Dr Alice Le Brigant
University Paris 1 Pantheon Sorbonne
Alice Le Brigant is an Assistant Professor in the Applied Mathematics team SAMM at University Paris 1 Pantheon Sorbonne. Previously, she was a Postdoctoral Fellow at the French Civil Aviation School, in collaboration with the Toulouse Mathematics Institute. She obtained her PhD in Applied Mathematics from the University of Bordeaux in 2017. Her research interests are at the interface of statistics and applied Riemannian geometry.
Fisher information geometry of beta and Dirichlet distributions
The Fisher information metric is a Riemannian metric defined on the parameter space of families of probability distributions. It provides geometric tools that are useful to perform statistics and learning on probability distributions, inside a given parametric family. It is well-known since the 1980s that in the case of normal distributions, Fisher information geometry amounts to hyperbolic geometry. In this talk we will investigate the geometry of Dirichlet distributions, and beta distributions as a particular case. We 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 learning algorithms such as K-means clustering.