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 bio-sequence 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) linear-Gaussian. 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 Rao-Blackwellised 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.

This paper describes the Graphical Models Toolkit (GMTK), an open source, publically available toolkit for developing graphical-model based speech recognition and general time series systems. Graphical models are a flexible, concise, and expressive probabilistic modeling framework with which one may rapidly specify a vast collection of statistical models. This paper begins with a brief description of the representational and computational aspects of the framework. Following that is a detailed description of GMTK’s features, including a language for specifying structures and probability distributions, logarithmic space exact training and decoding procedures, the concept of switching parents, and a generalized EM training method which allows arbitrary sub-Gaussian parameter tying. Taken together, these features endow GMTK with a degree of expressiveness and functionality that significantly complements other publically available packages. GMTK was recently used in the 2001 Johns Hopkins Summer Workshop, and experimental results are described in detail both herein and in a companion paper. 1.

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 information-theoretic 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 medium-vocabulary isolated-word 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...

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 language-modeling levels. A number of speech recognition techniques born directly out of the graphical-models paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov model-based 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.

Most HMM-based speech recognition systems use Gaussian mixtures as observation probability density functions. An important goal in all such systems is to improve parsimony. One method is to adjust the type of covariance matrices used. In this work, factored sparse inverse covariance matrices are introduced. Based on Í �Í factorization, the inverse covariance matrix can be represented using linear regressive coefficients which 1) correspond to sparse patterns in the inverse covariance matrix (and therefore represent conditional independence properties of the Gaussian), and 2), result in a method of partial tying of the covariance matrices without requiring non-linear EM update equations. Results show that the performance of full-covariance Gaussians can be matched by factored sparse inverse covariance Gaussians having significantly fewer parameters. 1.

In this paper, we investigate the use of dynamic Bayesian networks (DBNs) to explicitly represent models of hidden features, such as articulatory or other phonological features, for automatic speech recognition. In previous work using the idea of hidden features, the representation has typically been implicit, relying on a single hidden state to represent a combination of features. We present a class of DBN-based hidden feature models, and show that such a representation can be not only more expressive but also more parsimonious. We also describe a way of representing the acoustic observation model with fewer distributions using a product of models, each corresponding to a subset of the features. Finally, we describe our recent experiments using hidden feature models on the Aurora 2.0 corpus. 1.

Since their inception over thirty years ago, hidden Markov models (HMMs) have have become the predominant methodology for automatic speech recognition (ASR) systems — today, most state-of-the-art speech systems are HMM-based. There have been a number of ways to explain HMMs and to list their capabilities, each of these ways having both advantages and disadvantages. In an effort to better understand what HMMs can do, this tutorial analyzes HMMs by exploring a novel way in which an HMM can be defined, namely in terms of random variables and conditional independence assumptions. We prefer this definition as it allows us to reason more throughly about the capabilities of HMMs. In particular, it is possible to deduce that there are, in theory at least, no theoretical limitations to the class of probability distributions representable by HMMs. This paper concludes that, in search of a model to supersede the HMM for ASR, we should rather than trying to correct for HMM limitations in the general case, new models should be found based on their potential for better parsimony, computational requirements, and noise insensitivity.

A Hidden-Articulator Markov Model (HAMM) is a Hidden Markov Model (HMM) in which each state represents an articulatory configuration. Articulatory knowledge, known to be useful for speech recognition [4], is represented by specifying a mapping of phonemes to articulatory configurations; vocal tract dynamics are represented via transitions between articulatory configurations. In previous work [13], we extended the articulatory-feature model introduced by Erler [7] by using diphone units and a new technique for model initialization. By comparing it with a purely random model, we showed that the HAMM can take advantage of articulatory knowledge. In this paper, we extend that work in three ways. First, we decrease the number of parameters, making it comparable in size to standard HMMs. Second, we evaluate our model in noisy contexts, verifying that articulatory knowledge can provide benefits in adverse acoustic conditions. Third, we use a corpus of sideby -side speech and articulator tra...

Hidden Markov Models (HMMs) have been the state-of-the-art techniques for acoustic modeling despite their unrealistic independence assumptions and the very limited representational capacity of their hidden states. There are many proposals in the research community for deeper models that are capable of modeling the many types of variability present in the speech generation process. Deep Belief Networks (DBNs) have recently proved to be very effective for a variety of machine learning problems and this paper applies DBNs to acoustic modeling. On the standard TIMIT corpus, DBNs consistently outperform other techniques and the best DBN achieves a phone error rate (PER) of 23.0 % on the TIMIT core test set. 1

In recent years there has been growing interest in discriminative parameter training techniques, resulting from notable improvements in speech recognition performance on tasks ranging in size from digit recognition to Switchboard. Typified by Maximum Mutual Information training, these methods assume a fixed statistical modeling structure, and then optimize only the associated numerical parameters (such as means, variances, and transition matrices). In this paper, we explore the significantly different methodology of discriminative structure learning. Here, the fundamental dependency relationships between random variables in a probabilistic model are learned in a discriminative fashion, and are learned separately from the numerical parameters. In order to apply the principles of structural discriminability, we adopt the framework of graphical models, which allows an arbitrary set of variables with arbitrary conditional independence relationships to be modeled at each time frame. We present results using a new graphical modeling toolkit (described in a companion paper) from the recent 2001 Johns Hopkins Summer Workshop. These results indicate that significant gains result from discriminative structural analysis of both conventional MFCC and novel AM-FM features on the Aurora continuous digits task.