Data science and machine learning (deep learning in particular) have become a burgeoning domain with a great number of successes in science and technology. Most of the recently developed deep learning techniques are still at the “engineering” level based on trial and error. A complete theory of deep learning is still under development.

The purpose of this course is to introduce the theoretical foundation of data science with an emphasis on the mathematical understanding of machine learning. The course is divided into two

semesters:

• In the first semester, we will introduce the basic set up of statistical learning, optimization, classical learning methods such as support vector machines, kernel methods, dimensionality reduction, as well as advanced learning theories, providing a mathematical foundation for the study of neural networks in the following semester.

• The second semester will contain two parts. The first half of the course introduces some useful fundamental tools from probability and statistics, and more extensively the theory of neural networks including their approximation power and generalization properties. The second half is a seminar part of the course, covering selected advanced topics on optimization and generative modeling.

The expected outcome of this course is to prepare students with solid mathematical background of modern machine learning, and to get students engaged with new research topics in this area.

This course complements some earlier courses on machine learning and data sciences, such as MATH 697PA: ST-Math Foundtns/ProbabilistAI and STAT 697ML: ST- Stat Machine Learning.

## Department of Mathematics and Statistics