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Learning Bayesian Models with R

You're reading from   Learning Bayesian Models with R Become an expert in Bayesian Machine Learning methods using R and apply them to solve real-world big data problems

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Product type Paperback
Published in Oct 2015
Publisher Packt
ISBN-13 9781783987603
Length 168 pages
Edition 1st Edition
Languages
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Author (1):
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Hari Manassery Koduvely Hari Manassery Koduvely
Author Profile Icon Hari Manassery Koduvely
Hari Manassery Koduvely
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Table of Contents (11) Chapters Close

Preface 1. Introducing the Probability Theory FREE CHAPTER 2. The R Environment 3. Introducing Bayesian Inference 4. Machine Learning Using Bayesian Inference 5. Bayesian Regression Models 6. Bayesian Classification Models 7. Bayesian Models for Unsupervised Learning 8. Bayesian Neural Networks 9. Bayesian Modeling at Big Data Scale Index

Two-layer neural networks


Let us look at the formal definition of a two-layer neural network. We follow the notations and description used by David MacKay (reference 1, 2, and 3 in the References section of this chapter). The input to the NN is given by . The input values are first multiplied by a set of weights to produce a weighted linear combination and then transformed using a nonlinear function to produce values of the state of neurons in the hidden layer:

A similar operation is done at the second layer to produce final output values :

The function is usually taken as either a sigmoid function or . Another common function used for multiclass classification is softmax defined as follows:

This is a normalized exponential function.

All these are highly nonlinear functions exhibiting the property that the output value has a sharp increase as a function of the input. This nonlinear property gives neural networks more computational flexibility than standard linear or generalized linear models...

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