Traditional Markov Model Research Articles

A continuous density interpretation of discrete HMM systems and MMI-neural networks

The subject of this paper is the integration of the traditional vector quantizer (VQ) and discrete hidden Markov models (HMM) combination in the mixture emission density framework commonly used in automatic speech recognition (ASR). It is shown that the probability density of a system that consists of a VQ and a discrete classifier can be interpreted as a special case of a semi-continuous mixture model. Thus, the VQ parameters and the classifier can be trained jointly. In this framework, a gradient based VQ training method for single and multiple feature stream systems is derived. This leads to an approach that is directly related to the paradigm of maximum mutual information (MMI) neural networks, that has been successfully applied as VQ in ASR earlier. In continuous speech recognition experiments that were carried out for the Resource Management and Wall Street Journal databases the presented systems achieve recognition accuracies that compete well with comparable Gaussian mixture HMMs. Thus, we demonstrate that the performance degradations, often reported for discrete HMM systems, are not mainly caused by the vector quantization process in itself, but that they are due to the traditional separation of the VQ and the HMM during parameter estimation. These degradations can be avoided by training of the entire system as described here, while keeping the attractive computational speed of discrete HMMs.

The Hidden Markov Model of co-articulation and its application to the continuous speech recognition

The co-articulation is one of the main reasons that makes the speech recognition difficult. However, the traditional Hidden Markov Models(HMM) can not model the co-articulation, because they depend on the first-order assumption. In this paper, for modeling the co-articulation, a more perfect HMM than traditional first order HMM is proposed on the basis of the authors’ previous works(1997, 1998) and they give a method in that this HMM is used in continuous speech recognition by means of multilayer perceptrons(MLP), i.e. the hybrid HMM/MLP method with triple MLP structure. The experimental result shows that this new hybrid HMM/MLP method decreases error rate in comparison with authors’ previous works.

Two Markov Models and Their Application

Two different Markov models for cross-covariance and coregionalization modeling are proposed and compared in cokriging and stochastic simulation modes. The newly introduced Markov model 2 performs better in cases where the secondary data are defined on a larger support volume than the primary variable being estimated or simulated. Incorrect adoption of the more traditional Markov model 1 may result in cokriging estimated maps that are artificially too close to the secondary data map and in simulated realizations with too high nugget effect.

Modeling word occurrences for the compression of concordances

An earlier paper developed a procedure for compressing concordances, assuming that all alements occurred independently. The models introduced in that paper are extended here to take the possiblity of clustering into account. The concordance is conceptualized as a set of bitmaps, in which the bit locations reporesent documents, and the one-bits represent the occurrence of given terms. Hidden Markov Models (HMM's) are used to describe the clustering of the one-bits. However, for computational reasons, the HMM is approximated by traditional Markov models. A set of criteria is developed to constrain the allowable set of n -state models, and a full inventory is given for n ≤ 4. Graph-theoretic reduction and complementation operations are defined among the various models and are used to provide a structure relating the models studied. Finally, the new methods were tested on the concordances of the English Bible and of two of the world's largest full-text retrieval systems: the Tre´sor de la Langue Franc¸aise and the Responsa Project.

Effect of dynamical asymmetry on the viscosity of a random copolymer melt

The variation of the viscosity as a function of the sequence distribution in an A–B random copolymer melt is determined. The parameters that characterize the random copolymer are the fraction of A monomers f, the parameter λ which determines the correlation in the monomer identities along a chain and the Flory chi parameter χF which determines the strength of the enthalpic repulsion between monomers of type A and B. For λ≳0, there is a greater probability of finding like monomers at adjacent positions along the chain, and for λ<0 unlike monomers are more likely to be adjacent to each other. The traditional Markov model for the random copolymer melt is altered to remove ultraviolet divergences in the equations for the renormalized viscosity, and the phase diagram for the modified model has a binary fluid type transition for λ≳0 and does not exhibit a phase transition for λ<0. A mode coupling analysis is used to determine the renormalization of the viscosity due to the dependence of the bare viscosity on the local concentration field. Due to the dissipative nature of the coupling, there are nonlinearities both in the transport equation and in the noise correlation. The concentration dependence of the transport coefficient presents additional difficulties in the formulation due to the Ito–Stratonovich dilemma, and there is some ambiguity about the choice of the concentration to be used while calculating the noise correlation. In the Appendix, it is shown using a diagrammatic perturbation analysis that the Ito prescription for the calculation of the transport coefficient, when coupled with a causal discretization scheme, provides a consistent formulation that satisfies stationarity and the fluctuation dissipation theorem. This functional integral formalism is used in the present analysis, and consistency is verified for the present problem as well. The upper critical dimension for this type of renormalization is 2, and so there is no divergence in the viscosity in the vicinity of a critical point. The results indicate that there is a systematic dependence of the viscosity on λ and χF. The fluctuations tend to increase the viscosity for λ<0, and decrease the viscosity for λ≳0, and an increase in χF tends to decrease the viscosity.

Performance impacts of self-similarity in traffic

Recent measurement studies in Bellcore and elsewhere have convincingly established the presence of statistical self similarity in high-speed network traffic. What is less clear --- and as such the subject of intense current research --- is the impact of the self-similarity on network performance. Given that traditional queueing models of network performance do not model self-similarity, the validity of traditional models to predict network performance would be supported if it is shown that self-similarity does not have measurable impacts on performance. On the other hand, if the converse of this assertion were true, it would have significant impacts on the way networks are designed and analyzed, as well as open up new areas of research in mathematical modeling, queueing analysis, network design and control. The issues addressed in this session are therefore of fundamental importance in high-speed network research.Given that queueing behavior is dominated by traffic characteristics over the time scales of busy periods, it has been argued that phenomena that span many time scales, such as self-similarity, should not be relevant for queueing performance. However, the paper by Narayan, Erramilli and Willinger presents evidence that for data traffic, the long range dependence (which is related to the self-similarity in traffic) can dominate queueing behavior under a variety of conditions. Specifically, it is shown based on a series of carefully designed simulation experiments with actual traffic traces, that the queueing behavior with actual traces is considerably heavier than that predicted by traditional theory, and that these differences are attributable to long range dependence. The paper by Heyman and Lakshman investigates modeling of video traffic to predict cell loss performance with finite buffer systems, and they conclude that long-range dependence is not a crucial property in determining the finite buffer behavior of video conferences. In particular, a Markov chain model that does not model long-range dependence is nevertheless able to reproduce various operating characteristics over a wide range of loadings obtained with the actual video trace. Mukherjee, Adas, Klivansky and Song investigate the performance impacts of short-range and long-range correlation components using simulations with a fractional ARIMA model. They also discuss a strategy to provide quality of service guarantees with long range dependent traffic, as well as recent results on NSFNET traffic. Finally, the paper by Li describes a frequency-domain based analytical tool that matches a special class of Markov chains with traces exhibiting a variety of characteristics, including long-range dependence. Good agreement is reported between analytical queueing solutions of the matched Markov chains, and simulation results obtained video and data traffic traces.This session therefore brings together a wide range of viewpoints on this issue. Resolution of such seemingly conflicting conclusions lies in the fact that in performance analysis, answers sensitively depend on the specific details of a problem. Thus the proper question to ask is not whether or not self-similarity matters in queueing; but under what conditions it matters. Likewise, the question to ask is not whether a class of models is invalid; but to identify the conditions under which traditional Markov or self-similar traffic models are expected to be valid. Finally, given an understanding of statistical features that are relevant to a given problem, the challenge is to model these accurately and parsimoniously so that the model is useful in practical performance analysis. The work outlined in the abstracts below adds significantly to our understanding of these issues.

A stochastic version of Thiele's differential equation

Abstract Thiele's differential equation for the statewise reserves of a life insurance policy is viewed as a stochastic differential equation in a point process set-up. Special attention is given to the traditional Markov model and to a more general semi-Markov model. Finally, a numerical example with qualifying period for disabled lives is considered.

Economic-demographic models for forecasting interregional migration.

"A class of spatial economic-demographic forecasting models is proposed. The models combine elements of traditional Markov and economic gravity models. A base-period probability structure is modified by the changing relative distribution of economic opportunity. Estimation issues are addressed, and an empirical application to US interstate migration during the late 1970s is described. It is contended that the framework represents a merger of past demographic and economic modeling traditions in a spatial interaction framework."