Geodesic Least Squares: Robust Regression Using Information Geometry

: Geodesic least squares (GLS) is a regression technique that operates in spaces of probability distributions. Based on the minimization of the Rao geodesic distance between two probability models of the response variable, GLS is robust against outliers and model misspecification. The method is very simple, without any tuning parameters, owing to its solid foundations rooted in information geometry. Here, we illustrate the robustness properties of GLS using applications in the fields of magnetic confinement fusion and astrophysics. Additional interpretation is gained from visualizations using several models for the manifold of Gaussian probability distributions.