On Theoretical and Numerical Aspects of Optimal Transport and Its Regularizations
In this thesis, we explore theoretical and numerical problems related to optimal transport and its regularizations. In the first part of this thesis, we focus on the entropic regularization of optimal transport. We review, elaborate upon, and generalize prior work by R.Fortet, concerning existence a...
Saved in:
| Main Author: | |
|---|---|
| Format: | Dissertation |
| Language: | English |
| Published: |
ProQuest Dissertations & Theses
01-01-2018
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this thesis, we explore theoretical and numerical problems related to optimal transport and its regularizations. In the first part of this thesis, we focus on the entropic regularization of optimal transport. We review, elaborate upon, and generalize prior work by R.Fortet, concerning existence and uniqueness of solutions to a system of equations (‘the Schrodinger System’), which yields a solution to the regularized transport problem. In the second part, we explore a quadratic alternative to the entropic regular- ization for optimal transport over a graph. We analyze theoretically the behavior of the solution, and provide an easily-implemented Newton-type optimization al- gorithm. Finally, in the third part of the thesis, we provide an alternative way of numer- ically solving the classical optimal transport problem between two data samples generated from unknown distributions. Unlike classical methods that seek a point- by-point assignment, our method looks for a map that minimizes a numerically evaluated Kullback-Leibler divergence, and is based on an adverserial approach. |
|---|---|
| ISBN: | 9780438634473 0438634470 |