General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression
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 \(N\) d...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2015-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1099-4300/17/6/3898 |
| _version_ | 1811301214633066496 |
|---|---|
| author | Udo von Toussaint |
| author_facet | Udo von Toussaint |
| author_sort | Udo von Toussaint |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T07:04:58Z |
| format | Article |
| id | doaj.art-eccfddce2493419286df3041335e4a5f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T07:04:58Z |
| publishDate | 2015-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-eccfddce2493419286df3041335e4a5f2022-12-22T02:57:02ZengMDPI AGEntropy1099-43002015-06-011763898391210.3390/e17063898e17063898General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear RegressionUdo von Toussaint0Max-Planck-Institute for Plasmaphysics, Boltzmannstrasse 2, 85748 Garching, GermanyBased 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.http://www.mdpi.com/1099-4300/17/6/3898prior probabilitieshyperplanesgeometrical probabilityneural networks |
| spellingShingle | Udo von Toussaint General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression Entropy prior probabilities hyperplanes geometrical probability neural networks |
| title | General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression |
| title_full | General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression |
| title_fullStr | General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression |
| title_full_unstemmed | General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression |
| title_short | General Hyperplane Prior Distributions Based on Geometric Invariances for Bayesian Multivariate Linear Regression |
| title_sort | general hyperplane prior distributions based on geometric invariances for bayesian multivariate linear regression |
| topic | prior probabilities hyperplanes geometrical probability neural networks |
| url | http://www.mdpi.com/1099-4300/17/6/3898 |
| work_keys_str_mv | AT udovontoussaint generalhyperplanepriordistributionsbasedongeometricinvariancesforbayesianmultivariatelinearregression |