An Introduction to the Application of the Theory of Probabilistic Functions of a Markov Process to Automatic Speech Recognition

Levinson, Stephen E.; Rabiner, L. R.; Sondhi, M. M.

doi:10.1002/j.1538-7305.1983.tb03114.x

Cited by 779 publications

(316 citation statements)

References 16 publications

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“…BKT models are usually fit using the expectation maximization method (EM) [2], Conjugate Gradient Search [1], or discretized brute-force search [7].…”

Section: Bayesian Knowledge Tracingmentioning

confidence: 99%

“…Instead of a traditional Expectation Maximization (EM) method for learning BKT parameters, we base our method on the so-called optimization techniques approach described in [2] for the following reasons. First, EM does not directly optimize a likelihood of the student observations given BKT parameters (a standard metric for HMM).…”

Section: Bayesian Knowledge Tracing With Student-specific Parametersmentioning

confidence: 99%

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Individualized Bayesian Knowledge Tracing Models

Yudelson

Koedinger

Gordon

2013

Lecture Notes in Computer Science

293

112

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Abstract. Bayesian Knowledge Tracing (BKT)[1] is a user modeling method extensively used in the area of Intelligent Tutoring Systems. In the standard BKT implementation, there are only skill-specific parameters. However, a large body of research strongly suggests that studentspecific variability in the data, when accounted for, could enhance model accuracy [5,6,8]. In this work, we revisit the problem of introducing student-specific parameters into BKT on a larger scale. We show that student-specific parameters lead to a tangible improvement when predicting the data of unseen students, and that parameterizing students' speed of learning is more beneficial than parameterizing a priori knowledge.

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“…BKT models are usually fit using the expectation maximization method (EM) [2], Conjugate Gradient Search [1], or discretized brute-force search [7].…”

Section: Bayesian Knowledge Tracingmentioning

confidence: 99%

Section: Bayesian Knowledge Tracing With Student-specific Parametersmentioning

confidence: 99%

Individualized Bayesian Knowledge Tracing Models

Yudelson

Koedinger

Gordon

2013

Lecture Notes in Computer Science

293

112

View full text Add to dashboard Cite

show abstract

“…First, we set some initial values for λ. Then, we obtain new values of these parameters in each iteration, using increasing transformations, applying the Baum-Eagon inequality [10,11]. It is guaranteed that the new estimated values increase the value of the objective function and, therefore, its convergence.…”

Section: Cyclic Trainingmentioning

confidence: 99%

“…Let A = {a ij } be the matrix of transition probabilities between states (1 ≤ i, j ≤ n, where n is the number of states) and let B = {b ij } be the matrix of observation probabilities (1 ≤ i ≤ n and 1 ≤ j ≤ w) [2]. As we know that n j=0 a ij = 1 for 0 ≤ i ≤ n and that (3) is a polynomial with respect to A, the new estimation,ā ij , can be obtained with the Baum-Eagon inequality [10,11]. Applying logarithms and [10] to (3), we conclude that:…”

Section: Cyclic Trainingmentioning

confidence: 99%

EM Training of Hidden Markov Models for Shape Recognition Using Cyclic Strings

Palazón-González

Marzal

Vilar

2013

Neural Information Processing

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Abstract. Shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks. Most transformations are relatively easy to handle when contours are represented by strings. However, starting point invariance is difficult to achieve. One interesting possibility is the use of cyclic strings, which are strings with no starting and final points. Here we present the use of Hidden Markov Models for modelling cyclic strings and their training using Expectation Maximization. Experimental results show that our proposal outperforms other methods in the literature.

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“…[19][20][21][22][23][24][25] We have previously reported the application of hidden Markov models to the "two-color problem" where a molecule fluctuates between two states that can be distinguished based on the color of the fluorescence. 26 In that work, it was observed that estimation of two-state kinetic parameters was robust even in the presence of considerable background and spectral crosstalk in the data and for kinetic rates comparable to the photon count rates.…”

Section: Introductionmentioning

confidence: 99%

Hidden Markov Model Analysis of Multichromophore Photobleaching

et al. 2006

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The interpretation of single-molecule measurements is greatly complicated by the presence of multiple fluorescent labels. However, many molecular systems of interest consist of multiple interacting components. We investigate this issue using multiply labeled dextran polymers that we intentionally photobleach to the background on a single-molecule basis. Hidden Markov models allow for unsupervised analysis of the data to determine the number of fluorescent subunits involved in the fluorescence intermittency of the 6-carboxy-tetramethylrhodamine labels by counting the discrete steps in fluorescence intensity. The Bayes information criterion allows us to distinguish between hidden Markov models that differ by the number of states, that is, the number of fluorescent molecules. We determine information-theoretical limits and show via Monte Carlo simulations that the hidden Markov model analysis approaches these theoretical limits. This technique has resolving power of one fluorescing unit up to as many as 30 fluorescent dyes with the appropriate choice of dye and adequate detection capability. We discuss the general utility of this method for determining aggregation-state distributions as could appear in many biologically important systems and its adaptability to general photometric experiments.

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An Introduction to the Application of the Theory of Probabilistic Functions of a Markov Process to Automatic Speech Recognition

Cited by 779 publications

References 16 publications

Individualized Bayesian Knowledge Tracing Models

Individualized Bayesian Knowledge Tracing Models

EM Training of Hidden Markov Models for Shape Recognition Using Cyclic Strings

Hidden Markov Model Analysis of Multichromophore Photobleaching

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