Book Image

Learning Bayesian Models with R

By : Hari Manassery Koduvely
Book Image

Learning Bayesian Models with R

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)
10
Index

The Naïve Bayes classifier


The name Naïve Bayes comes from the basic assumption in the model that the probability of a particular feature is independent of any other feature given the class label . This implies the following:

Using this assumption and the Bayes rule, one can show that the probability of class , given features , is given by:

Here, is the normalization term obtained by summing the numerator on all the values of k. It is also called Bayesian evidence or partition function Z. The classifier selects a class label as the target class that maximizes the posterior class probability :

The Naïve Bayes classifier is a baseline classifier for document classification. One reason for this is that the underlying assumption that each feature (words or m-grams) is independent of others, given the class label typically holds good for text. Another reason is that the Naïve Bayes classifier scales well when there is a large number of documents.

There are two implementations of Naïve Bayes. In...