RT Journal Article
ID 3261384c6ba6c1c2
A1 Van Langenhove, Jan
A1 Lucor, D.
A1 Belme, A.
T1 ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2016
FD 2016-08-16
VO 6
IS 1
SP 57
OP 77
K1 uncertainty quantification
K1 polynomial chaos
K1 robust regression
K1 outliers
K1 model validation and verification
K1 compressed sensing
K1 weighted least squares
K1 l1-minimization
AB We propose a noniterative robust numerical method for the nonintrusive uncertainty quantification of multivariate stochastic problems with reasonably compressible polynomial representations. The approximation is robust to data outliers or noisy evaluations which do not fall under the regularity assumption of a stochastic truncation error but pertains to a more complete error model, capable of handling interpretations of physical/computational model (or measurement) errors. The method relies on the cross-validation of a pseudospectral projection of the response on generalized Polynomial Chaos approximation bases; this allows an initial model selection and assessment yielding a preconditioned response. We then apply a l1-penalized regression to the preconditioned response variable. Nonlinear test cases have shown this approximation to be more effective in reducing the effect of scattered data outliers than standard compressed sensing techniques and of comparable efficiency to iterated robust regression techniques.
PB Begell House
LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,6695b1fe0a01e538,3261384c6ba6c1c2.html