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Learning Bayesian Models with R

By : Hari Manassery Koduvely
Book Image

Learning Bayesian Models with R

By: Hari Manassery Koduvely

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Table of Contents (16 chapters)
Learning Bayesian Models with R
Learning Bayesian Models with 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
Introducing the Probability Theory
Introducing the Probability Theory
Probability distributions
Conditional probability
Bayesian theorem
Marginal distribution
Expectations and covariance
Exercises
References
Summary
2
The R Environment
The R Environment
Setting up the R environment and packages
Managing data in R
Writing R programs
Data visualization
Sampling
Exercises
References
Summary
3
Introducing Bayesian Inference
Introducing Bayesian Inference
Bayesian view of uncertainty
Exercises
References
Summary
4
Machine Learning Using Bayesian Inference
Machine Learning Using Bayesian Inference
Why Bayesian inference for machine learning?
Model overfitting and bias-variance tradeoff
Selecting models of optimum complexity
Bayesian averaging
An overview of common machine learning tasks
References
Summary
5
Bayesian Regression Models
Bayesian Regression Models
Generalized linear regression
The arm package
The Energy efficiency dataset
Regression of energy efficiency with building parameters
Simulation of the posterior distribution
Exercises
References
Summary
6
Bayesian Classification Models
Bayesian Classification Models
Performance metrics for classification
The Naïve Bayes classifier
The Bayesian logistic regression model
Exercises
References
Summary
7
Bayesian Models for Unsupervised Learning
Bayesian Models for Unsupervised Learning
Bayesian mixture models
Topic modeling using Bayesian inference
R packages for LDA
Exercises
References
Summary
8
Bayesian Neural Networks
Bayesian Neural Networks
Two-layer neural networks
Bayesian treatment of neural networks
The brnn R package
Deep belief networks and deep learning
Exercises
References
Summary
9
Bayesian Modeling at Big Data Scale
Bayesian Modeling at Big Data Scale
Distributed computing using Hadoop
RHadoop for using Hadoop from R
Spark – in-memory distributed computing
SparkR
Linear regression using SparkR
Computing clusters on the cloud
Other R packages for large scale machine learning
Exercises
References
Summary
Index
Index

Exercises

  1. By using the definition of conditional probability, show that any multivariate joint distribution of N random variables has the following trivial factorization:

  2. The bivariate normal distribution is given by:

    Here:

    By using the definition of conditional probability, show that the conditional distribution can be written as a normal distribution of the form where and .

  3. By using explicit integration of the expression in exercise 2, show that the marginalization of bivariate normal distribution will result in univariate normal distribution.

  4. In the following table, a dataset containing the measurements of petal and sepal sizes of 15 different Iris flowers are shown (taken from the Iris dataset, UCI machine learning dataset repository). All units are in cms:

    Sepal Length

    Sepal Width

    Petal Length

    Petal Width

    Class of Flower

    5.1

    3.5

    1.4

    0.2

    Iris-setosa

    4.9

    3

    1.4

    0.2

    Iris-setosa

    4.7

    3.2

    1.3

    0.2

    Iris-setosa

    4.6

    3.1

    1.5

    0.2

    Iris-setosa

    5

    3.6

    1.4

    0.2

    Iris-setosa

    7

    3.2

    4.7

    1.4

    Iris-versicolor

    6.4

    3.2

    4.5

    1.5

    Iris-versicolor

    6.9

    3.1

    4.9

    1.5

    Iris-versicolor

    5.5

    2.3

    4

    1.3

    Iris-versicolor

    6.5

    2.8

    4.6

    1.5

    Iris-versicolor

    6.3

    3.3

    6

    2.5

    Iris-virginica

    5.8

    2.7

    5.1

    1.9

    Iris-virginica

    7.1

    3

    5.9

    2.1

    Iris-virginica

    6.3

    2.9

    5.6

    1.8

    Iris-virginica

    6.5

    3

    5.8

    2.2

    Iris-virginica

    Answer the following questions:

    1. What is the probability of finding flowers with a sepal length more than 5 cm and a sepal width less than 3 cm?

    2. What is the probability of finding flowers with a petal length less than 1.5 cm; given that petal width is equal to 0.2 cm?

    3. What is the probability of finding flowers with a sepal length less than 6 cm and a petal width less than 1.5 cm; given that the class of the flower is Iris-versicolor?

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