Supervised learning of sheared distributions using linearized optimal transport

Understand

In this paper we study supervised learning tasks on the space of probability measures.

• We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework.
• In the embedding spaces, regular machine learning techniques are used to achieve linear separability.
• This idea has proved successful in applications and when the classes to be separated are generated by shifts and scalings of a fixed measure.