Intro to classical kernels

To understand how quantum kernel works, it is useful for the reader to have a basic grasp of how kernel methods works in the classical machine learning setting. For this reason, we have created a series of introductory tutorials that focus on classical kernels. Subsequently, we will follow this with another series of tutorials focused on quantum kernels.

In this first collection, we do not use quask to address any classical kernel-related tasks. Instead, we rely on the scikit learn package to illustrate fundamental concepts in the field. These tutorials will cover various topics, including how to transform a regression model into a kernel regressor, the concept of a feature map, what constitutes a kernel function, how to construct a kernel function from a feature map, the fundamentals of Support Vector Machines, and their applications in various machine learning tasks.

Note

This series of tutorial are not meant to cover all the basic notions regarding kernel methods. There are many books covering these topics. A useful reference is:

Steinwart Ingo and Christmann Andreas. (2008). Support Vector Machines. Springer Science & Business Media.

Contents

• Linear and Ridge regression
  • Linear Regression
  • Ridge regression
  • The Lagrangian multiplier method
  • References
• Kernel machines
  • Feature map and kernel functions
  • Kernel Ridge regression
• Support Vector Machines
  • Classifying linearly-separable data: the hard-margin SVM
  • Allowing few errors: the soft-margin SVM
  • Allowing non-linear boundaries: the kernel SVM
  • Novelty and outlier detection
  • References