A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains
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This article is published in Annals of Mathematical Statistics.The article was published on 1970-02-01 and is currently open access. It has received 4618 citations till now. The article focuses on the topics: Examples of Markov chains & Markov chain.read more
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Continuous speech recognition by statistical methods
TL;DR: Experimental results are presented that indicate the power of the methods and concern modeling of a speaker and of an acoustic processor, extraction of the models' statistical parameters and hypothesis search procedures and likelihood computations of linguistic decoding.
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A unifying review of linear Gaussian models
Sam T. Roweis,Zoubin Ghahramani +1 more
TL;DR: A new model for static data is introduced, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise, which shows how independent component analysis is also a variation of the same basic generative model.
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Deterministic annealing for clustering, compression, classification, regression, and related optimization problems
TL;DR: The deterministic annealing approach to clustering and its extensions has demonstrated substantial performance improvement over standard supervised and unsupervised learning methods in a variety of important applications including compression, estimation, pattern recognition and classification, and statistical regression.
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Hidden Markov processes
Yariv Ephraim,Neri Merhav +1 more
TL;DR: An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented and consistency and asymptotic normality of the maximum-likelihood parameter estimator were proved under some mild conditions.
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Learning string-edit distance
TL;DR: The stochastic model allows us to learn a string-edit distance function from a corpus of examples and is applicable to any string classification problem that may be solved using a similarity function against a database of labeled prototypes.
References
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Journal ArticleDOI
Statistical Inference for Probabilistic Functions of Finite State Markov Chains
Leonard E. Baum,Ted Petrie +1 more
Journal ArticleDOI
An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology
Leonard E. Baum,J. A. Eagon +1 more
TL;DR: In this paper, a polynomial with nonnegative coefficients homogeneous of degree d in its variables is shown to be polynomially homogeneous unless 3(3(x))>P(x), where 3(x)=x.
Book ChapterDOI
The Gamma Function
Willi Freeden,Martin Gutting +1 more
TL;DR: The Gamma function as discussed by the authors is a generalized factorial function that can be used to estimate the probability distribution of a probability distribution, and it has been used in many applications, e.g., as part of probability distributions.