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Entropy 2015, 17(7), 4602-4626; doi:10.3390/e17074602

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

1
Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium
2
Laboratory for Plasma Physics—Royal Military Academy (LPP-ERM/KMS), Avenue de la Renaissancelaan 30, B-1000 Brussels, Belgium 
This paper is an extended version of our paper published in the 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), 21–26 September 2014, Amboise, France.
Academic Editors: Frédéric Barbaresco and Ali Mohammad-Djafari
Received: 3 April 2015 / Revised: 20 June 2015 / Accepted: 25 June 2015 / Published: 1 July 2015
(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)
View Full-Text   |   Download PDF [2403 KB, uploaded 1 July 2015]   |  

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. View Full-Text
Keywords: regression analysis; information geometry; geodesic distance; scaling laws; nuclear fusion regression analysis; information geometry; geodesic distance; scaling laws; nuclear fusion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Verdoolaege, G. A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws. Entropy 2015, 17, 4602-4626.

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