About this course

The course will describe how to learn, or acquire context dependent meaningful information, from annotated point clouds in high dimensional space. We start with a description of a particular use case, deep molecular clinical Cancer patient data. We will here briefly describe the data generation process, biotech platforms and sampling and data protocols. The resulting data is annotated high dimensional point clouds, where each point represent an annotated patient data point. The core of the course is an introduction to mathematical tools to gain information around possible patterns (mathematical structures) in the resulting point cloud. We will cover some basic geometric measure theory (the “coalescence of high dimensional differential geometry and measure theory), high dimensional probability theory (the general study of high dimensional probability distributions and sampling from the distributions), some basic machine learning and deep learning, the Kernel method, (a computationally efficient framework translating many “linear learning methods” to a non-linear context). We will then finish with a little bit deeper dive into sampling, statistical inference and deep learning, practically illustrating what we can learn from our example Cancer data. PhD students interested in taking the course for credits should contact the organizers at the start of the course.

No registration needed.