2013/10/03 by Péter Kövesárki, Kovesarki, Peter, Ian C. Brock +1
Computer Science · Decision Sciences · Engineering · #62J02 #Computation (stat.CO) #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1310.1022
openalex publication_date 2013/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.