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Entropy 2015, 17(6), 3898-3912; doi:10.3390/e17063898

General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression

Max-Planck-Institute for Plasmaphysics, Boltzmannstrasse 2, 85748 Garching, Germany
Academic Editors: Frédéric Barbaresco and Ali Mohammad-Djafari
Received: 30 March 2015 / Revised: 1 June 2015 / Accepted: 2 June 2015 / Published: 10 June 2015
(This article belongs to the Special Issue Information, Entropy and Their Geometric Structures)
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Abstract

Based on geometric invariance properties, we derive an explicit prior distribution for the parameters of multivariate linear regression problems in the absence of further prior information. The problem is formulated as a rotationally-invariant distribution of \(L\)-dimensional hyperplanes in \(N\) dimensions, and the associated system of partial differential equations is solved. The derived prior distribution generalizes the already known special cases, e.g., 2D plane in three dimensions. View Full-Text
Keywords: prior probabilities; hyperplanes; geometrical probability; neural networks prior probabilities; hyperplanes; geometrical probability; neural networks
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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von Toussaint, U. General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression. Entropy 2015, 17, 3898-3912.

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