Évènement

Gaussian Mixture Models (GMMs) are widely used in applied fields to represent the probability distributions of real-world datasets. While optimal transport can compute distances or geodesics between such mixture models, the corresponding 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 optimal transport problem into a finite-dimensional problem with a simple discrete formulation. The resulting Mixture Wasserstein distance is particularly well-suited for applications where a clustering structure is present in the data.

To 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 parameters of the GMMs from the data. In this talk, after a brief overview of Mixture Wasserstein, we will explore how to make the entire framework differentiable. This enables the use of this distance for various machine learning and image processing tasks where the differentiability is key.