Statistical aspects of Optimal Transport

This proposal explores the use of optimal transport in statistics and machine learning as well as develop one simple application in chemistry. Optimal transport is a well established mathematical field whose actors have gone to receive the most prestigious recognitions. Its inventor, Leonid Kantorovich, received the Nobel Prize in Economics. Cedric Villani, who wrote the two most notable books on the topic, received the Fields Medal in 2010 and, more recently, another Fields Medal was awarded to Alessio Figalli for his work on optimal transport.

Beyond its mathematical depth, optimal transport has become a preponderant tool in many applications where data can be represented as probability distributions (images, point clouds, curves, word counts, etc). This useful feature translates into powerful tools ranging from clustering to dimension reduction.

A central goal of this MITACS project is to train the students to work on Statistical and Computational aspects of optimal transport by facing problems at the interface of Mathematics, Statistics and Data Sciences.

Faculty Supervisor:

Augusto Gerolin

Student:

Partner:

National Technical University of Ukraine

Discipline:

Mathematics

Sector:

Artificial Intelligence; Life Sciences (not health); Sustainability & the Environment

University:

University of Ottawa

Program: