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‎Contents.m

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% CHAPTER01
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% condEntropy - Compute conditional entropy z=H(x|y) of two discrete variables x and y.
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% entropy - Compute entropy z=H(x) of a discrete variable x.
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% jointEntropy - Compute joint entropy z=H(x,y) of two discrete variables x and y.
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% mutInfo - Compute mutual information I(x,y) of two discrete variables x and y.
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% nmi - Compute normalized mutual information I(x,y)/sqrt(H(x)*H(y)) of two discrete variables x and y.
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% nvi - Compute normalized variation information z=(1-I(x,y)/H(x,y)) of two discrete variables x and y.
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% relatEntropy - Compute relative entropy (a.k.a KL divergence) z=KL(p(x)||p(y)) of two discrete variables x and y.
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% CHAPTER02
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% logDirichlet - Compute log pdf of a Dirichlet distribution.
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% logGauss - Compute log pdf of a Gaussian distribution.
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% logKde - Compute log pdf of kernel density estimator.
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% logMn - Compute log pdf of a multinomial distribution.
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% logMvGamma - Compute logarithm multivariate Gamma function
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% logSt - Compute log pdf of a Student's t distribution.
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% logVmf - Compute log pdf of a von Mises-Fisher distribution.
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% logWishart - Compute log pdf of a Wishart distribution.
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% CHAPTER03
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% linReg - Fit linear regression model y=w'x+w0
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% linRegFp - Fit empirical Bayesian linear model with Mackay fixed point method (p.168)
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% linRegPred - Compute linear regression model reponse y = w'*X+w0 and likelihood
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% linRnd - Generate data from a linear model p(t|w,x)=G(w'x+w0,sigma), sigma=sqrt(1/beta)
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% CHAPTER04
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% binPlot - Plot binary classification result for 2d data
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% fda - Fisher (linear) discriminant analysis
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% logitBin - Logistic regression for binary classification optimized by Newton-Raphson method.
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% logitBinPred - Prediction of binary logistic regression model
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% logitMn - Multinomial regression for multiclass problem (Multinomial likelihood)
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% logitMnPred - Prediction of multiclass (multinomial) logistic regression model
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% sigmoid - Sigmod function
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% softmax - Softmax function
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% CHAPTER05
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% mlpReg - Train a multilayer perceptron neural network
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% mlpRegPred - Multilayer perceptron prediction
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% CHAPTER06
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% kn2sd - Transform a kernel matrix (or inner product matrix) to a squared distance matrix
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% knCenter - Centerize the data in the kernel space
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% knGauss - Gaussian (RBF) kernel K = exp(-|x-y|/(2s));
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% knKmeans - Perform kernel kmeans clustering.
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% knKmeansPred - Prediction for kernel kmeans clusterng
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% knLin - Linear kernel (inner product)
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% knPca - Kernel PCA
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% knPcaPred - Prediction for kernel PCA
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% knPoly - Polynomial kernel k(x,y)=(x'y+c)^o
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% knReg - Gaussian process (kernel) regression
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% knRegPred - Prediction for Gaussian Process (kernel) regression model
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% sd2kn - Transform a squared distance matrix to a kernel matrix.
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% CHAPTER07
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% rvmBinFp - Relevance Vector Machine (ARD sparse prior) for binary classification.
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% rvmBinPred - Prodict the label for binary logistic regression model
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% rvmRegFp - Relevance Vector Machine (ARD sparse prior) for regression
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% rvmRegPred - Compute RVM regression model reponse y = w'*X+w0 and likelihood
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% rvmRegSeq - Sparse Bayesian Regression (RVM) using sequential algorithm
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% CHAPTER08
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% MRF
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% mrfBethe - Compute Bethe energy
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% mrfBp - Undirected graph belief propagation for MRF
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% mrfGibbs - Compute Gibbs energy
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% mrfIsGa - Contruct a latent Ising MRF with Gaussian observation
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% mrfMf - Mean field for MRF
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% NaiveBayes
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% nbBern - Naive bayes classifier with indepenet Bernoulli.
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% nbBernPred - Prediction of naive Bayes classifier with independent Bernoulli.
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% nbGauss - Naive bayes classifier with indepenet Gaussian
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% nbGaussPred - Prediction of naive Bayes classifier with independent Gaussian.
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% CHAPTER09
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% kmeans - Perform kmeans clustering.
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% kmeansPred - Prediction for kmeans clusterng
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% kmeansRnd - Generate samples from a Gaussian mixture distribution with common variances (kmeans model).
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% kmedoids - Perform k-medoids clustering.
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% kseeds - Perform kmeans++ seeding
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% linRegEm - Fit empirical Bayesian linear regression model with EM (p.448 chapter 9.3.4)
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% mixBernEm - Perform EM algorithm for fitting the Bernoulli mixture model.
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% mixBernRnd - Generate samples from a Bernoulli mixture distribution.
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% mixGaussEm - Perform EM algorithm for fitting the Gaussian mixture model.
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% mixGaussPred - Predict label and responsibility for Gaussian mixture model.
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% mixGaussRnd - Genarate samples form a Gaussian mixture model.
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% rvmBinEm - Relevance Vector Machine (ARD sparse prior) for binary classification.
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% rvmRegEm - Relevance Vector Machine (ARD sparse prior) for regression
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% CHAPTER10
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% linRegVb - Variational Bayesian inference for linear regression.
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% mixGaussEvidence - Variational lower bound of the model evidence (log of marginal likelihood)
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% mixGaussVb - Variational Bayesian inference for Gaussian mixture.
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% mixGaussVbPred - Predict label and responsibility for Gaussian mixture model trained by VB.
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% rvmRegVb - Variational Bayesian inference for RVM regression.
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% CHAPTER11
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% dirichletRnd - Generate samples from a Dirichlet distribution.
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% discreteRnd - Generate samples from a discrete distribution (multinomial).
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% Gauss - Class for Gaussian distribution used by Dirichlet process
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% gaussRnd - Generate samples from a Gaussian distribution.
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% GaussWishart - Class for Gaussian-Wishart distribution used by Dirichlet process
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% mixDpGb - Collapsed Gibbs sampling for Dirichlet process (infinite) mixture model.
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% mixDpGbOl - Online collapsed Gibbs sampling for Dirichlet process (infinite) mixture model.
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% mixGaussGb - Collapsed Gibbs sampling for Dirichlet process (infinite) Gaussian mixture model (a.k.a. DPGM).
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% mixGaussSample - Genarate samples form a Gaussian mixture model with GaussianWishart prior.
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% CHAPTER12
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% fa - Perform EM algorithm for factor analysis model
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% pca - Principal component analysis
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% pcaEm - Perform EM-like algorithm for PCA (by Sam Roweis).
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% pcaEmC - Perform Constrained EM like algorithm for PCA.
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% ppcaEm - Perform EM algorithm to maiximize likelihood of probabilistic PCA model.
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% ppcaRnd - Generate data from probabilistic PCA model
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% ppcaVb - Perform variatioanl Bayeisan inference for probabilistic PCA model.
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% CHAPTER13
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% HMM
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% hmmEm - EM algorithm to fit the parameters of HMM model (a.k.a Baum-Welch algorithm)
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% hmmFilter - HMM forward filtering algorithm.
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% hmmRnd - Generate a data sequence from a hidden Markov model.
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% hmmSmoother - HMM smoothing alogrithm (normalized forward-backward or normalized alpha-beta algorithm).
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% hmmViterbi - Viterbi algorithm (calculated in log scale to improve numerical stability).
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% LDS
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% kalmanFilter - Kalman filter (forward algorithm for linear dynamic system)
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% kalmanSmoother - Kalman smoother (forward-backward algorithm for linear dynamic system)
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% ldsEm - EM algorithm for parameter estimation of linear dynamic system.
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% ldsPca - Subspace method for learning linear dynamic system.
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% ldsRnd - Generate a data sequence from linear dynamic system.
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% CHAPTER14
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% adaboostBin - Adaboost for binary classification (weak learner: kmeans)
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% adaboostBinPred - Prediction of binary Adaboost
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% mixLinPred - Prediction function for mxiture of linear regression
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% mixLinReg - Mixture of linear regression
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% mixLinRnd - Generate data from mixture of linear model
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% mixLogitBin - Mixture of logistic regression model for binary classification optimized by Newton-Raphson method
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% mixLogitBinPred - Prediction function for mixture of logistic regression

‎chapter07/rvmRegSeq.m

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function [model, llh] = rvmRegSeq(X, t)
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% TODO: beta is not updated.
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% Sparse Bayesian Regression (RVM) using sequential algorithm
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% Input:
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% X: d x n data

‎chapter08/NaiveBayes/nbGauss.m

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function model = nbGauss(X, t)
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% Naive bayes classifier with indepenet Gaussian, each dimension of data is
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% assumed from a 1d Gaussian distribution with independent mean and variance.
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% Naive bayes classifier with indepenet Gaussian
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% Each dimension of data is assumed from a 1d Gaussian distribution with independent mean and variance.
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% Input:
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% X: d x n data matrix
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% t: 1 x n label (1~k)

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