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Bayesian learning for neural networks / (1996)

Neal, Radford M.

New York [u.a.] :Springer,

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UID:

almafu_BV011024947

Umfang: XIV, 183 S. : , graph. Darst.

ISBN: 0-387-94724-8

Serie: Lecture notes in statistics 118

Inhalt: Artificial "neural networks" are now widely used as flexible models for regression classification applications, but questions remain regarding what these models mean, and how they can safely be used when training data is limited. Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. Use of these models in practice is made possible using Markov chain Monte Carlo techniques. Both the theoretical and computational aspects of this work are of wider statistical interest, as they contribute to a better understanding of how Bayesian methods can be applied to complex problems

Inhalt: Presupposing only the basic knowledge of probability and statistics, this book should be of interest to many researchers in statistics, engineering, and artificial intelligence. Software for Unix systems that implements the methods described is freely available over the Internet

Anmerkung: Zugl.: Diss.

Sprache: Englisch

Fachgebiete: Wirtschaftswissenschaften , Mathematik

RVK:

QH 233

RVK:

SI 856

RVK:

SK 820

RVK:

SK 830

Schlagwort(e): Datenanalyse ; Bayes-Verfahren ; Neuronales Netz ; Markov-Kette ; Monte-Carlo-Simulation ; Hochschulschrift ; Hochschulschrift ; Hochschulschrift ; Hochschulschrift

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URL: http://www.loc.gov/catdir/enhancements/fy0812/96022079-d.html

URL: http://www.loc.gov/catdir/enhancements/fy0812/96022079-t.html

URL: Inhaltsverzeichnis

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Bayesian learning for neural networks / (1996)

Neal, Radford M.,

New York :Springer,

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UID:

almahu_9949087841702882

Umfang: 1 online resource (193 pages) : , illustrations.

ISBN: 9781461207450 (e-book)

Serie: Lecture notes in statistics ; 118

Weitere Ausg.: Print version: Neal, Radford M. Bayesian learning for neural networks. New York : Springer, [1996] ISBN 9780387947242

Sprache: Englisch

Fachgebiete: Wirtschaftswissenschaften , Mathematik

RVK:

QH 233

RVK:

SI 856

RVK:

SK 820

RVK:

SK 830

Schlagwort(e): Electronic books. ; Hochschulschrift

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Bayesian Learning for Neural Networks (1996)

Neal, Radford M. ; SpringerLink 〈Online service〉

New York, NY :Springer New York :

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UID:

almahu_9947363017202882

Umfang: 204 p. , online resource.

ISBN: 9781461207450

Serie: Lecture Notes in Statistics, 118

Inhalt: Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence.

Anmerkung: 1 Introduction -- 1.1 Bayesian and frequentist views of learning -- 1.2 Bayesian neural networks -- 1.3 Markov chain Monte Carlo methods -- 1.4 Outline of the remainder of the book -- 2 Priors for Infinite Networks -- 2.1 Priors converging to Gaussian processes -- 2.2 Priors converging to non-Gaussian stable processes -- 2.3 Priors for nets with more than one hidden layer -- 2.4 Hierarchical models -- 3 Monte Carlo Implementation -- 3.1 The hybrid Monte Carlo algorithm -- 3.2 An implementation of Bayesian neural network learning -- 3.3 A demonstration of the hybrid Monte Carlo implementation -- 3.4 Comparison of hybrid Monte Carlo with other methods -- 3.5 Variants of hybrid Monte Carlo -- 4 Evaluation of Neural Network Models -- 4.1 Network architectures, priors, and training procedures -- 4.2 Tests of the behaviour of large networks -- 4.3 Tests of Automatic Relevance Determination -- 4.4 Tests of Bayesian models on real data sets -- 5 Conclusions and Further Work -- 5.1 Priors for complex models -- 5.2 Hierarchical Models — ARD and beyond -- 5.3 Implementation using hybrid Monte Carlo -- 5.4 Evaluating performance on realistic problems -- A Details of the Implementation -- A.1 Specifications -- A.1.1 Network architecture -- A.1.2 Data models -- A.1.3 Prior distributions for parameters and hyperparameters -- A.1.4 Scaling of priors -- A.2 Conditional distributions for hyperparameters -- A.2.1 Lowest-level conditional distributions -- A.2.2 Higher-level conditional distributions -- A.3 Calculation of derivatives -- A.3.1 Derivatives of the log prior density -- A.3.2 Log likelihood derivatives with respect to unit values -- A.3.3 Log likelihood derivatives with respect to parameters -- A.4 Heuristic choice of stepsizes -- A.5 Rejection sampling from the prior -- B Obtaining the software.

In: Springer eBooks

Weitere Ausg.: Printed edition: ISBN 9780387947242

Sprache: Englisch

DOI: 10.1007/978-1-4612-0745-0

URL: http://dx.doi.org/10.1007/978-1-4612-0745-0

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