Sinkhorn’s algorithm for optimaltransport

Abstract

The optimal transport distance provides us with a method of assigning a distance between two probability vectors. One downside of this metric is that it can be computationally expensive to compute. One method of estimating the optimal transport distance is by using an entropic regularization, which allows for the use of Sinkhorn’s theorem, providing a lower computational load. In this thesis we investigate the convergence of this method and utilise it to study the change of the attractor of the H´enon system. Our results show that the speed of convergence heavily depends on the level of desired accuracy, which is encapsulated by the regularization parameter λ. The results on the attractor show that it is important to use a large sample size of data points to be able to draw a solid conclusion.