Multivariate regression and fit function uncertainty

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propaga...

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Bibliographic Details
Published inarXiv.org
Main Authors Kovesarki, Peter, Brock, Ian C
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.10.2013
Subjects
Parameter uncertainty
Polynomials
Statistical analysis
Statistical methods
Training
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Summary:This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal fit function, as an alternative to the statistical bootstrap method. This uncertainty can be propagated further into a loss function like quantity, with which it is possible to calculate the expected loss function, and allows to select the optimal polynomial degree with statistical significance. Combined with simple phase space splitting methods, it is possible to model most features of the training data even with low degree polynomials or constants.
ISSN:2331-8422