Codpy - Advanced Tutorial

Abstract

CodPy stands for “Curse of dimensionality in Python” and is a Support Vector Machine (SVM), application oriented, Python library. It provides tools for machine learning, statistical learning, and numerical simulations, and consists of an implementation of a method based on the theory of reproducing kernel Hilbert spaces (RKHS). We provide here a follow up of the first part entitled CodPy - a tutorial. This document has several purposes. First of all, our main tools are presented here as a reference manual for users1 and encompasses two different classes of SVM tools. On one hand, we describe a kernel engineering technique, aiming to craft SVMs in order to adapt their kernels to a particular problem. On the other hand, as a tool available for any SVM, we present a rather complete set of differential operators, which are now in use for research and industrial problems. These operators provide us with elementary building block in order to design discrete algorithms for a broad set of partial differential equations. In addition, our metholology leads us quality tests that are applicable to any given kernel that can be input in a learning machine.