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[size=1.25]Part 1
- INTRODUCTION
- Chapter 1. Statistical Machine Learning
- 1.1. Types of Learning
- 1.2. Examples of Machine Learning Tasks
- 1.3. Structure of This Textbook
[size=1.25]Part 2
- STATISTICS AND PROBABILITY
- Chapter 2. Random Variables and Probability Distributions
- 2.1. Mathematical Preliminaries
- 2.2. Probability
- 2.3. Random Variable and Probability Distribution
- 2.4. Properties of Probability Distributions
- 2.5. Transformation of Random Variables
- Chapter 3. Examples of Discrete Probability Distributions
- 3.1. Discrete Uniform Distribution
- 3.2. Binomial Distribution
- 3.3. Hypergeometric Distribution
- 3.4. Poisson Distribution
- 3.5. Negative Binomial Distribution
- 3.6. Geometric Distribution
- Chapter 4. Examples of Continuous Probability Distributions
- 4.1. Continuous Uniform Distribution
- 4.2. Normal Distribution
- 4.3. Gamma Distribution, Exponential Distribution, and Chi-Squared Distribution
- 4.4. Beta Distribution
- 4.5. Cauchy Distribution and Laplace Distribution
- 4.6. t-Distribution and F-Distribution
- Chapter 5. Multidimensional Probability Distributions
- 5.1. Joint Probability Distribution
- 5.2. Conditional Probability Distribution
- 5.3. Contingency Table
- 5.4. Bayes’ Theorem
- 5.5. Covariance and Correlation
- 5.6. Independence
- Chapter 6. Examples of Multidimensional Probability Distributions
- 6.1. Multinomial Distribution
- 6.2. Multivariate Normal Distribution
- 6.3. Dirichlet Distribution
- 6.4. Wishart Distribution
- Chapter 7. Sum of Independent Random Variables
- 7.1. Convolution
- 7.2. Reproductive Property
- 7.3. Law of Large Numbers
- 7.4. Central Limit Theorem
- Chapter 8. Probability Inequalities
- 8.1. Union Bound
- 8.2. Inequalities for Probabilities
- 8.3. Inequalities for Expectation
- 8.4. Inequalities for the Sum of Independent Random Variables
- Chapter 9. Statistical Estimation
- 9.1. Fundamentals of Statistical Estimation
- 9.2. Point Estimation
- 9.3. Interval Estimation
- Chapter 10. Hypothesis Testing
- 10.1. Fundamentals of Hypothesis Testing
- 10.2. Test for Expectation of Normal Samples
- 10.3. Neyman-Pearson Lemma
- 10.4. Test for Contingency Tables
- 10.5. Test for Difference in Expectations of Normal Samples
- 10.6. Nonparametric Test for Ranks
- 10.7. Monte Carlo Test
[size=1.25]Part 3
- GENERATIVE APPROACH TO STATISTICAL PATTERN RECOGNITION
- Chapter 11. Pattern Recognition via Generative Model Estimation
- 11.1. Formulation of Pattern Recognition
- 11.2. Statistical Pattern Recognition
- 11.3. Criteria for Classifier Training
- 11.4. Generative and Discriminative Approaches
- Chapter 12. Maximum Likelihood Estimation
- 12.1. Definition
- 12.2. Gaussian Model
- 12.3. Computing the Class-Posterior Probability
- 12.4. Fisher’s Linear Discriminant Analysis (FDA)
- 12.5. Hand-Written Digit Recognition
- Chapter 13. Properties of Maximum Likelihood Estimation
- 13.1. Consistency
- 13.2. Asymptotic Unbiasedness
- 13.3. Asymptotic Efficiency
- 13.4. Asymptotic Normality
- 13.5. Summary
- Chapter 14. Model Selection for Maximum Likelihood Estimation
- 14.1. Model Selection
- 14.2. KL Divergence
- 14.3. AIC
- 14.4. Cross Validation
- 14.5. Discussion
- Chapter 15. Maximum Likelihood Estimation for Gaussian Mixture Model
- 15.1. Gaussian Mixture Model
- 15.2. MLE
- 15.3. Gradient Ascent Algorithm
- 15.4. EM Algorithm
- Chapter 16. Nonparametric Estimation
- 16.1. Histogram Method
- 16.2. Problem Formulation
- 16.3. KDE
- 16.4. NNDE
- Chapter 17. Bayesian Inference
- 17.1. Bayesian Predictive Distribution
- 17.2. Conjugate Prior
- 17.3. MAP Estimation
- 17.4. Bayesian Model Selection
- Chapter 18. Analytic Approximation of Marginal Likelihood
- 18.1. Laplace Approximation
- 18.2. Variational Approximation
- Chapter 19. Numerical Approximation of Predictive Distribution
- 19.1. Monte Carlo Integration
- 19.2. Importance Sampling
- 19.3. Sampling Algorithms
- Chapter 20. Bayesian Mixture Models
- 20.1. Gaussian Mixture Models
- 20.2. Latent Dirichlet Allocation (LDA)
[size=1.25]Part 4
- DISCRIMINATIVE APPROACH TO STATISTICAL MACHINE LEARNING
- Chapter 21. Learning Models
- 21.1. Linear-in-Parameter Model
- 21.2. Kernel Model
- 21.3. Hierarchical Model
- Chapter 22. Least Squares Regression
- 22.1. Method of LS
- 22.2. Solution for Linear-in-Parameter Model
- 22.3. Properties of LS Solution
- 22.4. Learning Algorithm for Large-Scale Data
- 22.5. Learning Algorithm for Hierarchical Model
- Chapter 23. Constrained LS Regression
- 23.1. Subspace-Constrained LS
- 23.2. ℓ2-Constrained LS
- 23.3. Model Selection
- Chapter 24. Sparse Regression
- 24.1. ℓ1-Constrained LS
- 24.2. Solving ℓ1-Constrained LS
- 24.3. Feature Selection by Sparse Learning
- 24.4. Various Extensions
- Chapter 25. Robust Regression
- 25.1. Nonrobustness of ℓ2-Loss Minimization
- 25.2. ℓ1-Loss Minimization
- 25.3. Huber Loss Minimization
- 25.4. Tukey Loss Minimization
- Chapter 26. Least Squares Classification
- 26.1. Classification by LS Regression
- 26.2. 0∕1-Loss and Margin
- 26.3. Multiclass Classification
- Chapter 27. Support Vector Classification
- 27.1. Maximum Margin Classification
- 27.2. Dual Optimization of Support Vector Classification
- 27.3. Sparseness of Dual Solution
- 27.4. Nonlinearization by Kernel Trick
- 27.5. Multiclass Extension
- 27.6. Loss Minimization View
- Chapter 28. Probabilistic Classification
- 28.1. Logistic Regression
- 28.2. LS Probabilistic Classification
- Chapter 29. Structured Classification
- 29.1. Sequence Classification
- 29.2. Probabilistic Classification for Sequences
- 29.3. Deterministic Classification for Sequences
[size=1.25]Part 5
- FURTHER TOPICS
- Chapter 30. Ensemble Learning
- 30.1. Decision Stump Classifier
- 30.2. Bagging
- 30.3. Boosting
- 30.4. General Ensemble Learning
- Chapter 31. Online Learning
- 31.1. Stochastic Gradient Descent
- 31.2. Passive-Aggressive Learning
- 31.3. Adaptive Regularization of Weight Vectors (AROW)
- Chapter 32. Confidence of Prediction
- 32.1. Predictive Variance for ℓ2-Regularized LS
- 32.2. Bootstrap Confidence Estimation
- 32.3. Applications
- Chapter 33. Semisupervised Learning
- 33.1. Manifold Regularization
- 33.2. Covariate Shift Adaptation
- 33.3. Class-balance Change Adaptation
- Chapter 34. Multitask Learning
- 34.1. Task Similarity Regularization
- 34.2. Multidimensional Function Learning
- 34.3. Matrix Regularization
- Chapter 35. Linear Dimensionality Reduction
- 35.1. Curse of Dimensionality
- 35.2. Unsupervised Dimensionality Reduction
- 35.3. Linear Discriminant Analyses for Classification
- 35.4. Sufficient Dimensionality Reduction for Regression
- 35.5. Matrix Imputation
- Chapter 36. Nonlinear Dimensionality Reduction
- 36.1. Dimensionality Reduction with Kernel Trick
- 36.2. Supervised Dimensionality Reduction with Neural Networks
- 36.3. Unsupervised Dimensionality Reduction with Autoencoder
- 36.4. Unsupervised Dimensionality Reduction with Restricted Boltzmann Machine
- 36.5. Deep Learning
- Chapter 37. Clustering
- 37.1. k-Means Clustering
- 37.2. Kernel k-Means Clustering
- 37.3. Spectral Clustering
- 37.4. Tuning Parameter Selection
- Chapter 38. Outlier Detection
- 38.1. Density Estimation and Local Outlier Factor
- 38.2. Support Vector Data Description
- 38.3. Inlier-Based Outlier Detection
- Chapter 39. Change Detection
- 39.1. Distributional Change Detection
- 39.2. Structural Change Detection
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