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 addresses the time-series modelling of high dimensional data. Currently, the hidden Markov model (HMM) is the most popular and successful model especially in speech recognition. However, there are well known shortcomings in HMMs particularly in the modelling of the correlation between successive observation vectors; that is, inter-frame correlation. Standard diagonal covariance matrix HMMs also lack the modelling of the spatial correlation in the feature vectors; that is, intra-frame correlation. Several other time-series models have been proposed recently especially in the segment model framework to address the inter-frame correlation problem such as Gauss-Markov and dynamical system segment models. The lack of intra-frame correlation has been compensated for with transform schemes such as semi-tied full covariance matrices (STC). All these models can be regarded as belonging to the broad class of generalised linear Gaussian models. Linear Gaussian models (LGM) are popular as many forms may be trained efficiently using the expectation maximisation algorithm. In this paper, several LGMs and generalised LGMs are reviewed. The models can be roughly categorised into four combinations according to two different state evolution and two different observation processes. The state evolution process can be based on a discrete finite state machine such as in the HMMs or a linear first-order Gauss-Markov process such as in the traditional linear dynamical systems. The observation process can be represented as a factor analysis model or a linear discriminant analysis model. General HMMs and schemes proposed to improve their performance such as STC can be regarded as special cases in this framework.

Abstract. This paper examines the applicability of some learning techniques for speech recognition, more precisely, for the classification of phonemes represented by a particular segment model. The methods compared were TiMBL (the IB1 algorithm), C4.5 (ID3 tree learning), OC1 (oblique tree learning), artificial neural nets (ANN), Gaussian mixture modeling (GMM) and, as a reference, an HMM recognizer was also trained on the same corpus. Before feeding them into the learners, the segmental features were additionally transformed using either linear discriminant analysis (LDA), principal component analysis (PCA) or independent component analysis (ICA). Each learner was tested with each transformation in order to find the best combination. Furthermore, we experimented with several feature sets such as filterbank energies, mel-frequency cepstral coefficients (MFCC) and gravity centers. We found LDA helped all the learners, in several cases quite considerably. PCA was beneficial only for some of the algorithms, while ICA improved the results quite rarely, and was bad for certain learning methods. From the learning viewpoint ANN was the most effective, and attained the same results independently of the transformation applied. GMM behaved worse, which shows the advantages of discriminative over generative learning. TiMBL produced reasonable results, while C4.5 and OC1 could not compete, no matter what transformation was tried.

Automatic continuous speech recognition (CSR) is sufficiently

The HMM assumption of conditional independence of observations causes a variety of problems for speech-recognition applications. Previous attempts to construct acoustic models that remove this assumption have suffered from a significant increase in the number of parameters to train. Another weakness of current acoustic models is that they do not account for the origin of derived features (estimated derivatives). We show how to both remove the independence assumption and properly account for derived features, with little or no increase in the number of parameters to train, by applying the principle of maximum entropy. We also show that ignoring the origins of derived features in training HMM acoustic models can lead to severe distortions of the effective language model. Evaluation of our maxent model on a simple problem cuts an already-low error rate in half compared to an equivalent HMM with the same number of parameters.

In most speech recognition systems today, all the acoustic variation associated with a phoneme is characterized in terms of the identity of its neighboring phonemes. The neighbors influence only the state observation density of a fixed Hidden Markov Model. Other sources of variation are captured implicitly by using Gaussian mixture models for the state observations. Consequently, these models can be very broad, particularly for casual spontaneous speech. In this thesis, we explore conditioning of phonemes on higher level linguistic structure, specifically syllable- and word-level structure to learn models for phonemes that are more specific to the context, reporting experimental results on a large vocabulary (35k words) conversational speech task (Switchboard). In particular, this thesis makes three main contributions related to wide context conditioning. First, we demonstrate that syllable- and word-level structure can be incorporated into current acoustic models to improve recognition accuracy over triphones. For a fixed number of parameters, these models are computationally more efficient than pentaphones, both in training and in testing. In addition, use of syllable and word features leads to a small but significant improvement in performance. The wide-contexts used in our acoustic model can implicitly capture re-syllabification effects to a certain extent. However, we find that explicitly modeling re-syllabification does not improve recognition further, because there are only a small number of phones that exhibit acoustic difference after re-syllabification. The second contribution addresses the difficulties that arise when a large number of additional conditioning features are used. As the number of conditioning features increases, the training cost can increase exponentially. Moreover, a large fraction of the training labels tends to have too few examples to have reliable statistics associated with them, and this could potentially cause decision trees to learn bad clusters. A new method has been developed for clustering with multiple stages, where each stage clusters a different subset of features, and also has a choice of using the partitions learned in the previous stages. Apart from reducing the risk of unreliable statistics, it is designed to ameliorate data fragmentation problem and is computationally less expensive. This method was successfully demonstrated with pentaphones, resulting in equivalent performance at a lower cost. Finally, a new algorithm is described to design context-specific HMMs. The idea is to model reduction of a phone for certain contexts, and to learn a more constrained topology. Using contextual information, the algorithm clusters HMM paths where each path has a different number of states. An HMM distance measure has been formulated to prune out the paths which are similar. During decoding, the paths are allocated dynamically for each sub-word unit according to their context. We investigated this algorithm to model phone topologies, finding improved characterization of speech given known word sequences but no significant improvement in word error rate.