Upon completion of this module, students will have a basic understanding of the mathematical concepts behind some of the key methods in artificial intelligence and machine learning. They will understand the connection between the mathematical structure and its practical implementation, and apply the studied methods in selected applications. A solid comprehension of the mathematical principles behind machine learning is essential in order to discern under which conditions methods work or do not work, and thereby obtain a principled and thorough understanding of the methods of machine learning.
In recent years, Artificial Intelligence has entered a new era, with remarkable impact on technology and economy. Most notably, this progress has been tied to the recent success of machine learning. This course will cover the mathematical foundations and exact concepts behind some of the most important methods in machine learning and artificial intelligence. The emphasis in this course will be on the rigorous mathematical principles behind how and why methods work (or do not work). Topics include the curses and blessings of dimensionality, randomized algorithms, linear and non-linear dimension reduction methods, graphs and clustering, community detection, sparsity and massive data, diffusion maps and intrinsic geometry of high-dimensional data, as well as convex and non-convex optimization.
Linear algebra and a basic background in probability as well as basic experience in programming (e.g. Matlab, Python) will be required. Some basic knowledge in optimization is recommended.
Teaching and learning methods
Mathematical methods, principles, and algorithms of artificial intelligence will be presented during the lecture on the blackboard and via slides.
Written final exam in form of a project report. Students will write a report in which they describe how they apply some of the methods and concepts acquired in this course in an application. The report may focus on either a theoretical analysis, on numerical aspects, and/or on practical elements of using mathematical methods in artificial intelligence and machine learning.
A detailed list of references will be provided. Some original works will be provided via download.