Introduction to statistical machine learning / / Masashi Sugiyama

• Record Nr.: UNINA9910583088403321
• Autore: Sugiyama Masashi <1974->
• Pubbl/distr/stampa: Amsterdam : , : Elsevier, , [2016]; ©2016
• ISBN: 0-12-802350-3
• Descrizione fisica: 1 online resource (535 p.)
• Disciplina: 006.3/1
• Soggetti: Machine learning - Statistical methods; Information science - Statistical methods; Pattern recognition systems
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Front Cover; Introduction to Statistical Machine Learning; Copyright; Table of Contents; Biography; Preface; 1 INTRODUCTION; 1 Statistical Machine Learning; 1.1 Types of Learning; 1.2 Examples of Machine Learning Tasks; 1.2.1 Supervised Learning; 1.2.2 Unsupervised Learning; 1.2.3 Further Topics; 1.3 Structure of This Textbook; 2 STATISTICS AND PROBABILITY; 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; 2.4.1 Expectation, Median, and Mode; 2.4.2 Variance and Standard Deviation2.4.3 Skewness, Kurtosis, and Moments; 2.5 Transformation of Random Variables; 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; 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 Distribution4.6 t-Distribution and F-Distribution; 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; 6 Examples of Multidimensional Probability Distributions; 6.1 Multinomial Distribution; 6.2 Multivariate Normal Distribution; 6.3 Dirichlet Distribution; 6.4 Wishart Distribution; 7 Sum of Independent Random Variables; 7.1 Convolution; 7.2 Reproductive Property; 7.3 Law of Large Numbers; 7.4 Central Limit Theorem8 Probability Inequalities; 8.1 Union Bound; 8.2 Inequalities for Probabilities; 8.2.1 Markov's Inequality and Chernoff's Inequality; 8.2.2 Cantelli's Inequality and Chebyshev's Inequality; 8.3 Inequalities for Expectation; 8.3.1 Jensen's Inequality; 8.3.2 Hölder's Inequality and Schwarz's Inequality; 8.3.3 Minkowski's Inequality; 8.3.4 Kantorovich's Inequality; 8.4 Inequalities for the Sum of Independent Random Variables; 8.4.1 Chebyshev's Inequality and Chernoff's Inequality; 8.4.2 Hoeffding's Inequality and Bernstein's Inequality; 8.4.3 Bennett's Inequality; 9 Statistical Estimation9.1 Fundamentals of Statistical Estimation; 9.2 Point Estimation; 9.2.1 Parametric Density Estimation; 9.2.2 Nonparametric Density Estimation; 9.2.3 Regression and Classification; 9.2.4 Model Selection; 9.3 Interval Estimation; 9.3.1 Interval Estimation for Expectation of Normal Samples; 9.3.2 Bootstrap Confidence Interval; 9.3.3 Bayesian Credible Interval; 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