book

Learning Probabilistic Graphical Models in R

by David Bellot

April 2016

Beginner to intermediate

250 pages

5h 38m

English

Packt Publishing

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What this book covers

Downloading the example codeErrataPiracyQuestions
Machine learning
Beliefs and uncertainty as probabilitiesConditional probabilityProbability calculus and random variablesSample space, events, and probabilityRandom variables and probability calculusJoint probability distributionsBayes' ruleInterpreting the Bayes' formulaA first example of Bayes' ruleA first example of Bayes' rule in R
Probabilistic modelsGraphs and conditional independenceFactorizing a distributionDirected modelsUndirected modelsExamples and applications
Building graphical modelsTypes of random variableBuilding graphsProbabilistic expert systemBasic structures in probabilistic graphical models
The sprinkler exampleThe medical expert systemModels with more than two layersTree structure
Introduction
How are empirical and model distribution related?The ML algorithm and its implementation in RApplication
Latent variables
Derivation of the EM algorithmApplying EM to graphical models
The Naive Bayes modelRepresentationLearning the Naive Bayes modelBayesian Naive Bayes
The prior distributionThe posterior distribution with the conjugacy propertyWhich values should we choose for the Beta parameters?
Definition
Sampling from a distribution
Standard distributions
An implementation in R
An implementation in R
General idea of the methodThe Metropolis-Hastings algorithm
Installing Stan and RStanA simple example in RStan
Linear regressionEstimating the parameters
Over-fitting a modelGraphical model of a linear modelPosterior distributionImplementation in RA stable implementationMore packages in R
Mixture models
The LDA modelVariational inferenceExamples
ReferencesBooks on the Bayesian theoryBooks on machine learningPapers

Content preview from Learning Probabilistic Graphical Models in R

Rejection sampling

Suppose we want to sample from a distribution that is not a simple one. Let's call this distribution p(x) and let's assume we can evaluate p(x) for any given value x, up to a normalizing constant Z, that is:

In this context, p(x) is too complex to sample from but we have another simpler distribution q(x) from which we can draw samples. Next, we assume there exists a constant k such that for all values of x. The function kq(x) is the comparison function as shown in the following figure: