Mathematical Foundations of Machine Learning

What it is about

You will learn the mathematical foundations of modern machine learning methods: structure, learning algorithms and approximation properties of neural networks, theory and application of kernel methods in reproducing kernel Hilbert spaces as well as qualitative aspects such as loss functions, risk and complexity questions. By the end you will be able to construct networks, discuss their approximation properties, apply kernel methods and assess the statistical efficiency of procedures.

What you will be able to do

• Understand basic concepts and notions of machine learning
• Construct and implement neural networks
• Discuss approximation properties of various network architectures
• Understand the theory of kernel methods in reproducing kernel Hilbert spaces
• Be able to apply kernel methods to nonlinear regression
• Assess the statistical efficiency of learning procedures

What the module consists of

• VorlesungDelivery of the theoretical content by lecture and presentation
• ÜbungDeepening and application of the content; working on examples and group work

Teaching method

• Vortrag/Präsentationfor structured transmission of the teaching content
• Selbststudium der Literaturfor deepening and independent engagement with the topics
• Übungen (teilweise Gruppenarbeit)for solving concrete questions and practical examples together