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