This short talk will address the connections and properties of the energy (including Cramer), and Wasserstein distances, and how they connect with Maximum Mean Discrepancy. We will dive into the similarities and differences among them, and how this impacts their behaviour in different ways. Some of the results are a contextualization of old studies, and some will be presented in this talk for the first time. A recurrent theme in the talk will be the study of the geometry of the space of probability distributions, and how this might shed clarity on the behaviour of different algorithms in practice.

BIO
I'm Martin Arjovsky, I'm currently doing my PhD at New York University, and being advised by Léon Bottou. I did my undergraduate and master's in the University of Buenos Aires, Argentina (my home country). In the middle I took a year off to do internships in different places (Google, Facebook, Microsoft, and the Université de Montréal). My master's thesis advisor was Yoshua Bengio, who also advised me during my stay at UdeM.
In general I'm interested in the intersection between learning and mathematics, how we can ground the different learning processes that are involved in different problems, and leverage this knowledge to develop better algorithms.