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Learning Bayesian Models with R

Learning Bayesian Models with R

By : Hari Manassery Koduvely
3.4 (7)
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Learning Bayesian Models with R

Learning Bayesian Models with R

3.4 (7)
By: Hari Manassery Koduvely

Overview of this book

Bayesian Inference provides a unified framework to deal with all sorts of uncertainties when learning patterns form data using machine learning models and use it for predicting future observations. However, learning and implementing Bayesian models is not easy for data science practitioners due to the level of mathematical treatment involved. Also, applying Bayesian methods to real-world problems requires high computational resources. With the recent advances in computation and several open sources packages available in R, Bayesian modeling has become more feasible to use for practical applications today. Therefore, it would be advantageous for all data scientists and engineers to understand Bayesian methods and apply them in their projects to achieve better results. Learning Bayesian Models with R starts by giving you a comprehensive coverage of the Bayesian Machine Learning models and the R packages that implement them. It begins with an introduction to the fundamentals of probability theory and R programming for those who are new to the subject. Then the book covers some of the important machine learning methods, both supervised and unsupervised learning, implemented using Bayesian Inference and R. Every chapter begins with a theoretical description of the method explained in a very simple manner. Then, relevant R packages are discussed and some illustrations using data sets from the UCI Machine Learning repository are given. Each chapter ends with some simple exercises for you to get hands-on experience of the concepts and R packages discussed in the chapter. The last chapters are devoted to the latest development in the field, specifically Deep Learning, which uses a class of Neural Network models that are currently at the frontier of Artificial Intelligence. The book concludes with the application of Bayesian methods on Big Data using the Hadoop and Spark frameworks.
Table of Contents (11 chapters)
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10
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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