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UID:18@frumam.cnrs-mrs.fr
DTSTART;TZID=Europe/Paris:20250704T160000
DTEND;TZID=Europe/Paris:20250704T170000
DTSTAMP:20250625T134612Z
URL:https://frumam.cnrs-mrs.fr/events/colloquium-julie-delon-universite-pa
 ris-cite/
SUMMARY:Colloquium : Julie Delon
DESCRIPTION:\nTitre : Differentiable Mixture Wasserstein\n\n\n\nGaussian Mi
 xture Models (GMMs) are widely used in applied fields to represent the pro
 bability distributions of real-world datasets. While optimal transport can
  compute distances or geodesics between such mixture models\, the correspo
 nding Wasserstein geodesics do not preserve the property of being a GMM. A
  few years ago\, it was demonstrated that restricting the set of possible 
 coupling measures to GMMs transforms the original infinitely dimensional o
 ptimal transport problem into a finite-dimensional problem with a simple d
 iscrete formulation. The resulting Mixture Wasserstein distance is particu
 larly well-suited for applications where a clustering structure is present
  in the data.\n\n\n\nTo make this framework compatible with discrete data\
 , such as those used in machine learning applications\, one approach is to
  use an inference algorithm like Expectation-Maximization to infer the par
 ameters of the GMMs from the data. In this talk\, after a brief overview o
 f Mixture Wasserstein\, we will explore how to make the entire framework d
 ifferentiable. This enables the use of this distance for various machine l
 earning and image processing tasks where the differentiability is key. &nb
 sp\;\n\n\n\n\n
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