Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics, vol.44, issue.2, pp.182-198, 2009. ,
Parametric hierarchical kriging for multi-fidelity aero-servo-elastic simulators-application to extreme loads on wind turbines, Prob. Eng. Mech, vol.55, pp.67-77, 2019. ,
Uncertainty propagation through deep neural networks, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01162550
Defects, damage, and repairs subject to high-cycle fatigue: Examples from wind farm tower design, Forensic, pp.546-555, 2009. ,
Hyperparameter selection in kernel principal component analysis, Journal of Computer Science, vol.10, issue.7, pp.1139-1150, 2014. ,
Probability concepts in engineering: emphasis on applications to civil and environmental engineering, 2007. ,
A survey of cross-validation procedures for model selection, Statistics Surveys, vol.4, pp.40-79, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00407906
, Standard Practices for Cycle Counting in Fatigue Analysis, ASTM E1049, p.85, 2017.
Cross validation and maximum likelihood estimations of hyper-parameters of Gaussian processes with model misspecifications, Comput. Stat. Data Anal, vol.66, pp.55-69, 2013. ,
Calibration and improved prediction of computer models by universal Kriging, Nucl. Sci. Eng, vol.176, pp.91-97, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01020594
STK: a Small (Matlab/Octave) Toolbox for Kriging, 2014. ,
Vines-a new graphical model for dependent random variables, The Annals of Statistics, vol.30, issue.4, pp.1031-1068, 2002. ,
Laplacian eigenmaps and spectral techniques for embedding and clustering, Advances in neural information processing systems, pp.585-591, 2002. ,
Out-of-sample extensions for lle, isomap, mds, eigenmaps, and spectral clustering, Advances in neural information processing systems, pp.177-184, 2004. ,
Representation of fatigue for wind turbine control, Wind Energy, vol.19, issue.12, pp.2189-2203, 2016. ,
Nonlinear programming, 1999. ,
Stochastic finite elements: a non intrusive approach by regression, Eur. J. Comput. Mech, vol.15, issue.1-3, pp.81-92, 2006. ,
, Pattern Recognition and Machine Learning (Information Science and Statistics), 2006.
Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis, 2009. ,
URL : https://hal.archives-ouvertes.fr/tel-00440197
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Eng. Mech, vol.25, pp.183-197, 2010. ,
Adaptive sparse polynomial chaos expansion based on Least Angle Regression, J. Comput. Phys, vol.230, pp.2345-2367, 2011. ,
Sparse feature learning for deep belief networks, Advances in neural information processing systems, pp.1185-1192, 2008. ,
, , 2016.
, Manifold Gaussian processes for regression, Neural Networks (IJCNN), 2016 International Joint Conference on, pp.3338-3345
Data dimensionality estimation methods: a survey, Pattern recognition, vol.36, issue.12, pp.2945-2954, 2003. ,
Marginalized denoising auto-encoders for nonlinear representations, International Conference on Machine Learning, pp.1476-1484, 2014. ,
A least-squares method for sparse low rank approximation of multivariate functions, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00861913
, Uncertainty Quantification, vol.3, issue.1, pp.897-921
Discrete least squares polynomial approximation with random evaluations -application to parametric and stochastic elliptic PDEs, ESAIM: Mathematical Modelling and Numerical Analysis, vol.49, issue.3, pp.815-837, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01352276
Time series feature extraction on basis of scalable hypothesis tests (tsfresha python package), Neurocomputing, vol.307, pp.72-77, 2018. ,
Active subspace methods in theory and practice: applications to kriging surfaces, SIAM Journal on Scientific Computing, vol.36, issue.4, pp.1500-1524, 2014. ,
ooDACE Toolbox: A Flexible Object-Oriented Kriging Implementation, Journal of Machine Learning Research, vol.15, pp.3183-3186, 2014. ,
Multidimensional Scaling, 2000. ,
Statistics for Spatial Data, Statistics for Spatial Data, pp.1-26, 1993. ,
Deep Gaussian processes, Artificial Intelligence and Statistics, pp.207-215, 2013. ,
The Bayesian approach to inverse problems, Handbook of Uncertainty Quantification, pp.311-428, 2017. ,
La maîtrise des incertitudes dans un contexte industriel : 1 e partie -Une approche méthodologique globale basée sur des exemples, J. Soc. Française Stat, vol.147, issue.3, pp.33-71, 2006. ,
La maîtrise des incertitudes dans un contexte industriel : 2 e partie -Revue des méthodes de modélisation statistique, physique et numérique, J. Soc. Française Stat, vol.147, issue.3, pp.73-106, 2006. ,
, Uncertainty in industrial practice -A guide to quantitative uncertainty management, 2008.
Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model, Reliab. Eng. Sys. Safety, vol.147, pp.156-169, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01432217
Geostatistical software library and user's guide, vol.119, p.147, 1992. ,
UCI machine learning repository, 2017. ,
A note on two problems in connexion with graphs, Numerische Mathematik, vol.1, pp.269-271, 1959. ,
Structural reliability methods, 1996. ,
High-dimensional Gaussian process bandits, Advances in Neural Information Processing Systems, pp.1025-1033, 2013. ,
Cross validation of Kriging in a unique neighborhood, J. Int. Assoc Math. Geology, vol.15, issue.6, pp.687-699, 1983. ,
DiceDesign and DiceEval: Two R packages for design and analysis of computer experiments, Journal of Statistical Software, vol.65, issue.11, pp.1-38, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-02065877
Additive covariance kernels for high-dimensional Gaussian process modeling, Annales de la Faculté de Sciences de Toulouse, vol.21, p.481, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00644934
AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation, Structural Safety, vol.33, issue.2, pp.145-154, 2011. ,
Least angle regression, Annals of Statistics, vol.32, pp.407-499, 2004. ,
Multifidelity uncertainty quantification using spectral stochastic discrepancy models, Handbook of Uncertainty Quantification, 2016. ,
Energy road map 2050, 2011. ,
Design and modeling for computer experiments, 2005. ,
Algorithm 97: Shortest path, Commun. ACM, vol.5, issue.6, p.345, 1962. ,
Learning functions of few arbitrary linear parameters in high dimensions, Foundations of Computational Mathematics, vol.12, issue.2, pp.229-262, 2012. ,
Engineering design via surrogate modelling: a practical guide, 2008. ,
Introduction to statistical pattern recognition, 2013. ,
, Orthogonal Polynomials: Computation and Approximation. Numerical Mathematics and Scientific Computation, 2004.
Stochastic finite elements -A spectral approach, 1991. ,
Stochastic finite element analysis of seismic soil-structure interaction, J. Eng. Mech, vol.128, pp.66-77, 2002. ,
Dimensionality reduction a short tutorial, 2006. ,
Domain adaptation for largescale sentiment classification: A deep learning approach, Proceedings of the 28th international conference on machine learning (ICML-11), pp.513-520, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00752091
Deep Learning, 2016. ,
Measuring invariances in deep networks, Advances in neural information processing systems, pp.646-654, 2009. ,
GPy: A Gaussian process framework in python, 2012. ,
Structural health monitoring of wind turbine blades by strain measurement and vibration analysis, 2011. ,
Fast iterative kernel principal component analysis, J. Mach. Learn. Res, vol.8, pp.1893-1918, 2007. ,
Neural network design, vol.20, 1996. ,
An algorithm for the principal component analysis of large data sets, SIAM Journal on Scientific computing, vol.33, issue.5, pp.2580-2594, 2011. ,
Alternative cokriging method for variable-fidelity surrogate modeling, AIAA journal, vol.50, issue.5, pp.1205-1210, 2012. ,
Forward stagewise regression and the monotone lasso, Electronic Journal of Statistics, vol.1, pp.1-29, 2007. ,
The elements of statistical learning: Data mining, inference and prediction, 2001. ,
Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides, Ecological modelling, vol.28, issue.4, pp.243-278, 1985. ,
A practical guide to training restricted boltzmann machines, Neural Networks: Tricks of the Trade, vol.7700, pp.599-619, 2012. ,
A fast learning algorithm for deep belief nets, Neural computation, vol.18, issue.7, pp.1527-1554, 2006. ,
Reducing the dimensionality of data with neural networks, Science, vol.313, issue.5786, pp.504-507, 2006. ,
Kernel PCA for novelty detection, Pattern Recogn, vol.40, issue.3, pp.863-874, 2007. ,
Multilayer feedforward networks are universal approximators, Neural networks, vol.2, issue.5, pp.359-366, 1989. ,
Scalable Gaussian process regression using deep neural networks, IJCAI, pp.3576-3582, 2015. ,
One-unit learning rules for independent component analysis, Advances in neural information processing systems, pp.480-486, 1997. ,
A review on global sensitivity analysis methods. In Uncertainty management in simulation-optimization of complex systems, pp.101-122, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00975701
A review on global sensitivity analysis methods. In Uncertainty Management in Simulation-Optimization of Complex Systems, pp.101-122, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00975701
Enhancing 1 -minimization estimates of polynomial chaos expansions using basis selection, J. Comput. Phys, vol.289, pp.18-34, 2015. ,
Dependence modeling with copulas, 2015. ,
Turbsim user's guide: Version 1.50, 2009. ,
The new modularization framework for the fast wind turbine cae tool, 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p.202, 2013. ,
Definition of a 5-mw reference wind turbine for offshore system development, 2009. ,
The palmgren-miner rule derived, In Tribology Series, vol.14, pp.175-179, 1989. ,
Hierarchical parallelisation for the solution of stochastic finite element equations, Computers & Structures, vol.83, pp.1033-1047, 2005. ,
A new surrogate modeling technique combining Kriging and polynomial chaos expansions -Application to uncertainty analysis in computational dosimetry, J. Comput. Phys, vol.286, pp.103-117, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01143146
SVD compression, unitary transforms, and computational complexity, IEEE transactions on signal processing, vol.47, issue.10, pp.2724-2729, 1999. ,
Global sensitivity analysis using low-rank tensor approximations, Reliab. Eng. Sys. Safety, vol.156, pp.64-83, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01428988
Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions, J. Comput. Phys, vol.321, pp.1144-1169, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01432141
Reliability analysis of high-dimensional models using low-rank tensor approximations, Prob. Eng. Mech, vol.46, pp.18-36, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01428991
Implications of historical trends in the electrical efficiency of computing, IEEE Annals of the History of Computing, vol.33, issue.3, pp.46-54, 2011. ,
A statistical approach to some basic mine valuation problems on the witwatersrand, Journal of the Southern African Institute of Mining and Metallurgy, vol.52, issue.6, pp.119-139, 1951. ,
Imagenet classification with deep convolutional neural networks, Advances in Neural Information Processing Systems, vol.25, pp.1097-1105, 2012. ,
Online kernel pca with entropic matrix updates, ACM International Conference Proceeding Series, vol.227, pp.465-472, 2007. ,
The pre-image problem in kernel methods, Proceedings of the 20th International Conference on Machine Learning (ICML-03), pp.408-415, 2003. ,
The Gaussian process modelling module in UQLab, Soft Comput. Civil Eng, vol.2, issue.3, pp.91-116, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01901966
UQLab user manual -Kriging (Gaussian process modelling), Safety & Uncertainty Quantification, 2019. ,
UQLab user manual -The Input module, Safety & Uncertainty Quantification, 2019. ,
Probabilistic non-linear principal component analysis with Gaussian process latent variable models, Journal of Machine Learning Research, vol.6, pp.1783-1816, 2005. ,
Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01428947
A stochastic projection method for fluid flow -II. Random process, J. Comput. Phys, vol.181, pp.9-44, 2002. ,
A generalization of the Nataf transformation to distributions with elliptical copula, Probabilistic Engineering Mechanics, vol.24, issue.2, pp.172-178, 2009. ,
, Structural reliability, 2009.
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural networks, vol.6, issue.6, pp.861-867, 1993. ,
Optimal discretization of random fields, J. Eng. Mech, vol.119, issue.6, pp.1136-1154, 1993. ,
On the use of kernel PCA for feature extraction in speech recognition, 2003. ,
Divergence measures based on the shannon entropy, IEEE Transactions on Information theory, vol.37, issue.1, pp.145-151, 1991. ,
Aspects of the Matlab toolbox DACE, Informatics and Mathematical Modelling, 2002. ,
UQLab user manual -Sensitivity analysis, Safety & Uncertainty Quantification, 2019. ,
Chair of Risk, Safety and Uncertainty Quantification, 2019. ,
UQLab: A framework for uncertainty quantification in Matlab, Vulnerability, Uncertainty, and Risk (Proc. 2nd, 2014. ,
, on Vulnerability, Risk Analysis and Management (ICVRAM2014), pp.2554-2563
Chair of Risk, Safety & Uncertainty Quantification, 2018. ,
An efficient methodology for modeling complex computer codes with Gaussian processes, Computational Statistics & Data Analysis, vol.52, issue.10, pp.4731-4744, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00239492
MATLAB and Statistics and Machine Learning Toolbox Release, 2017. ,
A logical calculus of the ideas immanent in nervous activity, The bulletin of mathematical biophysics, vol.5, issue.4, pp.115-133, 1943. ,
A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, vol.2, pp.239-245, 1979. ,
Structural reliability analysis and prediction, 1999. ,
Cumulative damage in fatigue, J. Appl. Mech, issue.9, pp.159-164, 1945. ,
Face recognition using kernel eigenfaces, Proceedings. 2000 International Conference on, vol.1, pp.37-40, 2000. ,
On the number of linear regions of deep neural networks, Advances in neural information processing systems, pp.2924-2932, 2014. ,
Quantilebased optimization under uncertainties using adaptive Kriging surrogate models, Struct. Multidisc. Optim, 2016. ,
Comparative study of Kriging and support vector regression for structural engineering applications, Paper #04018005, vol.4, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01893274
Machine learning: A probabilistic perspective. adaptive computation and machine learning, 2012. ,
Détermination des distributions dont les marges sont données, C. R. Acad. Sci. Paris, vol.225, pp.42-43, 1962. ,
An introduction to copulas, Lecture Notes in Statistics, vol.139, 2006. ,
Sparse coding with an overcomplete basis set: A strategy employed by v1?, Vision research, vol.37, issue.23, pp.3311-3325, 1997. ,
Fast dimensionality reduction and simple PCA, Intelligent Data Analysis, vol.2, issue.1-4, pp.203-214, 1998. ,
On estimation of a probability density function and mode, The Annals of Mathematical Statistics, vol.33, issue.3, pp.1065-1076, 1962. ,
, pyKriging: A Python Kriging Toolkit, 2015.
On lines and planes of closest fit to systems of points in space, Phil. Mag, vol.6, issue.2, pp.559-572, 1901. ,
Scikitlearn: Machine learning in python, Journal of machine learning research, vol.12, pp.2825-2830, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00650905
DiceOptim: Kriging-Based Optimization for Computer Experiments, 2016. ,
, Principles, Algorithms, and Applications, 1996.
Gaussian processes for machine learning. Adaptive computation and machine learning, 2006. ,
Gaussian Processes for Machine Learning (GPML) Toolbox, Journal of Machine Learning Research, vol.11, pp.3011-3015, 2010. ,
Wavelet functions and their polynomials, Geophysics, vol.9, issue.3, pp.314-323, 1944. ,
Contractive auto-encoders: Explicit invariance during feature extraction, Proceedings of the 28th International Conference on International Conference on Machine Learning, pp.833-840, 2011. ,
Stochastic simulation, vol.316, 2009. ,
A randomized algorithm for principal component analysis, SIAM Journal on Matrix Analysis and Applications, vol.31, issue.3, pp.1100-1124, 2009. ,
Remarks on a multivariate transformation, The Annals of Mathematical Statistics, vol.23, pp.470-472, 1952. ,
Remarks on some nonparametric estimates of a density function, The Annals of Mathematical Statistics, pp.832-837, 1956. ,
DiceKriging, DiceOptim : Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization, Journal of Statistical Software, vol.51, issue.1, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00495766
Nonlinear dimensionality reduction by locally linear embedding, Science, vol.290, pp.2323-2326, 2000. ,
A new definition of the rainflow cycle counting method, International journal of fatigue, vol.9, issue.2, pp.119-121, 1987. ,
Design and analysis of computer experiments, Stat. Sci, vol.4, pp.409-435, 1989. ,
, Sensitivity analysis, 2000.
The Design and Analysis of Computer Experiments, 2003. ,
UQLab user manual -Polynomial chaos Kriging, Chair of Risk, Safety & Uncertainty Quantification, 2019. ,
Polynomial-chaos-based Kriging, Int. J. Uncertainty Quantification, vol.5, issue.2, pp.171-193, 2015. ,
Nonlinear component analysis as a kernel eigenvalue problem, Neural Comput, vol.10, issue.5, pp.1299-1319, 1998. ,
Global sensitivity analysis for high-dimensional problems: How to objectively group factors and measure robustness and convergence while reducing computational cost. Environmental modelling & software 111, pp.282-299, 2019. ,
Density estimation for statistics and data analysis, 2018. ,
Fonctions de répartition à n dimensions et leurs marges, vol.8, p.11, 1959. ,
Practical Bayesian optimization of machine learning algorithms, Advances in neural information processing systems, pp.2951-2959, 2012. ,
Sensitivity estimates for nonlinear mathematical models, Math. Modeling & Comp. Exp, vol.1, pp.407-414, 1993. ,
Physical systems with random uncertainties: chaos representations with arbitrary probability measure, SIAM J. Sci. Comput, vol.26, issue.2, pp.395-410, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00686211
Polynomial chaos representation of databases on manifolds, J. Comp. Phys, vol.335, pp.201-221, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01448413
Interpolation of Spatial Data: Some Theory for Kriging, 1999. ,
A generalised solution to the out-ofsample extension problem in manifold learning, Twenty-Fifth AAAI Conference on Artificial Intelligence, pp.293-296, 2011. ,
Uncertainty propagation and sensitivity analysis in mechanical models -Contributions to structural reliability and stochastic spectral methods, 2007. ,
Extending Sammon mapping with Bregman divergences, Information Sciences, vol.187, pp.72-92, 2012. ,
Fatigue of materials, 1998. ,
A global geometric framework for nonlinear dimensionality reduction, Science, vol.290, issue.5500, pp.2319-2323, 2000. ,
, Lossy image compression with compressive autoencoders, 2017.
Regression shrinkage and selection via the Lasso, J. Royal Stat. Soc., Series B, vol.58, pp.267-288, 1996. ,
A bias correction for the minimum error rate in cross-validation, The Annals of Applied Statistics, pp.822-829, 2009. ,
Sparse kernel principal component analysis, Advances in Neural Information Processing Systems, vol.13, pp.633-639, 2001. ,
Mixtures of probabilistic principal component analyzers, Neural computation, vol.11, issue.2, pp.443-482, 1999. ,
Probabilistic principal component analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.3, pp.611-622, 1999. ,
A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas, Prob. Eng. Mech, vol.55, pp.1-16, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01901982
Data-driven polynomial chaos expansion for machine learning regression, J. Comp. Phys, vol.388, pp.601-623, 2019. ,
Chair of Risk, Safety & Uncertainty Quantification, 2019. ,
Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation, J. Comp. Phys, vol.321, pp.191-223, 2016. ,
Structural design optimization considering uncertainties, 2008. ,
Long-term o&m costs of wind turbines based on failure rates and repair costs, Proceedings WINDPOWER, American Wind Energy Association annual conference, pp.2-5, 2002. ,
Dimensionality reduction: a comparative review, J Mach Learn Res, vol.10, pp.66-71, 2009. ,
The Nature of Statistical Learning Theory, 1995. ,
, Statistical Learning Theory, 1998.
The curse of dimensionality in data mining and time series prediction, Computational Intelligence and Bioinspired Systems, vol.3512, pp.758-770, 2005. ,
Extracting and composing robust features with denoising autoencoders, Proceedings of the 25th international conference on Machine learning, pp.1096-1103, 2008. ,
Learning deep dynamical models from image pixels, IFAC-PapersOnLine, vol.48, issue.28, pp.1059-1064, 2015. ,
Learning a kernel matrix for nonlinear dimensionality reduction, Proceedings of the twenty-first international conference on Machine learning, p.106, 2004. ,
, , 1992.
, Screening, predicting, and computer experiments, Technometrics, vol.34, pp.15-25
Learning to find pre-images, Advances in neural information processing systems, pp.449-456, 2004. ,
EU energy policy to 2050-achieving 80-95% emissions reduction, 2011. ,
On a connection between kernel PCA and metric multidimensional scaling, Machine Learning, vol.46, issue.1, pp.11-19, 2002. ,
Deep kernel learning, Artificial Intelligence and Statistics, pp.370-378, 2016. ,
Experiments: Planning. Analysis, and Parameter Design Optimization, 2000. ,
Image denoising and inpainting with deep neural networks, Advances in neural information processing systems, pp.341-349, 2012. ,
Numerical methods for stochastic computations -A spectral method approach, 2010. ,
High-order collocation methods for differential equations with random inputs, SIAM J. Sci. Comput, vol.27, issue.3, pp.1118-1139, 2005. ,
The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput, vol.24, issue.2, pp.619-644, 2002. ,
Sliced-inverse-regressionaided rotated compressive sensing method for uncertainty quantification, 2018. ,
, Journal on Uncertainty Quantification, vol.6, issue.4, pp.1532-1554
Big-data tensor recovery for high-dimensional uncertainty quantification of process variations, IEEE Transactions on Components, Packaging and Manufacturing Technology, vol.7, issue.5, pp.687-697, 2017. ,