Following recent developments and in accordance with the restrictions imposed by our authorities, this event as well as all other planned activities of the semester Functional Data Analysis including the workshops, Bernoulli Lectures and the summer school are cancelled.
Designing Optimal Transport Algorithms by Justin Solomon
Recent progress in applied optimal transport has been fueled by the development of efficient, large-scale optimization algorithms for problems in this domain. In this tutorial, we will introduce strategies for formulating optimal transport algorithms in applications like machine learning, statistics, computer graphics/vision, and scientific computing. Particular methodologies will include regularization, stochastic computation, semi-discrete transport, and numerical differential equations. We also will show how these algorithms can be applied to broader tasks that involve a transport term, such as Bayesian inference, generative modeling, and interpolation.
Some Statistical Theory on Wasserstein Space by Yoav Zemel
Optimal transport and the associated Wasserstein metrics/spaces are becoming increasingly popular among statisticians, machine learners and data scientists. This course will introduce some of the underlying theory and the key features that make Wasserstein distance a versatile tool in statistics. Particular focus will be given to the Fréchet mean (or barycentre) with respect to the Wasserstein metric, and how it is closely linked with the problem of synchronising point processes subject to spatial deformations. If time permits, we will also show how principal component analysis can be carried out in Wasserstein space.