D-MORPH regression for modeling with fewer unknown parameters than observation data

DOI10.1007/S10910-012-0004-ZzbMath1314.62154OpenAlexW1977920854MaRDI QIDQ445417

Roberto Rey-de-Castro, Genyuan Li, Herschel Rabitz

Publication date: 24 August 2012

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-012-0004-z

zbMATH Keywords

regularizationridge regressionD-MORPH regressionleast-squares regression

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05)

Related Items (10)

Sequential experimental design based generalised ANOVA ⋮ Practical uncertainty quantification analysis involving statistically dependent random variables ⋮ Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA ⋮ Analytical HDMR formulas for functions expressed as quadratic polynomials with a multivariate normal distribution ⋮ Sparse and nonnegative sparse D-MORPH regression ⋮ A surrogate assisted adaptive framework for robust topology optimization ⋮ Multivariate function approximations using the D-MORPH algorithm ⋮ A surrogate based multi-fidelity approach for robust design optimization ⋮ Towards `\(h\)-\(p\) \textit{adaptive}' generalized ANOVA ⋮ Surrogate assisted active subspace and active subspace assisted surrogate -- a new paradigm for high dimensional structural reliability analysis

Uses Software

• Matlab
• ElemStatLearn
• PRMLT

Cites Work

• D-MORPH regression: Application to modeling with unknown parameters more than observation data
• A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem
• Smoothing spline ANOVA for exponential families, with application to the Wisconsin epidemiological study of diabetic retinopathy. (The 1994 Neyman Memorial Lecture)
• The elements of statistical learning. Data mining, inference, and prediction
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