We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
This course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and implement methods to analyze diverse data types, such as imag ...
This course provides an introduction to stochastic optimal control and dynamic programming (DP), with a variety of engineering
applications. The course focuses on the DP principle of optimality, and its utility in deriving and approximating solutions to an ...
Statistics lies at the foundation of data science, providing a unifying theoretical and methodological backbone for the diverse tasks enountered in this emerging field. This course rigorously develops the key notions and methods of statistics, with an emph ...
In this lecture series some important objects of random geometry are introduced and studied. In particular, the relation between the Gaussian free field and random walks / Brownian motions is explored. This provides a toolbox of techniques for studying mat ...
The students study and apply fundamental concepts and algorithms of computer graphics for rendering, geometry
synthesis, and animation. They design and implement their own interactive graphics programs. ...
Machine learning and data analysis are becoming increasingly central in many sciences and applications. In this course, fundamental principles and methods of machine learning will be introduced, analyzed and practically implemented. ...
The focus of this reading group is to delve into the concept of the "Magnitude of Metric Spaces". This approach offers an alternative approach to persistent homology to describe a metric space across varying resolutions. It can be used to estimate an intri ...