Hidden Markov models have been used to restore recorded signals of single ion channels buried in background noise. Parameter estimation and signal restoration are usually carried out through likelihood maximization by using variants of the Baum-Welch forward-backward procedures. This paper presents an alternative approach for dealing with this inferential task. The inferences are made by using ...

This paper presents a new method of feature dimension reduction in hidden Markov modeling (HMM) for speech recognition. The key idea is to apply reduced rank maximum likelihood estimation in the M-step of the usual Baum-Welch algorithm for estimating HMM parameters such that the estimates of the Gaussian distribution parameters are restricted in a sub-space of reduced dimensionality. There are ...

Hidden Markov modeling (HMM) techniques have been applied in the past few years to characterize single ion channel current events at low signal-to-noise ratios (SNR’s). In this paper, an adaptation of the forward-backward procedure and Baum–Welch algorithm is presented to model ion channel kinetics under conditions of correlated and state-dependent excess noise like that observed in patch-clamp...

The success of many real-world applications demonstrates that hidden Markov models (HMMs) are highly effective in one-dimensional pattern recognition problems such as speech recognition. Research is now focussed on extending HMMs to 2-D and possibly 3-D applications which arise in gesture, face, and handwriting recognition. Although the HMM has become a major workhorse of the pattern recognitio...

We derive the Baum-Welch algorithm for hidden Markov models (HMMs) through an information-theoretical approach using cross-entropy instead of the Lagrange multiplier approach which is universal in machine learning literature. The proposed approach provides a more concise derivation of the Baum-Welch method and naturally generalizes to multiple observations. Introduction The basic hidden Markov ...

We claim to give the definitive theory of what we call the ‘kneejerk mapping’, which is the basis for a class of optimization algorithms introduced by Baum, and promoted by Dempster, Laird, and Rubin under the name ‘EM algorithm’. Introduction We give the definitive theory of the knee-jerk mapping, to be defined below. This mapping has been investigated by many people, most notably Baum ([2], [...

We consider the problem of maximizing certain positive rational functions of a form that includes statistical constructs such as conditional mixture densities and conditional hidden Markov models. The wellknown Baum-Welch and expectation maximization (EM) algorithms do not apply to rational functions and are therefore limited to the simpler maximum-likelihood form of such models. Our main resul...

We develop a finite KK-theory of C∗-algebras following ArlettazH.Inassaridze’s approach to finite algebraic K-theory [1] . The BrowderKaroubi-Lambre’s theorem on the orders of the elements for finite algebraic K-theory [ , ] is extended to finite KK-theory. A new bivariant theory, called torsion KK-theory is defined as the direct limit of finite KK-theories. Such bivariant K-theory has almost a...