Learning_Kernel_Classifiers_-_Theory_and_Algorithms

nickchen

1 Introduction 1
1.1 The Learning Problem and (Statistical) Inference 1
1.1.1 Supervised Learning . . . . . . . . . . . . . . . 3
1.1.2 Unsupervised Learning . . . . . . . . . . . . . . 6
1.1.3 Reinforcement Learning . . . . . . . . . . . . . 7
1.2 Learning Kernel Classifiers 8
1.3 The Purposes of Learning Theory 11
I LEARNING ALGORITHMS
2 Kernel Classifiers from a Machine Learning Perspective 17
2.1 The Basic Setting 17
2.2 Learning by Risk Minimization 24
2.2.1 The (Primal) Perceptron Algorithm . . . . . . . 26
2.2.2 RegularizedRiskFunctionals . . . . . . . . . . 27
2.3 Kernels and Linear Classifiers 30
2.3.1 TheKernelTechnique . . . . . . . . . . . . . . 33
2.3.2 Kernel Families . . . . . . . . . . . . . . . . . . 36
2.3.3 The Representer Theorem . . . . . . . . . . . . 47
2.4 Support Vector Classification Learning 49
2.4.1 Maximizing theMargin . . . . . . . . . . . . . 49
2.4.2 Soft Margins—Learning with Training Error . . 53
2.4.3 Geometrical Viewpoints on Margin Maximization 56
2.4.4 The ν–Trick andOtherVariants . . . . . . . . . 58

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