A contribution to Optimal Transport on incomparable spaces

Understand

Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points.

• Many machine learning applications are derived from this theory, at the frontier between mathematics and optimization.
• This thesis proposes to study the complex scenario in which the different data belong to incomparable spaces.
• In particular we address the following questions: how to define and apply Optimal Transport between graphs, between structured data? How can it be adapted when the data are varied and not embedded in the same metric space? This thesis proposes a set of Optimal Transport tools for these different cases.