University of Washington

The Wasserstein distance is a powerful tool in modern machine learning to metrize the space of probability distributions in a way that takes into account the geometry of the domain. Therefore, a lot of attention has been devoted in the literature to...

Detecting differences and building classifiers between distributions, given only finite samples, are important tasks in a number of scientific fields. Optimal transport (OT) has evolved as the most natural concept to measure the distance between...

Optimal transportation, at its core, is a powerful framework for obtaining structured yet general couplings between general probability measures based on matching underlying characteristics. This framework lends itself naturally to applications in...

Modern machine learning methods, in particular deep learning approaches, have enjoyed unparalleled success in a variety of challenging application fields like image recognition, medical image reconstruction, and natural language processing. While a...

Our introduction of the notion of a non-linear Kantorovich operator was motivated by the celebrated duality in the mass transport problem, hence the name. In retrospect, we realized that they -and their iterates- were omnipresent in several branches...

The sign test (Arbuthnott, 1710) and the Wilcoxon signed-rank test (Wilcoxon, 1945) are among the first examples of a nonparametric test. These procedures — based on signs, (absolute) ranks and signed-ranks — yield distribution-free tests for...

Poincaré-Einstein spaces are a generalization of the Poincaré model of hyperbolic space. They were introduced to study holographically the conformal geometry of the boundary at infinity. This geometric correspondence underlies the AdS/CFT...

Random high-dimensional cost functions and random probability distributions arise in a number of applied fields. For instance, in high-dimensional statistics, an M-estimator is the solution of a random optimization problem (the randomness being...

A useful way of producing samples from a given measure ν on a state space Ω is by providing a Markov chain whose stationary measure in ν. In order to be able to sample efficiently, one needs to show that the chain "mixes" quickly in terms of the rate...

Topology is the branch of mathematics concerned with shapes and their spatial properties. In this talk I’ll show how several ideas from classic algebraic topology – like cohomology, classifying spaces and vector bundles – can be used in machine...