ContentsBiography . .ivPreface. vPART 1INTRODUCTIONCHAPTER 1Statistical Machine Learning1.1Types of Learning 31.2Examples of Machine Learning Tasks . 41.2.1Supervised Learning 41.2.2Unsupervised Learning . 51.2.3Further Topics 61.3Structure of This Textbook . 8PART 2STATISTICS AND PROBABILITYCHAPTER 2Random Variables and Probability Distributions2.1Mathematical Preliminaries . 112.2Probability . 132.3Random Variable and Probability Distribution 142.4Properties of Probability Distributions 162.4.1Expectation, Median, and Mode . 162.4.2Variance and Standard Deviation 182.4.3Skewness, Kurtosis, and Moments 192.5Transformation of Random Variables 22CHAPTER 3Examples of Discrete Probability Distributions3.1Discrete Uniform Distribution . 253.2Binomial Distribution . 263.3Hypergeometric Distribution. 273.4Poisson Distribution . 313.5Negative Binomial Distribution . 333.6Geometric Distribution 35CHAPTER 4Examples of Continuous Probability Distributions4.1Continuous Uniform Distribution . 374.2Normal Distribution 374.3Gamma Distribution, Exponential Distribution, and Chi-Squared Distribution . 414.4Beta Distribution . 444.5Cauchy Distribution and Laplace Distribution 474.6t-Distribution and F-Distribution . 49CHAPTER 5Multidimensional Probability Distributions5.1Joint Probability Distribution 515.2Conditional Probability Distribution . 525.3Contingency Table 535.4Bayes’ Theorem. 535.5Covariance and Correlation 555.6Independence . 56CHAPTER 6Examples of Multidimensional Probability Distributions616.1Multinomial Distribution . 616.2Multivariate Normal Distribution . 626.3Dirichlet Distribution 636.4Wishart Distribution . 70CHAPTER 7Sum of Independent Random Variables7.1Convolution 737.2Reproductive Property 747.3Law of Large Numbers 747.4Central Limit Theorem 77CHAPTER 8Probability Inequalities8.1Union Bound 818.2Inequalities for Probabilities 828.2.1Markov’s Inequality and Chernoff’s Inequality 828.2.2Cantelli’s Inequality and Chebyshev’s Inequality 838.3Inequalities for Expectation . 848.3.1Jensen’s Inequality 848.3.2H?lder’s Inequality and Schwarz’s Inequality . 858.3.3Minkowski’s Inequality . 868.3.4Kantorovich’s Inequality . 878.4Inequalities for the Sum of Independent Random Vari-ables 878.4.1Chebyshev’s Inequality and Chernoff’s Inequality 888.4.2Hoeffding’s Inequality and Bernstein’s Inequality 888.4.3Bennett’s Inequality. 89CHAPTER 9Statistical Estimation9.1Fundamentals of Statistical Estimation 919.2Point Estimation 929.2.1Parametric Density Estimation . 929.2.2Nonparametric Density Estimation 939.2.3Regression and Classification. 939.2.4Model Selection 949.3Interval Estimation. 959.3.1Interval Estimation for Expectation of Normal Samples. 959.3.2Bootstrap Confidence Interval 969.3.3Bayesian Credible Interval. 97CHAPTER 10Hypothesis Testing10.1Fundamentals of Hypothesis Testing 9910.2Test for Expectation of Normal Samples 10010.3Neyman-Pearson Lemma . 10110.4Test for Contingency Tables 10210.5Test for Difference in Expectations of Normal Samples 10410.5.1 Two Samples without Correspondence . 10410.5.2 Two Samples with Correspondence 10510.6Nonparametric Test for Ranks. 10710.6.1 Two Samples without Correspondence . 10710.6.2 Two Samples with Correspondence 10810.7Monte Carlo Test . 108PART 3GENERATIVE APPROACH TO STATISTICAL PATTERN RECOGNITIONCHAPTER 11Pattern Recognition via Generative Model Estimation11311.1Formulation of Pattern Recognition . 11311.2Statistical Pattern Recognition . 11511.3Criteria for Classifier Training . 11711.3.1 MAP Rule 11711.3.2 Minimum Misclassification Rate Rule 11811.3.3 Bayes Decision Rule 11911.3.4 Discussion . 12111.4Generative and Discriminative Approaches 121CHAPTER 12Maximum Likelihood Estimation12.1Definition. 12312.2Gaussian Model. 12512.3Computing the Class-Posterior Probability . 12712.4Fisher’s Linear Discriminant Analysis (FDA