The goal of this  course is to introduce and deepen kernel methods as a major tool in nonparametric approaches to machine learning.

  In this course you will (re)discover that linear methods extend to nonlinear by using the famous kernel trick. Linear regression, linear classification and linear dimensionality reduction approaches  will be highlighted as typical examples of this  family of  approaches. You will also learn how to think about machine learning in terms of hypothesis spaces and regularization choices, by leveraging a unique hyperparameter: the kernel. This will raise the issue of kernel  design and learning. We will then show that the kernel trick is  also interesting in the output space by tackling multi-task and structured prediction.

Eventually, we will present an overview of the still-open question of scaling up kernel methods and will discuss the links between kernel  machines and neural networks.

The course is punctuated by 3 practical sessions (3H00, 1H30, 1H30).