We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence.

A modification is described to the use of mean field approximations in the E step of EM algorithms for analysing data from latent structure models, as described by Ghahramani (1995), among others. The modification involves second-order Taylor approximations to expectations computed in the E step. The potential benefits of the method are illustrated using very simple latent profile models.

We propose and analyze an algorithm that approximates solutions to the problem of optimal stopping in a discounted irreducible aperiodic Markov chain. The scheme involves the use of linear combinations of fixed basis functions to approximate a Q-function. The weights of the linear combination are incrementally updated through an iterative process similar to Q-Iearning, involving simulation of the underlying Markov chain. Due to space limitations, we only provide an overview of a proof of convergence (with probability 1) and bounds on the approximation error. This is the first theoretical result that establishes the soundness of a Q-Iearninglike algorithm when combined with arbitrary linear function approximators to solve a sequential decision problem.

We present new results about the temporal-difference learning algorithm, as applied to approximating the cost-to-go function of a Markov chain using linear function approximators. The algorithm we analyze performs online updating of a parameter vector during a single endless trajectory of an aperiodic irreducible finite state Markov chain. Results include convergence (with probability 1), a characterization of the limit of convergence, and a bound on the resulting approximation error. In addition to establishing new and stronger results than those previously available, our analysis is based on a new line of reasoning that provides new intuition about the dynamics of temporal-difference learning. Furthermore, we discuss the implications of two counterexamples with regards to the Significance of online updating and linearly parameterized function approximators. 1 INTRODUCTION The problem of predicting the expected long-term future cost (or reward) of a stochastic dynamic system manifests itself in both time-series prediction and control.

This paper presents a new approach to speech recognition with hybrid HMM/ANN technology. While the standard approach to hybrid HMMI ANN systems is based on the use of neural networks as posterior probability estimators, the new approach is based on the use of mutual information neural networks trained with a special learning algorithm in order to maximize the mutual information between the input classes of the network and its resulting sequence of firing output neurons during training. It is shown in this paper that such a neural network is an optimal neural vector quantizer for a discrete hidden Markov model system trained on Maximum Likelihood principles. One of the main advantages of this approach is the fact, that such neural networks can be easily combined with HMM's of any complexity with context-dependent capabilities. It is shown that the resulting hybrid system achieves very high recognition rates, which are now already on the same level as the best conventional HMM systems with continuous parameters, and the capabilities of the mutual information neural networks are not yet entirely exploited.

Humans use visual as well as auditory speech signals to recognize spoken words. A variety of systems have been investigated for performing this task. The main purpose of this research was to systematically compare the performance of a range of dynamic visual features on a speechreading task. We have found that normalization of images to eliminate variation due to translation, scale, and planar rotation yielded substantial improvements in generalization performance regardless of the visual representation used. In addition, the dynamic information in the difference between successive frames yielded better performance than optical-flow based approaches, and compression by local low-pass filtering worked surprisingly better than global principal components analysis (PCA). These results are examined and possible explanations are explored.

We describe the implementation of a hidden Markov model state decoding system, a component for a wordspotting speech recognition system. The key specification for this state decoder design is microwatt power dissipation; this requirement led to a continuoustime, analog circuit implementation. We characterize the operation of a 10-word (81 state) state decoder test chip.

This paper discusses a probabilistic model-based approach to clustering sequences, using hidden Markov models (HMMs). The problem can be framed as a generalization of the standard mixture model approach to clustering in feature space. Two primary issues are addressed. First, a novel parameter initialization procedure is proposed, and second, the more difficult problem of determining the number of clusters K, from the data, is investigated. Experimental results indicate that the proposed techniques are useful for revealing hidden cluster structure in data sets of sequences.

By adapting a framework used for supervised learning, we construct iterative algorithms that maximize the likelihood of the observations while also attempting to stay "close" to the current estimated parameters. We use a bound on the relative entropy between the two HMMs as a distance measure between them. The result is new iterative training algorithms which are similar to the EM (Baum-Welch) algorithm for training HMMs. The proposed algorithms are composed of a step similar to the expectation step of Baum-Welch and a new update of the parameters which replaces the maximization (re-estimation) step. The algorithm takes only negligibly more time per iteration and an approximated version uses the same expectation step as Baum-Welch.

We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence.