This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science.
Learning objective
Understanding the theoretical and practical aspects of relevant optimization methods used in data science. Learning general paradigms to deal with optimization problems arising in data science.
Content
This course teaches an overview of modern optimization methods, with applications in particular for machine learning and data science.
In the first part of the course, we will discuss how classical first and second order methods such as gradient descent and Newton's method can be adapated to scale to large datasets, in theory and in practice. We also cover some new algorithms and paradigms that have been developed specifically in the context of data science. The emphasis is not so much on the application of these methods (many of which are covered in other courses), but on understanding and analyzing the methods themselves.
In the second part, we discuss convex programming relaxations as a powerful and versatile paradigm for designing efficient algorithms to solve computational problems arising in data science. We will learn about this paradigm and develop a unified perspective on it through the lens of the sum-of-squares semidefinite programming hierarchy. As applications, we are discussing non-negative matrix factorization, compressed sensing and sparse linear regression, matrix completion and phase retrieval, as well as robust estimation.
Prerequisites / Notice
As background, we require material taught in the course "252-0209-00L Algorithms, Probability, and Computing". It is not necessary that participants have actually taken the course, but they should be prepared to catch up if necessary.
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination
written 120 minutes
Additional information on mode of examination
At two times in the course of the semester, we will hand out specially marked exercises or term projects - the written part of the solutions are expected to be typeset in LaTeX or similar. Solutions will be graded, and the grades will account for 20% of the final grade. Assignments can be discussed with colleagues, but we expect an independent writeup.
Written aids
None
This information can be updated until the beginning of the semester; information on the examination timetable is binding.
Performance assessment as a semester course