A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws

TL;DR

This paper introduces geodesic least squares regression (GLS), a robust method based on minimizing Rao geodesic distance on probabilistic manifolds, effective for power law scaling laws with uncertain data.

Contribution

The paper presents a novel regression technique, GLS, that improves robustness over traditional methods by utilizing geodesic distances on probabilistic manifolds.

Findings

GLS outperforms OLS in robustness with uncertain data

Demonstrates effectiveness on synthetic power law data

Successfully applied to magnetic confinement fusion scaling law

Abstract

In regression analysis for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS). The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.