D-MORPH regression: Application to modeling with unknown parameters more than observation data

DOI10.1007/s10910-010-9722-2zbMath1303.62032OpenAlexW2067029773MaRDI QIDQ607593

Genyuan Li, Herschel Rabitz

Publication date: 22 November 2010

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

Full work available at URL: https://doi.org/10.1007/s10910-010-9722-2

zbMATH Keywords

regularizationsmoothing splinesridge regressionleast-squares regressionorthonormal polynomialD-MORPH

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Ridge regression; shrinkage estimators (Lasso) (62J07)

Related Items (16)

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 ⋮ General formulation of HDMR component functions with independent and correlated variables ⋮ Learning physics by data for the motion of a sphere falling in a non-Newtonian fluid ⋮ D-MORPH regression for modeling with fewer unknown parameters than observation data ⋮ 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 ⋮ High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions ⋮ Multivariate function approximations using the D-MORPH algorithm ⋮ A surrogate based multi-fidelity approach for robust design optimization ⋮ Generalized Sobol sensitivity indices for dependent variables: numerical methods ⋮ 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 ⋮ Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark

Uses Software

• Matlab
• ElemStatLearn
• PRMLT

Cites Work

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• A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem
• General foundations of high-dimensional model representations
• Smoothing spline ANOVA for exponential families, with application to the Wisconsin epidemiological study of diabetic retinopathy. (The 1994 Neyman Memorial Lecture)
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Learning MATLAB
• High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics
• Ridge Regression: Biased Estimation for Nonorthogonal Problems
• The elements of statistical learning. Data mining, inference, and prediction

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