From 2012, Deep Learning has become more and more popular.
Since the 1950s, a lot of Machine Learning theories and algorithms have been discovered and popularly investigated. A recent one is Generative Adversarial Networks, introduced in 2014, which can learn to create data that is similar to the given data. For example, if you provide enough human face pictures for training, the successful model will create new face pictures which are different from any copies of the input. Someone calls it creativity. How does it work? Mathematically, suppose all human face pictures form a distribution on some picture space, GAN is able to learn this distribution from the input sample data, or to create another distribution which is close to the original one. Under this framework, different topologies on the probability space would need various algorithms to implement this idea. In this talk, we will look into an outstanding algorithm in 2017, so called Wasserstein GAN, which deploys a special metric on probability space, the Wasserstein distance, which has been introduced and widely developed in the Optimal Transport theory. I will also spend some time on a brief introduction to Monge-Kantorovich problem, Kantorovich duality, and, if time permits, other applications of Optimal Transport.
Everyone is welcome!