Mathematics for Data Science

The course starts from a review of linear vector spaces, along with basic concepts such as subspaces, linear independence,  notions of length, and dual spaces. The first principal objective are Hilbert spaces, where we will work out the projection theorem, direct sums, as well as the Riesz representation theorem. As the second principal objective we discuss convex optimization that is of great importance when devising loss functions and solving models. We close the course with the study of reproducing kernel Hilbert spaces, along with the representer theorem and its classical applications, such as kernel ridge regression, support vector machines, as well as classification. 

The main objectives of this course are the development of mathematical underpinnings of models and methods in data science and machine learning. After having taken the course, students will have improved abilities to study original research papers in the field, and they will have developed knowledge of the most important models. They will be able to understand better the trade offs between model complexity, and out-of-sample performance. 

In presenza

The course is structured through alternating theory and practice sessions. Students will solve take-home exams and quizzes.

The final course assessment is an open-book final written exam.