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Learning Probabilistic Graphical Models in R

Book Description

Familiarize yourself with probabilistic graphical models through real-world problems and illustrative code examples in R

About This Book

  • Predict and use a probabilistic graphical models (PGM) as an expert system

  • Comprehend how your computer can learn Bayesian modeling to solve real-world problems

  • Know how to prepare data and feed the models by using the appropriate algorithms from the appropriate R package

  • Who This Book Is For

    This book is for anyone who has to deal with lots of data and draw conclusions from it, especially when the data is noisy or uncertain. Data scientists, machine learning enthusiasts, engineers, and those who curious about the latest advances in machine learning will find PGM interesting.

    What You Will Learn

  • Understand the concepts of PGM and which type of PGM to use for which problem

  • Tune the model’s parameters and explore new models automatically

  • Understand the basic principles of Bayesian models, from simple to advanced

  • Transform the old linear regression model into a powerful probabilistic model

  • Use standard industry models but with the power of PGM

  • Understand the advanced models used throughout today's industry

  • See how to compute posterior distribution with exact and approximate inference algorithms

  • In Detail

    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.

    Style and approach

    This book gives you a detailed and step-by-step explanation of each mathematical concept, which will help you build and analyze your own machine learning models and apply them to real-world problems. The mathematics is kept simple and each formula is explained thoroughly.

    Downloading the example code for this book. You can download the example code files for all Packt books you have purchased from your account at http://www.PacktPub.com. If you purchased this book elsewhere, you can visit http://www.PacktPub.com/support and register to have the code file.

    Table of Contents

    1. Learning Probabilistic Graphical Models in R
      1. Table of Contents
      2. Learning Probabilistic Graphical Models in R
      3. Credits
      4. About the Author
      5. About the Reviewers
      6. www.PacktPub.com
        1. eBooks, discount offers, and more
          1. Why subscribe?
      7. Preface
        1. What this book covers
        2. What you need for this book
        3. Who this book is for
        4. Conventions
        5. Reader feedback
        6. Customer support
          1. Downloading the example code
          2. Errata
          3. Piracy
          4. Questions
      8. 1. Probabilistic Reasoning
        1. Machine learning
        2. Representing uncertainty with probabilities
          1. Beliefs and uncertainty as probabilities
          2. Conditional probability
          3. Probability calculus and random variables
            1. Sample space, events, and probability
            2. Random variables and probability calculus
          4. Joint probability distributions
          5. Bayes' rule
            1. Interpreting the Bayes' formula
            2. A first example of Bayes' rule
            3. A first example of Bayes' rule in R
        3. Probabilistic graphical models
          1. Probabilistic models
          2. Graphs and conditional independence
          3. Factorizing a distribution
          4. Directed models
          5. Undirected models
          6. Examples and applications
        4. Summary
      9. 2. Exact Inference
        1. Building graphical models
          1. Types of random variable
          2. Building graphs
            1. Probabilistic expert system
            2. Basic structures in probabilistic graphical models
        2. Variable elimination
        3. Sum-product and belief updates
        4. The junction tree algorithm
        5. Examples of probabilistic graphical models
          1. The sprinkler example
          2. The medical expert system
          3. Models with more than two layers
          4. Tree structure
        6. Summary
      10. 3. Learning Parameters
        1. Introduction
        2. Learning by inference
        3. Maximum likelihood
          1. How are empirical and model distribution related?
          2. The ML algorithm and its implementation in R
          3. Application
        4. Learning with hidden variables – the EM algorithm
          1. Latent variables
        5. Principles of the EM algorithm
          1. Derivation of the EM algorithm
          2. Applying EM to graphical models
        6. Summary
      11. 4. Bayesian Modeling – Basic Models
        1. The Naive Bayes model
          1. Representation
          2. Learning the Naive Bayes model
          3. Bayesian Naive Bayes
        2. Beta-Binomial
          1. The prior distribution
          2. The posterior distribution with the conjugacy property
          3. Which values should we choose for the Beta parameters?
        3. The Gaussian mixture model
          1. Definition
        4. Summary
      12. 5. Approximate Inference
        1. Sampling from a distribution
        2. Basic sampling algorithms
          1. Standard distributions
        3. Rejection sampling
          1. An implementation in R
        4. Importance sampling
          1. An implementation in R
        5. Markov Chain Monte-Carlo
          1. General idea of the method
          2. The Metropolis-Hastings algorithm
        6. MCMC for probabilistic graphical models in R
          1. Installing Stan and RStan
          2. A simple example in RStan
        7. Summary
      13. 6. Bayesian Modeling – Linear Models
        1. Linear regression
          1. Estimating the parameters
        2. Bayesian linear models
          1. Over-fitting a model
          2. Graphical model of a linear model
          3. Posterior distribution
          4. Implementation in R
          5. A stable implementation
          6. More packages in R
        3. Summary
      14. 7. Probabilistic Mixture Models
        1. Mixture models
        2. EM for mixture models
        3. Mixture of Bernoulli
        4. Mixture of experts
        5. Latent Dirichlet Allocation
          1. The LDA model
          2. Variational inference
          3. Examples
        6. Summary
      15. A. Appendix
        1. References
          1. Books on the Bayesian theory
          2. Books on machine learning
          3. Papers
      16. Index