Read A Generalized Mellin Transform for the Analysis of Learning Machines

A Generalized Mellin Transform for the Analysis of Learning Machines

Stanford University. Stanford Electronics Laboratories

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Description:This work introduces a generalization of the Mellin integral transform, and then applies it as a new technique for the analysis of statistical learning machines. Specifically, this transform technique is demonstrated for Bayes' estimation and binary detection of communication signals in the framework of statistical decision theory. It is shown that the use of the Mellin transform markedly simplifies the analysis of sequential estimation of an unknown parameter in a statistical population, whether or not an optimum (admissible) decision rule is used for processing the observations. The loss function, which need not be error-squared, or the likelihood ratio is treated as a random variable, and is described by a transform expression derived from the basic Bayes' learning or estimation equation. This transform expression for the loss is the Mellin transform pair to the probability density of the loss, and contains, as unspecified parameters, the number of observations, the a priori assumptions about the unknown parameter that is to be estimated, and the decision (data processing) rule. The transform expression for the loss is shown to be a convenient and appealing measure of the performance of the learning machine. Convergence, bias, and the rate of convergence of the estimation procedure are readily displayed through the transform associated with the loss function. The average cost of errors for a binary detector, previously adapted through the use of sequential estimation, is derived through the convolution integral and Parseval's relationships for the Mellin transform. (Author).We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A Generalized Mellin Transform for the Analysis of Learning Machines. To get started finding A Generalized Mellin Transform for the Analysis of Learning Machines, you are right to find our website which has a comprehensive collection of manuals listed.
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Pages: 156

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: 1965

ISBN: djsFAAAAIAAJ

Description: This work introduces a generalization of the Mellin integral transform, and then applies it as a new technique for the analysis of statistical learning machines. Specifically, this transform technique is demonstrated for Bayes' estimation and binary detection of communication signals in the framework of statistical decision theory. It is shown that the use of the Mellin transform markedly simplifies the analysis of sequential estimation of an unknown parameter in a statistical population, whether or not an optimum (admissible) decision rule is used for processing the observations. The loss function, which need not be error-squared, or the likelihood ratio is treated as a random variable, and is described by a transform expression derived from the basic Bayes' learning or estimation equation. This transform expression for the loss is the Mellin transform pair to the probability density of the loss, and contains, as unspecified parameters, the number of observations, the a priori assumptions about the unknown parameter that is to be estimated, and the decision (data processing) rule. The transform expression for the loss is shown to be a convenient and appealing measure of the performance of the learning machine. Convergence, bias, and the rate of convergence of the estimation procedure are readily displayed through the transform associated with the loss function. The average cost of errors for a binary detector, previously adapted through the use of sequential estimation, is derived through the convolution integral and Parseval's relationships for the Mellin transform. (Author).We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A Generalized Mellin Transform for the Analysis of Learning Machines. To get started finding A Generalized Mellin Transform for the Analysis of Learning Machines, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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A Generalized Mellin Transform for the Analysis of Learning Machines

A Generalized Mellin Transform for the Analysis of Learning Machines

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