目錄
Preface
Reading Guide
1 Introduction
1.1 Statistical Learning
1.2 Support Vector Machines: An Overview
1.3 History of SVMs and Geometrical Interpretation
1.4 Alternatives to SVMs
2 Loss Functions and Their Risks
2.1 Loss Functions: Definition and Examples
2.2 Basic Properties of Loss Functions and Their Risks
2.3 Margin-Based Losses for Classification Problems
2.4 Distance-Based Losses for Regression Problems
2.5 Further Reading and Advanced Topics
2.6 Summary
2.7 Exercises
3 Surrogate Loss Functions (*)
3.1 Inner Risks and the Calibration Function
3.2 Asymptotic Theory of Surrogate Losses
3.3 Inequalities between Excess Risks
3.4 Surrogates for Unweighted Binary Classification
3.5 Surrogates for Weighted Binary Classification
3.6 Template Loss Functions
3.7 Surrogate Losses for Regression Problems
3.8 Surrogate Losses for the Density Level Problem
3.9 Self-Calibrated Loss Functions
3.10 Further Reading and Advanced Topics
3.11 Summary
3.12 Exercises
4 Kernels and Reproducing Kernel Hilbert Spaces
4.1 Basic Properties and Examples of Kernels
4.2 The Reproducing Kernel Hilbert Space of a Kernel
4.3 Properties of RKHSs
4.4 Gaussian Kernels and Their RKHSs
4.5 Mercer's Theorem (*)
4.6 Large Reproducing Kernel Hilbert Spaces
4.7 Further Reading and Advanced Topics
4.8 Summary
4.9 Exercises
5 Infinite-Sample Versions of Support Vector Machines
5.1 Existence and Uniqueness of SVM Solutions
5.2 A General Representer Theorem
5.3 Stability of Infinite-Sample SVMs
5.4 Behavior for Small Regularization Parameters
5.5 Approximation Error of RKHSs
5.6 Further Reading and Advanced Topics
5.7 Summary
5.8 Exercises
6 Basic Statistical Analysis of SVMs
6.1 Notions of Statistical Learning
6.2 Basic Concentration Inequalities
6.3 Statistical Analysis of Empirical Risk Minimization
6.4 Basic Oracle Inequalities for SVMs
6.5 Data-Dependent Parameter Selection for SVMs
6.6 Further Reading and Advanced Topics
6.7 Summary
6.8 Exercises
7 Advanced Statistical Analysis of SVMs (*)
7.1 Why Do We Need a Refined Analysis?
7.2 A Refined Oracle Inequality for ERM
7.3 Some Advanced Machinery
7.4 Refined Oracle Inequalities for SVMs
7.5 Some Bounds on Average Entropy Numbers
7.6 Further Reading and Advanced Topics
7.7 Summary
7.8 Exercises
8 Support Vector Machines for Classification
8.1 Basic Oracle Inequalities for Classifying with SVMs
8.2 Classifying with SVMs Using Gaussian Kernels
8.3 Advanced Concentration Results for SVMs (*)
8.4 Sparseness of SVMs Using the Hinge Loss
8.5 Classifying with other Margin-Based Losses (*)
8.6 Further Reading and Advanced Topics
8.7 Summary
8.8 Exercises
9 Support Vector Machines for Regression
9.1 Introduction
9.2 Consistency
9.3 SVMs for Quantile Regression
9.4 Numerical Results for Quantile Regression
9.5 Median Regression with the eps-Insensitive Loss (*)
9.6 Further Reading and Advanced Topics
9.7 Summary
9.8 Exercises
10 Robustness
10.1 Motivation
10.2 Approaches to Robust Statistics
10.3 Robustness of SVMs for Classification
10.4 Robustness of SVMs for Regression (*)
10.5 Robust Learning from Bites (*)
10.6 Further Reading and Advanced Topics
10.7 Summary
10.8 Exercises
11 Computational Aspects
11.1 SVMs, Convex Programs, and Duality
11.2 Implementation Techniques
11.3 Determination of Hyperparameters
11.4 Software Packages
11.5 Further Reading and Advanced Topics
11.6 Summary
11.7 Exercises
12 Data Mining
12.1 Introduction
12.2 CRISP-DM Strategy
12.3 Role of SVMs in Data Mining
12.4 Software Tools for Data Mining
12.5 Further Reading and Advanced Topics
12.6 Summary
12.7 Exercises
Appendix
A.1 Basic Equations, Inequalities, and Functions
A.2 Topology
A.3 Measure and Integration Theory
A.3.1 Some Basic Facts
A.3.2 Measures on Topological Spaces
A.3.3 Aumann's Measurable Selection Principle
A.4 Probability Theory and Statistics
A.4.1 Some Basic Facts
A.4.2 Some Limit Theorems
A.4.3 The Weak* Topology and Its Metrization
A.5 Functional Analysis
A.5.1 Essentials on Banach Spaces and Linear Operators
A.5.2 Hilbert Spaces
A.5.3 The Calculus in Normed Spaces
A.5.4 Banach Space Valued Integration
A.5.5 Some Important Banach Spaces
A.5.6 Entropy Numbers
A.6 Convex Analysis
A.6.1 Basic Properties of Convex Functions
A.6.2 Subdifferential Calculus for Convex Functions
A.6.3 Some Further Notions of Convexity
A.6.4 The Fenchel-Legendre Bi-conjugate
A.6.5 Convex Programs and Lagrange Multipliers
A.7 Complex Analysis
A.8 Inequalities Involving Rademacher Sequences
A.9 Talagrand's Inequality
References
Notation and Symbols
Abbreviations
Author Index
Subject Index
[