Support Vector Machines (SVM) and Kernel Methods · Introduction

Introduction

What this guide covers

A rigorous mathematical exposition, from maximum margin hyperplane geometry to functional Hilbert spaces (RKHS), representation theorems and convex optimization.

Overview

Topics covered

Introduction
Support Vector Machines and Kernel Methods
Fundamentals of Statistical Learning
1.1 Empirical Risk Minimization vs. Structural
1.2 The Vapnik-Chervonenkis Dimension (VC Dimension)
1.3 Vapnik Generalization Bound

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

R(f) = \mathbb{E}_{(\mathbf{X},Y) \sim P}[\mathbb{L}(f(\mathbf{X}), Y)] = \int_{\mathcal{X} \times \mathcal{Y}} \mathbb{L}(f(\mathbf{x}), y)\, dP(\mathbf{x}, y)

View LaTeX source

R(f) = \mathbb{E}_{(\mathbf{X},Y) \sim P}[\mathbb{L}(f(\mathbf{X}), Y)] = \int_{\mathcal{X} \times \mathcal{Y}} \mathbb{L}(f(\mathbf{x}), y)\, dP(\mathbf{x}, y)