# About the seminar

This seminar aims to increase the links between the different laboratories in Saclay in the field of Applied Maths, Statistics and Machine Learning. The Seminar is organized every first Tuesday of the month with 2 presentations followed by a small refreshment. The localization of the seminar will change to accommodate the different labs.

### Organization

Due to access restriction, you need to register for the seminar. A link is provided in the description and should also be sent with the seminar announcement. It will also help us organize for the food quantities. If you think you will come, please register! (even if you are unsure)

To not miss the next seminar, please subscribe to the announcement mailing list palaisien@inria.fr.

You can also add the calendar from the seminar to your own calendar (see below).

### Next seminars

Alternatively, a powerful approach consists in keeping the problem as such, and regularizing the data instead to fall back to cases that can be solved efficiently. In particular, representing the data using elliptical distributions, which are fully described by their mean vector and covariance matrix, leads to one of the very few cases of closed-form expressions for OT. Indeed, for such distributions, the Wasserstein distance can be decomposed as the sum of the Euclidean distance between means and the Bures distance between covariance matrices, which defines a Riemannian metric on the set of positive semi-definite matrices.

In this talk, we show how the Bures-Wasserstein distance can be used in machine learning applications, by presenting scalable algorithms for computing and differentiating the Bures metric. In particular, we show that a suitable reparameterization allows to emulate Riemannian gradient descent in a projection-free Euclidean setting. Finally, we show that the Bures-Wasserstein geometry can seamlessly incorporate other methods for approximating OT, such as low-dimensional projections or entropic regularization, and propose applications to probabilistic word embeddings.

### Scientific Committee

The program and the organization of this seminar is driven by a scientific committee composed of members of the different laboratories in Saclay. The members of the committee are currently:

- Arlot Sylvain (LMO, Université Paris-Sud)
- Blanchard Gilles (LMO, Université Paris-Sud)
- Brault Romain (ThereSIS, Thales)
- Brunel Victor-Emmanuel (CREST, ENSAE)
- Chiquet Julien (MIA, Agro Paris)
- Dieuleveut Aymeric (CMAP, Ecole polytechnique)
- Goude Yannig (R&D, EDF)
- Kalogeratos Argyris (CMLA, ENS Paris-Saclay)
- Kuhn Estelle (MaIAGE, Inra)
- Moreau Thomas (Parietal, Inria)
- Mozharovskyi Pavlo (LTCI, Telecom Paris)
- Pascal Frederic (L2S, CentraleSupelec)
- Quercini Gianluca (LRI, CentraleSupelec)
- Tami Myriam (MICS, CentraleSupelec)

### Funding

This seminar is made possible with financial support of the ENSAE and DataIA.