Index
A
- ancestral sampling
- about / Sampling from a distribution
- arm package
- about / More packages in R
B
- basic sampling algorithms
- about / Basic sampling algorithms
- standard distributions / Standard distributions
- Bayes' rule
- conditional probability / Bayes' rule
- formula, interpreting / Interpreting the Bayes' formula
- example / A first example of Bayes' rule
- Bayes' rule, in R
- example / A first example of Bayes' rule in R
- Bayesian Linear models
- about / Bayesian linear models
- over-fitting / Over-fitting a model
- graphical model / Graphical model of a linear model
- posterior distribution / Posterior distribution
- implementation, in R / Implementation in R
- stable implementation / A stable implementation
- packages / More packages in R
- packages, in R / More packages in R
- Bayesian Naive Bayes
- about / Bayesian Naive Bayes
- Bayesian theory
- references / Books on the Bayesian theory
- bayesm package
- about / More packages in R
- Bayes rule
- about / Bayes' rule
- Bernoulli distribution
- about / Beta-Binomial
- Beta-Binomial
- about / Beta-Binomial
- prior distribution / The prior distribution
- posterior distribution, with conjugacy property / The posterior distribution with the conjugacy property
- values, selecting for Beta parameters / Which values should we choose for the Beta parameters?
- Binomial distribution
- about / Beta-Binomial
- Blocked Nose / Graphs and conditional independence
- bnlearn R package
C
- cluster nodes
- about / The junction tree algorithm
- conjugacy property
- continuous random variable
- about / Types of random variable
- Cough / Graphs and conditional independence
D
- d-separation
- about / Building graphs
- Dirichlet distribution
- about / Bayesian Naive Bayes
- discrete random variable
- about / Types of random variable
- discrete random variables / A first example of Bayes' rule
- discrete sepal width (dsw)
- about / Introduction
E
- empirical distribution
- relating, to model distribution / How are empirical and model distribution related?
- Expectation Maximization (EM) algorithm
- with hidden variables / Learning with hidden variables – the EM algorithm
- principles / Principles of the EM algorithm
- derivation / Derivation of the EM algorithm
- applying, to graphical models / Applying EM to graphical models
- for mixture models / EM for mixture models
G
- gating function
- about / Mixture of experts
- Gaussian mixture model
- about / The Gaussian mixture model
- example / The Gaussian mixture model
- defining / Definition
- glmnet package
- about / Posterior distribution, More packages in R
- graphical model
- of Bayesian Linear models / Graphical model of a linear model
- graphical models
- building / Building graphical models
- random variable, types / Types of random variable
- graphs, building / Building graphs
- Expectation Maximization (EM) algorithm, applying to / Applying EM to graphical models
- graphs
- building / Building graphs
- probabilistic expert system / Probabilistic expert system
- probabilistic graphical models, basic structures / Basic structures in probabilistic graphical models
H
- Headache / Graphs and conditional independence
- Hidden Markov Model
- hidden variables
- about / Learning with hidden variables – the EM algorithm
- Expectation Maximization (EM) algorithm, using / Learning with hidden variables – the EM algorithm
- latent variables / Latent variables
I
- importance sampling
- about / Standard distributions, An implementation in R, Importance sampling
- implementation, in R / An implementation in R
- importance weight
- about / Importance sampling
J
- joint probability distribution, uncertainty
- about / Joint probability distributions
- marginalization / Joint probability distributions
- junction tree
- building / The junction tree algorithm
- about / The junction tree algorithm
- junction tree algorithm
- about / The junction tree algorithm
- implementing / The junction tree algorithm
- Junction Tree Algorithm / Examples and applications
K
- Kullback-Leibler divergence
L
- L1-penalization (Lasso)
- about / Estimating the parameters
- L2 penalization
- about / Estimating the parameters
- Lasso
- about / Posterior distribution
- Latent Dirichlet Allocation (LDA)
- about / Latent Dirichlet Allocation
- graphical model / The LDA model
- variational inference / Variational inference
- examples / Examples
- latent variable models
- latent variables
- about / Latent variables
- using / The Gaussian mixture model
- learning by inference
- about / Learning by inference
- probability, estimating / Learning by inference
- likelihood / Interpreting the Bayes' formula
- linear regression
- about / Linear regression
- example / Linear regression
- parameters, estimating / Estimating the parameters
- log-likelihood
- about / Applying EM to graphical models
M
- machine learning
- about / Machine learning
- references / Books on machine learning
- Markov Chain Monte-Carlo (MCMC)
- about / Standard distributions
- Markov Chain Monte Carlo (MCMC)
- about / Importance sampling, Markov Chain Monte-Carlo
- methods / General idea of the method
- Metropolis-Hastings algorithm / The Metropolis-Hastings algorithm
- for probabilistic graphical models / MCMC for probabilistic graphical models in R
- Stan, installing / Installing Stan and RStan
- RStan, installing / Installing Stan and RStan
- Markov Model
- maximum likelihood
- estimation / Maximum likelihood
- empirical distribution, relating to model distribution / How are empirical and model distribution related?
- ML algorithm, implementing / The ML algorithm and its implementation in R
- application / Application
- Maximum Likelihood Estimator (MLE)
- about / Posterior distribution
- medical expert system
- about / The medical expert system
- Metropolis-Hastings algorithm
- mixing proportions
- about / Definition
- mixture components
- about / Definition
- mixture models
- about / Mixture models
- example / Mixture models
- Expectation Maximization (EM) algorithm, using / EM for mixture models
- mixture of Bernoulli
- about / Mixture of Bernoulli
- mixture of experts
- about / Mixture of experts
- ML algorithm
- implementing / The ML algorithm and its implementation in R
- model distribution
- relating, to empirical distribution / How are empirical and model distribution related?
N
- Naive Bayes model
- about / The Naive Bayes model
- example / The Naive Bayes model
- representation / Representation
- implementing / Learning the Naive Bayes model
- Bayesian Naive Bayes / Bayesian Naive Bayes
- Noisy-OR model
- about / The medical expert system
O
- over-fitting
- about / Bayesian Naive Bayes
- solving, with Bayesian Linear models / Over-fitting a model
P
- packages, R
- glmnet package / More packages in R
- bayesm package / More packages in R
- arm package / More packages in R
- parameter learning
- Iris dataset, loading / Introduction
- Iris dataset, estimating / Introduction
- plate notation
- about / Learning by inference
- posterior distribution / Interpreting the Bayes' formula
- with conjugacy property / The posterior distribution with the conjugacy property
- used, with Bayesian Linear models / Posterior distribution
- prior distribution / Interpreting the Bayes' formula
- about / Beta-Binomial, The prior distribution
- probabilistic expert system
- example / Probabilistic expert system
- reference link / Probabilistic expert system
- about / Probabilistic expert system
- probabilistic graphical models
- basic structures / Basic structures in probabilistic graphical models
- Markov Chain Monte Carlo (MCMC) / MCMC for probabilistic graphical models in R
- Probabilistic Graphical Models (PGM)
- about / Probabilistic graphical models
- probabilistic models / Probabilistic models
- graphs and conditional independence / Graphs and conditional independence
- distribution, factorizing / Factorizing a distribution
- directed models / Directed models
- undirected models / Undirected models
- example / Examples and applications
- applications / Examples and applications
- probabilistic graphical models, examples
- sprinkler example / The sprinkler example
- medical expert system / The medical expert system
- models, with more than two layers / Models with more than two layers
- tree structure / Tree structure
- probability calculus, uncertainty
- sample space / Sample space, events, and probability
- realization / Sample space, events, and probability
- event / Sample space, events, and probability
- probability / Sample space, events, and probability
- and random variables / Random variables and probability calculus
- pseudo-random numbers
- about / Basic sampling algorithms
R
- R
- rejection sampling, implementation / An implementation in R
- importance sampling, implementation / An implementation in R
- Markov Chain Monte Carlo (MCMC) / MCMC for probabilistic graphical models in R
- Bayesian Linear models, implementing / Implementation in R
- random variable
- about / Types of random variable
- discrete random variable / Types of random variable
- continuous random variable / Types of random variable
- random variables, uncertainty
- about / Random variables and probability calculus
- probability distribution / Random variables and probability calculus
- rejection sampling
- about / Standard distributions, Rejection sampling
- implementation, in R / An implementation in R
- ridge regression
- about / Estimating the parameters
- RStan
- URL / Installing Stan and RStan
- installing / Installing Stan and RStan
- example / A simple example in RStan
S
- sampling
- from distribution / Sampling from a distribution
- Season / Graphs and conditional independence
- seed
- about / Basic sampling algorithms
- separator nodes
- about / The junction tree algorithm
- Sneezing / Graphs and conditional independence
- sprinkler example
- about / The sprinkler example
- Stan
- installing / Installing Stan and RStan
- standard distributions
- about / Standard distributions
- stop words
- about / The LDA model
- structural learning / Factorizing a distribution
- sum-product variable elimination algorithm
- about / Sum-product and belief updates
- implementing / Sum-product and belief updates
T
- tree structure
- about / Tree structure
U
- uncertainty
- representing, with probabilities / Representing uncertainty with probabilities
- as probabilities / Beliefs and uncertainty as probabilities
- frequentist interpretation / Beliefs and uncertainty as probabilities
- Bayesian interpretation / Beliefs and uncertainty as probabilities
- conditional probability / Conditional probability
- probability calculus / Probability calculus and random variables
- random variables / Random variables and probability calculus
- joint probability distributions / Joint probability distributions
- Bayes' rule / Bayes' rule
V
- variable elimination
- about / Variable elimination
- variational inference
- about / Variational inference