Journal ArticleDOI
A robust and efficient stepwise regression method for building sparse polynomial chaos expansions
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TLDR
The results show that the developed sparse regression technique is able to identify the most significant PC contributions describing the problem and the most important stochastic features are captured at a reduced computational cost compared to the LAR method.About:
This article is published in Journal of Computational Physics.The article was published on 2017-03-01. It has received 95 citations till now. The article focuses on the topics: Polynomial chaos & Polynomial regression.read more
Citations
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Journal ArticleDOI
Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression
Kai Cheng,Zhenzhou Lu +1 more
TL;DR: This paper develops a full PCE meta-model based on support vector regression technique using an orthogonal polynomials kernel function, and establishes accurate meta- model for global sensitivity analysis of complex models.
Journal ArticleDOI
Structural reliability analysis based on ensemble learning of surrogate models
Kai Cheng,Zhenzhou Lu +1 more
TL;DR: A new adaptive approach is developed for reliability analysis by ensemble learning of multiple competitive surrogate models, including Kriging, polynomial chaos expansion and support vector regression, that is very efficient for estimating failure probability (>10−4) of complex system with less computational costs than the traditional single surrogate model.
Journal ArticleDOI
Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark
TL;DR: Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with many input parameters, relying on only few model evaluations as discussed by the authors.
Journal ArticleDOI
Surrogate-assisted global sensitivity analysis: an overview
TL;DR: An overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, Polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation are presented.
Journal ArticleDOI
Sparse polynomial chaos expansion based on D-MORPH regression
Kai Cheng,Zhenzhou Lu +1 more
TL;DR: Results show that the developed method is superior to the LAR-based sparse PCE in terms of efficiency and accuracy.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
An Introduction To Compressive Sampling
TL;DR: The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.
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