Optimal Transport: from Theory to Data science
Julie Delon (Univ. Paris Cité)
| When |
Dec 16, 2024
from 11:00 to 12:00 |
|---|---|
| Where | Salle des Thèses |
| Contact Name | Nelly Pustelnik |
| Attendees |
Julie Delon |
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In 1781, Gaspard Monge published his Mémoire sur la théorie des déblais et des remblais, in which he studied how to move a pile of sand from one location to another in an "optimal" way. Nearly two centuries later, in the 1940s, Leonid Kantorovich reformulated the problem, this time to optimally allocate resources in economics. He proved the existence of solutions and was awarded the Nobel Prize in Economics in 1975 for this work. Optimal transport was born.
Today, optimal transport is the focus of numerous theoretical and applied research studies and finds significant applications in unexpected fields. Over the past fifteen years, crucial progress has been made in the numerical computation of optimal transport solutions, making it practical for comparing, interpolating, or aligning high-dimensional probability distributions. In this presentation, we will illustrate how optimal transport can be used today to solve complex problems in image processing and, more broadly, in data analysis.