• Cover Page
• Half Title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• 1 Introduction
  • 1.1 Machine learning: what and why?
    • 1.1.1 Types of machine learning
  • 1.2 Supervised learning
    • 1.2.1 Classification
    • 1.2.2 Regression
  • 1.3 Unsupervised learning
    • 1.3.1 Discovering clusters
    • 1.3.2 Discovering latent factors
    • 1.3.3 Discovering graph structure
    • 1.3.4 Matrix completion
  • 1.4 Some basic concepts in machine learning
    • 1.4.1 Parametric vs non-parametric models
    • 1.4.2 A simple non-parametric classifier: K-nearest neighbors
    • 1.4.3 The curse of dimensionality
    • 1.4.4 Parametric models for classification and regression
    • 1.4.5 Linear regression
    • 1.4.6 Logistic regression
    • 1.4.7 Overfitting
    • 1.4.8 Model selection
    • 1.4.9 No free lunch theorem
• 2 Probability
  • 2.1 Introduction
  • 2.2 A brief review of probability theory
    • 2.2.1 Discrete random var
    • 2.2.2 Fundamental rules
    • 2.2.3 Bayes rule
    • 2.2.4 Independence and conditional independence
    • 2.2.5 Continuous random variables
    • 2.2.6 Quantiles
    • 2.2.7 Mean and variance
  • 2.3 Some common discrete distributions
    • 2.3.1 The binomial and Bernoulli distributions
    • 2.3.2 The multinomial and multinoulli distributions
    • 2.3.3 The Poisson distribution
    • 2.3.4 The empirical distribution
  • 2.4 Some common continuous distributions
    • 2.4.1 Gaussian (normal) distribution
    • 2.4.2 Degenerate pdf
    • 2.4.3 The Laplace distribution
    • 2.4.4 The gamma distribution
    • 2.4.5 The beta distribution
    • 2.4.6 Pareto distribution
  • 2.5 Joint probability distributions
    • 2.5.1 Covariance and correlation
    • 2.5.2 The multivariate Gaussian
    • 2.5.3 Multivariate Student t distribution
    • 2.5.4 Dirichlet distribution
  • 2.6 Transformations of random variables
    • 2.6.1 Linear transformations
    • 2.6.2 General transformations
    • 2.6.3 Central limit theorem
  • 2.7 Monte Carlo approximation
    • 2.7.1 Example: change of variables, the MC way
    • 2.7.2 Example: estimating π by Monte Carlo integration
    • 2.7.3 Accuracy of Monte Carlo approximation
  • 2.8 Information theory
    • 2.8.1 Entropy
    • 2.8.2 KL divergence
    • 2.8.3 Mutual information
• 3 Generative Models for Discrete Data
  • 3.1 Introduction
  • 3.2 Bayesian concept learning
    • 3.2.1 Likelihood
    • 3.2.2 Prior
    • 3.2.3 Posterior
    • 3.2.4 Posterior predictive distribution
    • 3.2.5 A more complex prior
  • 3.3 The beta-binomial model
    • 3.3.1 Likelihood
    • 3.3.2 Prior
    • 3.3.3 Posterior
    • 3.3.4 Posterior predictive distribution
  • 3.4 The Dirichlet-multinomial model
    • 3.4.1 Likelihood
    • 3.4.2 Prior
    • 3.4.3 Posterior
    • 3.4.4 Posterior predictive
  • 3.5 Naive Bayes classifiers
    • 3.5.1 Model fitting
    • 3.5.2 Using the model for prediction
    • 3.5.3 The log-sum-exp trick
    • 3.5.4 Feature selection using mutual information
    • 3.5.5 Classifying documents using bag of words
• 4 Gaussian Models
  • 4.1 Introduction
    • 4.1.1 Notation
    • 4.1.2 Basics
    • 4.1.3 MLE for an MVN
    • 4.1.4 Maximum entropy derivation of the Gaussian *
  • 4.2 Gaussian discriminant analysis
    • 4.2.1 Quadratic discriminant analysis (QDA)
    • 4.2.2 Linear discriminant analysis (LDA)
    • 4.2.3 Two-class LDA
    • 4.2.4 MLE for discriminant analysis
    • 4.2.5 Strategies for preventing overfitting
    • 4.2.6 Regularized LDA *
    • 4.2.7 Diagonal LDA
    • 4.2.8 Nearest shrunken centroids classifier *
  • 4.3 Inference in jointly Gaussian distributions
    • 4.3.1 Statement of the result
    • 4.3.2 Examples
    • 4.3.3 Information form
    • 4.3.4 Proof of the result *
  • 4.4 Linear Gaussian systems
    • 4.4.1 Statement of the result
    • 4.4.2 Examples
    • 4.4.3 Proof of the result *
  • 4.5 Digression: The Wishart distribution *
    • 4.5.1 Inverse Wishart distribution
    • 4.5.2 Visualizing the Wishart distribution *
  • 4.6 Inferring the parameters of an MVN
    • 4.6.1 Posterior distribution of μ
    • 4.6.2 Posterior distribution of Σ *
    • 4.6.3 Posterior distribution of μ and Σ *
    • 4.6.4 Sensor fusion with unknown precisions *
• 5 Bayesian Statistics
  • 5.1 Introduction
  • 5.2 Summarizing posterior distributions
    • 5.2.1 MAP estimation
    • 5.2.2 Credible intervals
    • 5.2.3 Inference for a difference in proportions
  • 5.3 Bayesian model selection
    • 5.3.1 Bayesian Occam’s razor
    • 5.3.2 Computing the marginal likelihood (evidence)
    • 5.3.3 Bayes factors
    • 5.3.4 Jeffreys-Lindley paradox *
  • 5.4 Priors
    • 5.4.1 Uninformative priors
    • 5.4.2 Jeffreys priors *
    • 5.4.3 Robust priors
    • 5.4.4 Mixtures of conjugate priors
  • 5.5 Hierarchical Bayes
    • 5.5.1 Example: modeling related cancer rates
  • 5.6 Empirical Bayes
    • 5.6.1 Example: beta-binomial model
    • 5.6.2 Example: Gaussian-Gaussian model
  • 5.7 Bayesian decision theory
    • 5.7.1 Bayes estimators for common loss functions
    • 5.7.2 The false positive vs false negative tradeoff
    • 5.7.3 Other topics *
• 6 Frequentist Statistics
  • 6.1 Introduction
  • 6.2 Sampling distribution of an estimator
    • 6.2.1 Bootstrap
    • 6.2.2 Large sample theory for the MLE *
  • 6.3 Frequentist decision theory
    • 6.3.1 Bayes risk
    • 6.3.2 Minimax risk
    • 6.3.3 Admissible estimators
  • 6.4 Desirable properties of estimators
    • 6.4.1 Consistent estimators
    • 6.4.2 Unbiased estimators
    • 6.4.3 Minimum variance estimators
    • 6.4.4 The bias-variance tradeoff
  • 6.5 Empirical risk minimization
    • 6.5.1 Regularized risk minimization
    • 6.5.2 Structural risk minimization
    • 6.5.3 Estimating the risk using cross validation
    • 6.5.4 Upper bounding the risk using statistical learning theory *
    • 6.5.5 Surrogate loss functions
  • 6.6 Pathologies of frequentist statistics *
    • 6.6.1 Counter-intuitive behavior of confidence intervals
    • 6.6.2 p-values considered harmful
    • 6.6.3 The likelihood principle
    • 6.6.4 Why isn’t everyone a Bayesian?
• 7 Linear Regression
  • 7.1 Introduction
  • 7.2 Model specification
  • 7.3 Maximum likelihood estimation (least squares)
    • 7.3.1 Derivation of the MLE
    • 7.3.2 Geometric interpretation
    • 7.3.3 Convexity
  • 7.4 Robust linear regression *
  • 7.5 Ridge regression
    • 7.5.1 Basic idea
    • 7.5.2 Numerically stable computation *
    • 7.5.3 Connection with PCA *
    • 7.5.4 Regularization effects of big data
  • 7.6 Bayesian linear regression
    • 7.6.1 Computing the posterior
    • 7.6.2 Computing the posterior predictive
    • 7.6.3 Bayesian inference when σ2 is unknown *
    • 7.6.4 EB for linear regression (evidence procedure)
• 8 Logistic Regression
  • 8.1 Introduction
  • 8.2 Model specification
  • 8.3 Model fitting
    • 8.3.1 MLE
    • 8.3.2 Steepest descent
    • 8.3.3 Newton’s method
    • 8.3.4 Iteratively reweighted least squares (IRLS)
    • 8.3.5 Quasi-Newton (variable metric) methods
    • 8.3.6 2e regularization
    • 8.3.7 Multi-class logistic regression
  • 8.4 Bayesian logistic regression
    • 8.4.1 Laplace approximation
    • 8.4.2 Derivation of the BIC
    • 8.4.3 Gaussian approximation for logistic regression
    • 8.4.4 Approximating the posterior predictive
    • 8.4.5 Residual analysis (outlier detection) *
  • 8.5 Online learning and stochastic optimization
    • 8.5.1 Online learning and regret minimization
    • 8.5.2 Stochastic optimization and risk minimization
    • 8.5.3 The LMS algorithm
    • 8.5.4 The perceptron algorithm
    • 8.5.5 A Bayesian view
  • 8.6 Generative vs discriminative classifiers
    • 8.6.1 Pros and cons of each approach
    • 8.6.2 Dealing with missing data
    • 8.6.3 Fisher’s linear discriminant analysis (FLDA) *
• 9 Generalized Linear Models and the Exponential Family
  • 9.1 Introduction
  • 9.2 The exponential family
    • 9.2.1 Definition
    • 9.2.2 Examples
    • 9.2.3 Log partition function
    • 9.2.4 MLE for the exponential family
    • 9.2.5 Bayes for the exponential family *
    • 9.2.6 Maximum entropy derivation of the exponential family *
  • 9.3 Generalized linear models (GLMs)
    • 9.3.1 Basics
    • 9.3.2 ML and MAP estimation
    • 9.3.3 Bayesian inference
  • 9.4 Probit regression
    • 9.4.1 ML/MAP estimation using gradient-based optimization
    • 9.4.2 Latent variable interpretation
    • 9.4.3 Ordinal probit regression *
    • 9.4.4 Multinomial probit models *
  • 9.5 Multi-task learning
    • 9.5.1 Hierarchical Bayes for multi-task learning
    • 9.5.2 Application to personalized email spam filtering
    • 9.5.3 Application to domain adaptation
    • 9.5.4 Other kinds of prior
  • 9.6 Generalized linear mixed models *
    • 9.6.1 Example: semi-parametric GLMMs for medical data
    • 9.6.2 Computational issues
  • 9.7 Learning to rank *
    • 9.7.1 The pointwise approach
    • 9.7.2 The pairwise approach
    • 9.7.3 The listwise approach
    • 9.7.4 Loss functions for ranking
• 10 Directed Graphical Models (Bayes Nets)
  • 10.1 Introduction
    • 10.1.1 Chain rule
    • 10.1.2 Conditional independence
    • 10.1.3 Graphical models
    • 10.1.4 Graph terminology
    • 10.1.5 Directed graphical models
  • 10.2 Examples
    • 10.2.1 Naive Bayes classifiers
    • 10.2.2 Markov and hidden Markov models
    • 10.2.3 Medical diagnosis
    • 10.2.4 Genetic linkage analysis *
    • 10.2.5 Directed Gaussian graphical models *
  • 10.3 Inference
  • 10.4 Learning
    • 10.4.1 Plate notation
    • 10.4.2 Learning from complete data
    • 10.4.3 Learning with missing and/or latent variables
  • 10.5 Conditional independence properties of DGMs
    • 10.5.1 d-separation and the Bayes Ball algorithm (global Markov properties)
    • 10.5.2 Other Markov properties of DGMs
    • 10.5.3 Markov blanket and full conditionals
  • 10.6 Influence (decision) diagrams *
• 11 Mixture Models and the EM Algorithm
  • 11.1 Latent variable models
  • 11.2 Mixture models
    • 11.2.1 Mixtures of Gaussians
    • 11.2.2 Mixture of multinoullis
    • 11.2.3 Using mixture models for clustering
    • 11.2.4 Mixtures of experts
  • 11.3 Parameter estimation for mixture models
    • 11.3.1 Unidentifiability
    • 11.3.2 Computing a MAP estimate is non-convex
  • 11.4 The EM algorithm
    • 11.4.1 Basic idea
    • 11.4.2 EM for GMMs
    • 11.4.3 EM for mixture of experts
    • 11.4.4 EM for DGMs with hidden variables
    • 11.4.5 EM for the Student distribution *
    • 11.4.6 EM for probit regression *
    • 11.4.7 Theoretical basis for EM *
    • 11.4.8 Online EM
    • 11.4.9 Other EM variants *
  • 11.5 Model selection for latent variable models
    • 11.5.1 Model selection for probabilistic models
    • 11.5.2 Model selection for non-probabilistic methods
  • 11.6 Fitting models with missing data
    • 11.6.1 EM for the MLE of an MVN with missing data
• 12 Latent Linear Models
  • 12.1 Factor analysis
    • 12.1.1 FA is a low rank parameterization of an MVN
    • 12.1.2 Inference of the latent factors
    • 12.1.3 Unidentifiability
    • 12.1.4 Mixtures of factor analysers
    • 12.1.5 EM for factor analysis models
    • 12.1.6 Fitting FA models with missing data
  • 12.2 Principal components analysis (PCA)
    • 12.2.1 Classical PCA: statement of the theorem
    • 12.2.2 Proof *
    • 12.2.3 Singular value decomposition (SVD)
    • 12.2.4 Probabilistic PCA
    • 12.2.5 EM algorithm for PCA
  • 12.3 Choosing the number of latent dimensions
    • 12.3.1 Model selection for FA/PPCA
    • 12.3.2 Model selection for PCA
  • 12.4 PCA for categorical data
  • 12.5 PCA for paired and multi-view data
    • 12.5.1 Supervised PCA (latent factor regression)
    • 12.5.2 Partial least squares
    • 12.5.3 Canonical correlation analysis
  • 12.6 Independent Component Analysis (ICA)
    • 12.6.1 Maximum likelihood estimation
    • 12.6.2 The FastICA algorithm
    • 12.6.3 Using EM
    • 12.6.4 Other estimation principles *
• 13 Sparse Linear Models
  • 13.1 Introduction
  • 13.2 Bayesian variable selection
    • 13.2.1 The spike and slab model
    • 13.2.2 From the Bernoulli-Gaussian model to 0 regularization
    • 13.2.3 Algorithms
  • 13.3 e1 regularization: basics
    • 13.3.1 Why does e1 regularization yield sparse solutions?
    • 13.3.2 Optimality conditions for lasso
    • 13.3.3 Comparison of least squares, lasso, ridge and subset selection
    • 13.3.4 Regularization path
    • 13.3.5 Model selection
    • 13.3.6 Bayesian inference for linear models with Laplace priors
  • 13.4 e1 regularization: algorithms
    • 13.4.1 Coordinate descent
    • 13.4.2 LARS and other homotopy methods
    • 13.4.3 Proximal and gradient projection methods
    • 13.4.4 EM for lasso
  • 13.5 e1 regularization: extensions
    • 13.5.1 Group Lasso
    • 13.5.2 Fused lasso
    • 13.5.3 Elastic net (ridge and lasso combined)
  • 13.6 Non-convex regularizers
    • 13.6.1 Bridge regression
    • 13.6.2 Hierarchical adaptive lasso
    • 13.6.3 Other hierarchical priors
  • 13.7 Automatic relevance determination (ARD)/sparse Bayesian learning (SBL)
    • 13.7.1 ARD for linear regression
    • 13.7.2 Whence sparsity?
    • 13.7.3 Connection to MAP estimation
    • 13.7.4 Algorithms for ARD *
    • 13.7.5 ARD for logistic regression
  • 13.8 Sparse coding *
    • 13.8.1 Learning a sparse coding dictionary
    • 13.8.2 Results of dictionary learning from image patches
    • 13.8.3 Compressed sensing
    • 13.8.4 Image inpainting and denoising
• 14 Kernels
  • 14.1 Introduction
  • 14.2 Kernel functions
    • 14.2.1 RBF kernels
    • 14.2.2 Kernels for comparing documents
    • 14.2.3 Mercer (positive definite) kernels
    • 14.2.4 Linear kernels
    • 14.2.5 Matern kernels
    • 14.2.6 String kernels
    • 14.2.7 Pyramid match kernels
    • 14.2.8 Kernels derived from probabilistic generative models
  • 14.3 Using kernels inside GLMs
    • 14.3.1 Kernel machines
    • 14.3.2 L1VMs, RVMs, and other sparse vector machines
  • 14.4 The kernel trick
    • 14.4.1 Kernelized nearest neighbor classification
    • 14.4.2 Kernelized K-medoids clustering
    • 14.4.3 Kernelized ridge regression
    • 14.4.4 Kernel PCA
  • 14.5 Support vector machines (SVMs)
    • 14.5.1 SVMs for regression
    • 14.5.2 SVMs for classification
    • 14.5.3 Choosing C
    • 14.5.4 Summary of key points
    • 14.5.5 A probabilistic interpretation of SVMs
  • 14.6 Comparison of discriminative kernel methods
  • 14.7 Kernels for building generative models
    • 14.7.1 Smoothing kernels
    • 14.7.2 Kernel density estimation (KDE)
    • 14.7.3 From KDE to KNN
    • 14.7.4 Kernel regression
    • 14.7.5 Locally weighted regression
• 15 Gaussian Processes
  • 15.1 Introduction
  • 15.2 GPs for regression
    • 15.2.1 Predictions using noise-free observations
    • 15.2.2 Predictions using noisy observations
    • 15.2.3 Effect of the kernel parameters
    • 15.2.4 Estimating the kernel parameters
    • 15.2.5 Computational and numerical issues *
    • 15.2.6 Semi-parametric GPs *
  • 15.3 GPs meet GLMs
    • 15.3.1 Binary classification
    • 15.3.2 Multi-class classification
    • 15.3.3 GPs for Poisson regression
  • 15.4 Connection with other methods
    • 15.4.1 Linear models compared to GPs
    • 15.4.2 Linear smoothers compared to GPs
    • 15.4.3 SVMs compared to GPs
    • 15.4.4 L1VM and RVMs compared to GPs
    • 15.4.5 Neural networks compared to GPs
    • 15.4.6 Smoothing splines compared to GPs *
    • 15.4.7 RKHS methods compared to GPs *
  • 15.5 GP latent variable model
  • 15.6 Approximation methods for large datasets
• 16 Adaptive Basis Function Models
  • 16.1 Introduction
  • 16.2 Classification and regression trees (CART)
    • 16.2.1 Basics
    • 16.2.2 Growing a tree
    • 16.2.3 Pruning a tree
    • 16.2.4 Pros and cons of trees
    • 16.2.5 Random forests
    • 16.2.6 CART compared to hierarchical mixture of experts *
  • 16.3 Generalized additive models
    • 16.3.1 Backfitting
    • 16.3.2 Computational efficiency
    • 16.3.3 Multivariate adaptive regression splines (MARS)
  • 16.4 Boosting
    • 16.4.1 Forward stagewise additive modeling
    • 16.4.2 L2boosting
    • 16.4.3 AdaBoost
    • 16.4.4 LogitBoost
    • 16.4.5 Boosting as functional gradient descent
    • 16.4.6 Sparse boosting
    • 16.4.7 Multivariate adaptive regression trees (MART)
    • 16.4.8 Why does boosting work so well?
    • 16.4.9 A Bayesian view
  • 16.5 Feedforward neural networks (multilayer perceptrons)
    • 16.5.1 Convolutional neural networks
    • 16.5.2 Other kinds of neural networks
    • 16.5.3 A brief history of the field
    • 16.5.4 The backpropagation algorithm
    • 16.5.5 Identifiability
    • 16.5.6 Regularization
    • 16.5.7 Bayesian inference
  • 16.6 Ensemble learning
    • 16.6.1 Stacking
    • 16.6.2 Error-correcting output codes
    • 16.6.3 Ensemble learning is not equivalent to Bayes model averaging
  • 16.7 Experimental comparison
    • 16.7.1 Low-dimensional features
    • 16.7.2 High-dimensional features
  • 16.8 Interpreting black-box models
• 17 Markov and Hidden Markov Models
  • 17.1 Introduction
  • 17.2 Markov models
    • 17.2.1 Transition matrix
    • 17.2.2 Application: Language modeling
    • 17.2.3 Stationary distribution of a Markov chain *
    • 17.2.4 Application: Google’s PageRank algorithm for web page ranking
  • 17.3 Hidden Markov models
    • 17.3.1 Applications of HMMs
  • 17.4 Inference in HMMs
    • 17.4.1 Types of inference problems for temporal models
    • 17.4.2 The forwards algorithm
    • 17.4.3 The forwards-backwards algorithm
    • 17.4.4 The Viterbi algorithm
    • 17.4.5 Forwards filtering, backwards sampling
  • 17.5 Learning for HMMs
    • 17.5.1 Training with fully observed data
    • 17.5.2 EM for HMMs (the Baum-Welch algorithm)
    • 17.5.3 Bayesian methods for “fitting” HMMs *
    • 17.5.4 Discriminative training
    • 17.5.5 Model selection
  • 17.6 Generalizations of HMMs
    • 17.6.1 Variable duration (semi-Markov) HMMs
    • 17.6.2 Hierarchical HMMs
    • 17.6.3 Input-output HMMs
    • 17.6.4 Auto-regressive and buried HMMs
    • 17.6.5 Factorial HMM
    • 17.6.6 Coupled HMM and the influence model
    • 17.6.7 Dynamic Bayesian networks (DBNs)
• 18 State Space Models
  • 18.1 Introduction
  • 18.2 Applications of SSMs
    • 18.2.1 SSMs for object tracking
    • 18.2.2 Robotic SLAM
    • 18.2.3 Online parameter learning using recursive least squares
    • 18.2.4 SSM for time series forecasting *
  • 18.3 Inference in LG-SSM
    • 18.3.1 The Kalman filtering algorithm
    • 18.3.2 The Kalman smoothing algorithm
  • 18.4 Learning for LG-SSM
    • 18.4.1 Identifiability and numerical stability
    • 18.4.2 Training with fully observed data
    • 18.4.3 EM for LG-SSM
    • 18.4.4 Subspace methods
    • 18.4.5 Bayesian methods for “fitting” LG-SSMs
  • 18.5 Approximate online inference for non-linear, non-Gaussian SSMs
    • 18.5.1 Extended Kalman filter (EKF)
    • 18.5.2 Unscented Kalman filter (UKF)
    • 18.5.3 Assumed density filtering (ADF)
  • 18.6 Hybrid discrete/continuous SSMs
    • 18.6.1 Inference
    • 18.6.2 Application: data association and multi-target tracking
    • 18.6.3 Application: fault diagnosis
    • 18.6.4 Application: econometric forecasting
• 19 Undirected Graphical Models (Markov Random Fields)
  • 19.1 Introduction
  • 19.2 Conditional independence properties of UGMs
    • 19.2.1 Key properties
    • 19.2.2 An undirected alternative to d-separation
    • 19.2.3 Comparing directed and undirected graphical models
  • 19.3 Parameterization of MRFs
    • 19.3.1 The Hammersley-Clifford theorem
    • 19.3.2 Representing potential functions
  • 19.4 Examples of MRFs
    • 19.4.1 Ising model
    • 19.4.2 Hopfield networks
    • 19.4.3 Potts model
    • 19.4.4 Gaussian MRFs
    • 19.4.5 Markov logic networks *
  • 19.5 Learning
    • 19.5.1 Training maxent models using gradient methods
    • 19.5.2 Training partially observed maxent models
    • 19.5.3 Approximate methods for computing the MLEs of MRFs
    • 19.5.4 Pseudo likelihood
    • 19.5.5 Stochastic maximum likelihood
    • 19.5.6 Feature induction for maxent models *
    • 19.5.7 Iterative proportional fitting (IPF) *
  • 19.6 Conditional random fields (CRFs)
    • 19.6.1 Chain-structured CRFs, MEMMs and the label-bias problem
    • 19.6.2 Applications of CRFs
    • 19.6.3 CRF training
  • 19.7 Structural SVMs
    • 19.7.1 SSVMs: a probabilistic view
    • 19.7.2 SSVMs: a non-probabilistic view
    • 19.7.3 Cutting plane methods for fitting SSVMs
    • 19.7.4 Online algorithms for fitting SSVMs
    • 19.7.5 Latent structural SVMs
• 20 Exact Inference for Graphical Models
  • 20.1 Introduction
  • 20.2 Belief propagation for trees
    • 20.2.1 Serial protocol
    • 20.2.2 Parallel protocol
    • 20.2.3 Gaussian BP *
    • 20.2.4 Other BP variants *
  • 20.3 The variable elimination algorithm
    • 20.3.1 The generalized distributive law *
    • 20.3.2 Computational complexity of VE
    • 20.3.3 A weakness of VE
  • 20.4 The junction tree algorithm *
    • 20.4.1 Creating a junction tree
    • 20.4.2 Message passing on a junction tree
    • 20.4.3 Computational complexity of JTA
    • 20.4.4 JTA generalizations *
  • 20.5 Computational intractability of exact inference in the worst case
    • 20.5.1 Approximate inference
• 21 Variational Inference
  • 21.1 Introduction
  • 21.2 Variational inference
    • 21.2.1 Alternative interpretations of the variational objective
    • 21.2.2 Forward or reverse KL? *
  • 21.3 The mean field method
    • 21.3.1 Derivation of the mean field update equations
    • 21.3.2 Example: mean field for the Ising model
  • 21.4 Structured mean field *
    • 21.4.1 Example: factorial HMM
  • 21.5 Variational Bayes
    • 21.5.1 Example: VB for a univariate Gaussian
    • 21.5.2 Example: VB for linear regression
  • 21.6 Variational Bayes EM
    • 21.6.1 Example: VBEM for mixtures of Gaussians *
  • 21.7 Variational message passing and VIBES
  • 21.8 Local variational bounds *
    • 21.8.1 Motivating applications
    • 21.8.2 Bohning’s quadratic bound to the log-sum-exp function
    • 21.8.3 Bounds for the sigmoid function
    • 21.8.4 Other bounds and approximations to the log-sum-exp function
    • 21.8.5 Variational inference based on upper bounds
• 22 More Variational Inference
  • 22.1 Introduction
  • 22.2 Loopy belief propagation: algorithmic issues
    • 22.2.1 A brief history
    • 22.2.2 LBP on pairwise models
    • 22.2.3 LBP on a factor graph
    • 22.2.4 Convergence
    • 22.2.5 Accuracy of LBP
    • 22.2.6 Other speedup tricks for LBP *
  • 22.3 Loopy belief propagation: theoretical issues *
    • 22.3.1 UGMs represented in exponential family form
    • 22.3.2 The marginal polytope
    • 22.3.3 Exact inference as a variational optimization problem
    • 22.3.4 Mean field as a variational optimization problem
    • 22.3.5 LBP as a variational optimization problem
    • 22.3.6 Loopy BP vs mean field
  • 22.4 Extensions of belief propagation *
    • 22.4.1 Generalized belief propagation
    • 22.4.2 Convex belief propagation
  • 22.5 Expectation propagation
    • 22.5.1 EP as a variational inference p
    • 22.5.2 Optimizing the EP objective using moment matching
    • 22.5.3 EP for the clutter problem
    • 22.5.4 LBP is a special case of EP
    • 22.5.5 Ranking players using TrueSkill
    • 22.5.6 Other applications of EP
  • 22.6 MAP state estimation
    • 22.6.1 Linear programming relaxation
    • 22.6.2 Max-product belief propagation
    • 22.6.3 Graphcuts
    • 22.6.4 Experimental comparison of graphcuts and BP
    • 22.6.5 Dual decomposition
• 23 Monte Carlo Inference
  • 23.1 Introduction
  • 23.2 Sampling from standard distributions
    • 23.2.1 Using the cdf
    • 23.2.2 Sampling from a Gaussian (Box-Muller method)
  • 23.3 Rejection sampling
    • 23.3.1 Basic idea
    • 23.3.2 Example
    • 23.3.3 Application to Bayesian statistics
    • 23.3.4 Adaptive rejection sampling
    • 23.3.5 Rejection sampling in high dimensions
  • 23.4 Importance sampling
    • 23.4.1 Basic idea
    • 23.4.2 Handling unnormalized distributions
    • 23.4.3 Importance sampling for a DGM: likelihood weighting
    • 23.4.4 Sampling importance resampling (SIR)
  • 23.5 Particle filtering
    • 23.5.1 Sequential importance sampling
    • 23.5.2 The degeneracy problem
    • 23.5.3 The resampling step
    • 23.5.4 The proposal distribution
    • 23.5.5 Application: robot localization
    • 23.5.6 Application: visual object tracking
    • 23.5.7 Application: time series forecasting
  • 23.6 Rao-Blackwellised particle filtering (RBPF)
    • 23.6.1 RBPF for switching LG-SSMs
    • 23.6.2 Application: tracking a maneuvering target
    • 23.6.3 Application: Fast SLAM
• 24 Markov Chain Monte Carlo (MCMC) Inference
  • 24.1 Introduction
  • 24.2 Gibbs sampling
    • 24.2.1 Basic idea
    • 24.2.2 Example: Gibbs sampling for the Ising model
    • 24.2.3 Example: Gibbs sampling for inferring the parameters of a GMM
    • 24.2.4 Collapsed Gibbs sampling *
    • 24.2.5 Gibbs sampling for hierarchical GLMs
    • 24.2.6 BUGS and JAGS
    • 24.2.7 The Imputation Posterior (IP) algorithm
    • 24.2.8 Blocking Gibbs sampling
  • 24.3 Metropolis Hastings algorithm
    • 24.3.1 Basic idea
    • 24.3.2 Gibbs sampling is a special case of MH
    • 24.3.3 Proposal distributions
    • 24.3.4 Adaptive MCMC
    • 24.3.5 Initialization and mode hopping
    • 24.3.6 Why MH works *
    • 24.3.7 Reversible jump (trans-dimensional) MCMC *
  • 24.4 Speed and accuracy of MCMC
    • 24.4.1 The burn-in phase
    • 24.4.2 Mixing rates of Markov chains *
    • 24.4.3 Practical convergence diagnostic
    • 24.4.4 Accuracy of MCMC
    • 24.4.5 How many chains?
  • 24.5 Auxiliary variable MCMC *
    • 24.5.1 Auxiliary variable sampling for logistic regression
    • 24.5.2 Slice sampling
    • 24.5.3 Swendsen Wang
    • 24.5.4 Hybrid/Hamiltonian MCMC *
  • 24.6 Annealing methods
    • 24.6.1 Simulated annealing
    • 24.6.2 Annealed importance sampling
    • 24.6.3 Parallel tempering
  • 24.7 Approximating the marginal likelihood
    • 24.7.1 The candidate method
    • 24.7.2 Harmonic mean estimate
    • 24.7.3 Annealed importance sampling
• 25 Clustering
  • 25.1 Introduction
    • 25.1.1 Measuring (dis)similarity
    • 25.1.2 Evaluating the output of clustering methods *
  • 25.2 Dirichlet process mixture models
    • 25.2.1 From finite to infinite mixture models
    • 25.2.2 The Dirichlet process
    • 25.2.3 Applying Dirichlet processes to mixture modeling
    • 25.2.4 Fitting a DP mixture model
  • 25.3 Affinity propagation
  • 25.4 Spectral clustering
    • 25.4.1 Graph Laplacian
    • 25.4.2 Normalized graph Laplacian
    • 25.4.3 Example
  • 25.5 Hierarchical clustering
    • 25.5.1 Agglomerative clustering
    • 25.5.2 Divisive clustering
    • 25.5.3 Choosing the number of clusters
    • 25.5.4 Bayesian hierarchical clustering
  • 25.6 Clustering datapoints and features
    • 25.6.1 Biclustering
    • 25.6.2 Multi-view clustering
• 26 Graphical Model Structure Learning
  • 26.1 Introduction
  • 26.2 Structure learning for knowledge discovery
    • 26.2.1 Relevance networks
    • 26.2.2 Dependency networks
  • 26.3 Learning tree structures
    • 26.3.1 Directed or undirected tree?
    • 26.3.2 Chow-Liu algorithm for finding the ML tree structure
    • 26.3.3 Finding the MAP forest
    • 26.3.4 Mixtures of trees
  • 26.4 Learning DAG structures
    • 26.4.1 Markov equivalence
    • 26.4.2 Exact structural inference
    • 26.4.3 Scaling up to larger graphs
  • 26.5 Learning DAG structure with latent variables
    • 26.5.1 Approximating the marginal likelihood when we have missing data
    • 26.5.2 Structural EM
    • 26.5.3 Discovering hidden variables
    • 26.5.4 Case study: Google’s Rephil
    • 26.5.5 Structural equation models *
  • 26.6 Learning causal DAGs
    • 26.6.1 Causal interpretation of DAGs
    • 26.6.2 Using causal DAGs to resolve Simpson’s paradox
    • 26.6.3 Learning causal DAG structures
  • 26.7 Learning undirected Gaussian graphical models
    • 26.7.1 MLE for a GGM
    • 26.7.2 Graphical lasso
    • 26.7.3 Bayesian inference for GGM structure *
    • 26.7.4 Handling non-Gaussian data using copulas *
  • 26.8 Learning undirected discrete graphical models
    • 26.8.1 Graphical lasso for MRFs/CRFs
    • 26.8.2 Thin junction trees
• 27 Latent Variable Models for Discrete Data
  • 27.1 Introduction
  • 27.2 Distributed state LVMs for discrete data
    • 27.2.1 Mixture models
    • 27.2.2 Exponential family PCA
    • 27.2.3 LDA and mPCA
    • 27.2.4 GaP model and non-negative matrix factorization
  • 27.3 Latent Dirichlet allocation (LDA)
    • 27.3.1 Basics
    • 27.3.2 Unsupervised discovery of topics
    • 27.3.3 Quantitatively evaluating LDA as a language model
    • 27.3.4 Fitting using (collapsed) Gibbs sampling
    • 27.3.5 Example
    • 27.3.6 Fitting using batch variational inference
    • 27.3.7 Fitting using online variational inference
    • 27.3.8 Determining the number of topics
  • 27.4 Extensions of LDA
    • 27.4.1 Correlated topic model
    • 27.4.2 Dynamic topic model
    • 27.4.3 LDA-HMM
    • 27.4.4 Supervised LDA
  • 27.5 LVMs for graph-structured data
    • 27.5.1 Stochastic block model
    • 27.5.2 Mixed membership stochastic block model
    • 27.5.3 Relational topic model
  • 27.6 LVMs for relational data
    • 27.6.1 Infinite relational model
    • 27.6.2 Probabilistic matrix factorization for collaborative filtering
  • 27.7 Restricted Boltzmann machines (RBMs)
    • 27.7.1 Varieties of RBMs
    • 27.7.2 Learning RBMs
    • 27.7.3 Applications of RBMs
• 28 Deep Learning
  • 28.1 Introduction
  • 28.2 Deep generative models
    • 28.2.1 Deep directed networks
    • 28.2.2 Deep Boltzmann machines
    • 28.2.3 Deep belief networks
    • 28.2.4 Greedy layer-wise learning of DBNs
  • 28.3 Deep neural networks
    • 28.3.1 Deep multi-layer perceptrons
    • 28.3.2 Deep auto-encoders
    • 28.3.3 Stacked denoising auto-encoders
  • 28.4 Applications of deep networks
    • 28.4.1 Handwritten digit classification using DBNs
    • 28.4.2 Data visualization and feature discovery using deep auto-encoders
    • 28.4.3 Information retrieval using deep auto-encoders (semantic hashing)
    • 28.4.4 Learning audio features using 1d convolutional DBNs
    • 28.4.5 Learning image features using 2d convolutional DBNs
  • 28.5 Discussion
• Notation
• Bibliography
• Index to Code
• Index to Keywords

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