The Geometry of Kernel Methods and Kernel Range Spaces

I will start by overviewing kernel methods in machine learning, and how the simple kernel trick allows one to effortlessly turn intuitive linear methods into non-linear ones. While these methods can seem mysterious, I’ll try to give insight into the geometry that arises, especially in kernel SVM. This will lead into kernel range spaces, which describes all the ways one can inspection a data set with a kernel. From there I will discuss approximation of these with coresets, and just approximating the spaces themselves which leads to surprising results in high dimensions.