Multivariate polynomial regression regularized via fit function uncertainty

15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research

物理学;计算机科学

Kövesárki, Péter^1 ; Brock, Ian C^2

University of Wroclaw, Poland^1

University of Bonn, Germany^2

关键词: Central Limit Theorem;    Input parameter;    Multivariate polynomial regressions;    Polynomial degree;    Splitting method;    Statistical bootstrap;    Statistical significance;    Training sample;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/523/1/012029/pdf
DOI  :  10.1088/1742-6596/523/1/012029

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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.