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Learning Probabilistic Graphical Models in R

Book Image

Learning Probabilistic Graphical Models in R

Overview of this book

Probabilistic graphical models (PGM, also known as graphical models) are a marriage between probability theory and graph theory. Generally, PGMs use a graph-based representation. Two branches of graphical representations of distributions are commonly used, namely Bayesian networks and Markov networks. R has many packages to implement graphical models. We’ll start by showing you how to transform a classical statistical model into a modern PGM and then look at how to do exact inference in graphical models. Proceeding, we’ll introduce you to many modern R packages that will help you to perform inference on the models. We will then run a Bayesian linear regression and you’ll see the advantage of going probabilistic when you want to do prediction. Next, you’ll master using R packages and implementing its techniques. Finally, you’ll be presented with machine learning applications that have a direct impact in many fields. Here, we’ll cover clustering and the discovery of hidden information in big data, as well as two important methods, PCA and ICA, to reduce the size of big problems.

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Learning Probabilistic Graphical Models in R
Apr, 2016 | 250 pages
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Table of Contents (15 chapters)
Learning Probabilistic Graphical Models in R
Learning Probabilistic Graphical Models in R
Credits
Credits
About the Author
About the Author
About the Reviewers
About the Reviewers
www.PacktPub.com
www.PacktPub.com
Preface
Preface
Free Chapter
1
Probabilistic Reasoning
Probabilistic Reasoning
Machine learning
Representing uncertainty with probabilities
Probabilistic graphical models
Summary
2
Exact Inference
Exact Inference
Building graphical models
Variable elimination
Sum-product and belief updates
The junction tree algorithm
Examples of probabilistic graphical models
Summary
3
Learning Parameters
Learning Parameters
Introduction
Learning by inference
Maximum likelihood
Learning with hidden variables – the EM algorithm
Principles of the EM algorithm
Summary
4
Bayesian Modeling – Basic Models
Bayesian Modeling – Basic Models
The Naive Bayes model
Beta-Binomial
The Gaussian mixture model
Summary
5
Approximate Inference
Approximate Inference
Sampling from a distribution
Basic sampling algorithms
Rejection sampling
Importance sampling
Markov Chain Monte-Carlo
MCMC for probabilistic graphical models in R
Summary
6
Bayesian Modeling – Linear Models
Bayesian Modeling – Linear Models
Linear regression
Bayesian linear models
Summary
7
Probabilistic Mixture Models
Probabilistic Mixture Models
Mixture models
EM for mixture models
Mixture of Bernoulli
Mixture of experts
Latent Dirichlet Allocation
Summary
Appendix
Appendix
References
Index
Index

Examples of probabilistic graphical models

In this last section we will show several examples of PGM that are good candidates for exact inference. The goal of this section is to show realistic yet simple examples of what can be done and to provide the reader with ideas for developing his or her own models.

The sprinkler example

This is an historical example which has been used in many textbooks. It is rather simple and shows a simple reasoning.

Let's say we look at our garden and see the grass is wet. We want to know why the grass is wet. There are two possibilities: either it was raining before or we forgot to turn off the sprinkler. Moreover, we can observe the sky. If it's cloudy, chances are it was raining before. However, if it was cloudy then presumably we didn't turn on the sprinkler, so it is more likely, in this case, we would have not forgotten to turn off the sprinkler.

This is a little example of causal reasoning that can be represented by a PGM. We identify four random variables...

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