Alice Le Brigant
SAAM – University Paris 1
21/10/2021 – h. 2 p.m.
Bio: Alice is an assistant professor in the Applied Mathematics team SAMM at University Paris 1 Pantheon Sorbonne since September 2019. Previously, she was a post-doc at the French Civil Aviation School in Toulouse. She did my PhD at the University of Bordeaux under the supervision of Marc Arnaudon and Frédéric Barbaresco (Thales).
Title: Fisher information geometry of beta and Dirichlet distributions
Abstract: The Fisher information metric provides a Riemannian framework to compare probability distributions inside a parametric family. The most well-known example is the univariate gaussian case, where the Fisher information geometry amounts to hyperbolic geometry. In this talk we will investigate the Fisher information geometry of Dirichlet distributions and show that it is negatively curved and geodesically complete. This guarantees the uniqueness of the notion of mean and makes it a suitable geometry to apply the K-means algorithm. We illustrate the use of the Fisher information geometry of beta distributions, a particular case of Dirichlet distributions, to compare and classify histograms of medical data.