By Robert A. Dunne

ISBN-10: 0470148144

ISBN-13: 9780470148143

ISBN-10: 0471741086

ISBN-13: 9780471741084

An obtainable and updated therapy that includes the relationship among neural networks and statistics

A Statistical method of Neural Networks for development reputation offers a statistical therapy of the Multilayer Perceptron (MLP), that is the main normal of the neural community types. This e-book goals to respond to questions that come up while statisticians are first faced with this kind of version, equivalent to:

How strong is the version to outliers?

may well the version be made extra powerful?

Which issues can have a excessive leverage?

What are solid beginning values for the correct set of rules?

Thorough solutions to those questions and lots of extra are integrated, in addition to labored examples and chosen difficulties for the reader. Discussions at the use of MLP types with spatial and spectral facts also are incorporated. additional remedy of hugely vital imperative features of the MLP are supplied, similar to the robustness of the version within the occasion of outlying or extraordinary info; the effect and sensitivity curves of the MLP; why the MLP is a reasonably strong version; and adjustments to make the MLP extra powerful. the writer additionally presents rationalization of numerous misconceptions which are frequent in present neural community literature.

in the course of the ebook, the MLP version is prolonged in different instructions to teach statistical modeling strategy could make useful contributions, and additional exploration for becoming MLP versions is made attainable through the R and S-PLUS® codes which are on hand at the book's similar website. A Statistical method of Neural Networks for development acceptance effectively connects logistic regression and linear discriminant research, hence making it a severe reference and self-study consultant for college students and execs alike within the fields of arithmetic, data, computing device technological know-how, and electric engineering.

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**Extra resources for A statistical approach to neural networks for pattern recognition**

**Example text**

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1) With each random variable X we associate another function p( · ), called the probability mass function of X (abbreviated as pmf ), defined for all real x by p(x) = P[X = x]. 28 2 PROBABILITY AND RANDOM VARIABLES Thus, if x is a value that X cannot assume, then p(x) = 0. The set T of all x such p(x) > 0 is either finite or countably infinite. For a proof see Cramer [2, p. 52]. (A set is countably infinite or denumerable if it can be put into one-to-one correspondence with the positive integers and thus enumerated x l9 x 2 , x 3 , ) The random variable X is said to be discrete if Σ P(*)=I X € T where T = {x : p(x) > 0}.

11), when Y is contin uous. The Stieltjes integral can also be used to evaluate £[/ι(^)] when Y is neither discrete nor continuous, but this is beyond the scope of the book. The interested reader can consult Parzen [4, pp. 233-235] or Apostol [5, Chapter 7]. The next theorem shows how to evaluate E\X\ E[Xk] in terms of E[X | Y] and E[Xk \ Y]. 1 Let X and Y be jointly distributed random var iables. 13) — oo and E[E[Xk \Y]]=\ E[Xk \Y = y] dFY{y) = E[Xk\ k = 1, 2, 3, .... 14) for the cases (a) X and Y are discrete, and (b) X and Y are continuous.

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