Cited by 66 (1 self)
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Abstract—An unsupervised learning algorithm that can obtain a probabilistic model of an object composed of a collection of parts (a moving human body in our examples) automatically from unlabeled training data is presented. The training data include both useful “foreground ” features as well as features that arise from irrelevant background clutter—the correspondence between parts and detected features is unknown. The joint probability density function of the parts is represented by a mixture of decomposable triangulated graphs which allow for fast detection. To learn the model structure as well as model parameters, an EMlike algorithm is developed where the labeling of the data (part assignments) is treated as hidden variables. The unsupervised learning technique is not limited to decomposable triangulated graphs. The efficiency and effectiveness of our algorithm is demonstrated by applying it to generate models of human motion automatically from unlabeled image sequences, and testing the learned models on a variety of sequences. Index Terms—Unsupervised learning, human motion, decomposable triangulated graph, probabilistic models, greedy search, EM algorithm, mixture models. 1
Dynamic Bayesian Multinets
, 2000
"... In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how informationtheoretic criterion functions can be used to induce spa ..."
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Cited by 59 (18 self)
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In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how informationtheoretic criterion functions can be used to induce sparse, discriminative, and classconditional network structures that yield an optimal approximation to the class posterior probability, and therefore are useful for the classification task. Using a new structure learning heuristic, the resulting models are tested on a mediumvocabulary isolatedword speech recognition task. It is demonstrated that these discriminatively structured dynamic Bayesian multinets, when trained in a maximum likelihood setting using EM, can outperform both HMMs and other dynamic Bayesian networks with a similar number of parameters. 1 Introduction While Markov chains are sometimes a useful model for sequences, such simple independence assumptions can lead...
Semisupervised Learning of Classifiers: Theory, Algorithms and Their Application to HumanComputer Interaction
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2004
"... Automatic classification is one of the basic tasks required in any pattern recognition and human computer interaction application. In this paper we discuss training probabilistic classifiers with labeled and unlabeled data. We provide a new analysis that shows under what conditions unlabeled data ..."
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Cited by 59 (15 self)
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Automatic classification is one of the basic tasks required in any pattern recognition and human computer interaction application. In this paper we discuss training probabilistic classifiers with labeled and unlabeled data. We provide a new analysis that shows under what conditions unlabeled data can be used in learning to improve classification performance. We also show that if the conditions are violated, using unlabeled data can be detrimental to classification performance. We discuss the implications of this analysis to a specific type of probabilistic classifiers, Bayesian networks, and propose a new structure learning algorithm that can utilize unlabeled data to improve classification. Finally, we show how the resulting algorithms are successfully employed in two applications related to humancomputer interaction and pattern recognition; facial expression recognition and face detection.
Human Tracking with Mixtures of Trees
, 2001
"... Treestructured probabilistic models admit simple, fast inference. However, they are not well suited to phenomena such as occlusion, where multiple components of an object may disappear simultaneously. Mixtures of trees appear to address this problem, at the cost of representing a large mixture. We ..."
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Cited by 59 (6 self)
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Treestructured probabilistic models admit simple, fast inference. However, they are not well suited to phenomena such as occlusion, where multiple components of an object may disappear simultaneously. Mixtures of trees appear to address this problem, at the cost of representing a large mixture. We demonstrate an efficient and compact representation of this mixture, which admits simple learning and inference algorithms. We use this method to build an automated tracker for Muybridge sequences of a variety of human activities. Tracking is difficult, because the temporal dependencies rule out simple inference methods. We show how to use our model for efficient inference, using a method that employs alternate spatial and temporal inference. The result is a tracker that (a) uses a very loose motion model, and so can track many different activities at a variable frame rate and (b) is entirely automatic. 1.
Thin Junction Trees
 Advances in Neural Information Processing Systems 14
, 2001
"... We present an algorithm that induces a class of models with thin junction treesmodels that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the l ..."
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Cited by 50 (1 self)
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We present an algorithm that induces a class of models with thin junction treesmodels that are characterized by an upper bound on the size of the maximal cliques of their triangulated graph. By ensuring that the junction tree is thin, inference in our models remains tractable throughout the learning process. This allows both an efficient implementation of an iterative scaling parameter estimation algorithm and also ensures that inference can be performed efficiently with the final model. We illustrate the approach with applications in handwritten digit recognition and DNA splice site detection.
Semisupervised learning of mixture models
 In Proc of the 20th Int’l Conf. on Machine Learning
, 2003
"... This paper analyzes the performance of semisupervised learning of mixture models. We show that unlabeled data can lead to an increase in classification error even in situations where additional labeled data would decrease classification error. We present a mathematical analysis of this “degradation ..."
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Cited by 40 (5 self)
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This paper analyzes the performance of semisupervised learning of mixture models. We show that unlabeled data can lead to an increase in classification error even in situations where additional labeled data would decrease classification error. We present a mathematical analysis of this “degradation ” phenomenon and show that it is due to the fact that bias may be adversely affected by unlabeled data. We discuss the impact of these theoretical results to practical situations. 1.
Unsupervised Learning of a Probabilistic Grammar for Object Detection and Parsing
 in Advances in Neural Information Processing Systems 19
, 2007
"... We introduce a Probabilistic GrammarMarkov Model (PGMM) which couples probabilistic context free grammars and Markov Random Fields. These PGMMs are generative models defined over attributed features and are used to detect and classify objects in natural images. PGMMs are designed so that they can p ..."
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Cited by 39 (11 self)
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We introduce a Probabilistic GrammarMarkov Model (PGMM) which couples probabilistic context free grammars and Markov Random Fields. These PGMMs are generative models defined over attributed features and are used to detect and classify objects in natural images. PGMMs are designed so that they can perform rapid inference, parameter learning, and the more difficult task of structure induction. PGMMs can deal with unknown 2D pose (position, orientation, and scale) in both inference and learning, different appearances, or aspects, of the model. The PGMMs can be learnt in an unsupervised manner where the image can contain one of an unknown number of objects of different categories or even be pure background. We first study the weakly supervised case, where each image contains an example of the (single) object of interest, and then generalize to less supervised cases. The goal of this paper is theoretical but, to provide proof of concept, we demonstrate results from this approach on a subset of the Caltech dataset (learning on a training set and evaluating on a testing set). Our results are generally comparable with the current state of the art, and our inference is performed in less than five seconds.