Chair of applied mathematics OQUAIDO

Optimization and uncertainty quantification for expensive data

Cross classification scientific production
Inversion /
Categorical inputs J13 P5 S1 J12 P8
Stochastic codes P3 P4 J15
Functional inputs/outputs
High number of inputs
J10 J7 J10 J15 P6 J2 J5 J14 J16 J10 P9
Specific constraints P2 S2 J6 J8 C2 C3
High number of data S3 S4 J3 J4 P1
Other topics J1 J1 J9 S1 S5 J11 C1 P7

Software(*) (S)

  1. kergp: Kernel laboratory. This package, created during the ReDICE consortium, has been enriched with new functionalities: categorical variables, radial kernels, optimizer choices, etc.
  2. lineqGPR : Gaussian Process Regression Models with Linear Inequality Constraints.
  3. nestedKriging : Nested kriging models for large data sets.
  4. specgp: Construction of kernels by the spectral approach, suitable e.g. for large datasets.
  5. libKriging: This is an ongoing software project, to enhance an industrial usage of OQUAIDO results. libKriging will include fast and portable implementations for GP modeling, with a wide test coverage.
Several notebooks and vignettes have been written to ease the discovery of these packages. There are often delivered within the packages, as part of the documentation. Finally, another package, called mixgp, dedicated to Kriging models with both discrete and continuous input variables, has been developped in the first years of the Chair. It is now included in kergp.

Publications in journals (J)

  1. Universal Prediction Distribution for Surrogate Models, M. Ben Salem, O. Roustant, F. Gamboa, and L. Tomaso (2017), SIAM/ASA Journal on Uncertainty Quantification, 5 (1), 1086-1109.
  2. Poincaré inequalities on intervals - application to sensitivity analysis O. Roustant, F. Barthe and B. Iooss (2017), Electronic Journal of Statistics, 11 (2), 3081-3119.
  3. Variational Fourier Features for Gaussian Processes J. Hensman, N. Durrande and A. Solin (2018), Journal of Machine Learning Research, 8, 1-52.
  4. Nested Kriging predictions for datasets with a large number of observations, D. Rullière, N. Durrande, F. Bachoc and C. Chevalier (2018), Statistics and Computing, 28 (4), 849-867.
  5. Sensitivity Analysis Based on Cramér von Mises Distance, F. Gamboa, T. Klein, and A. Lagnoux (2018), SIAM/ASA Journal on Uncertainty Quantification, 6 (2), 522-548.
  6. Finite-dimensional Gaussian approximation with linear inequality constraints, A.F. López-Lopera, F. Bachoc, N. Durrande and O. Roustant (2018), SIAM/ASA J. Uncertainty Quantification, 6 (3), 1224–1255.
  7. Data-driven stochastic inversion via functional quantization, M.R. El Amri, C. Helbert, O. Lepreux, M. Munoz Zuniga, C. Prieur and D. Sinoquet (2020), Statistics and Computing, 30 (3), 525-541 (published online on Sept. 13 2019).
  8. Maximum likelihood estimation for Gaussian processes under inequality constraints, F. Bachoc, A. Lagnoux and A.F. López-Lopera (2019), Electronic Journal of Statistics, 13 (2), 2921-2969.
  9. Profile extrema for visualizing and quantifying uncertainties on excursion regions. Application to coastal flooding., D. Azzimonti, D. Ginsbourger, J. Rohmer and D. Idier (2019), Technometrics, 61 (4), 474-493.
  10. Sequential dimension reduction for learning features of expensive black-box functions, M. Ben Salem, F. Bachoc, O. Roustant, F. Gamboa F and L. Tomaso (2019), SIAM/ASA Journal on Uncertainty Quantification, 7 (4), 1369-1397 .
  11. Karhunen-Loève decomposition of Gaussian measures on Banach spaces, X. Bay and J.C. Croix (2019), Probability and Mathematical Statistics, 39 (2), 279-297.
  12. Group kernels for Gaussian process metamodels with categorical inputs, O. Roustant, E. Padonou, Y. Deville, A. Clément, G. Perrin, J. Giorla and H. Wynn (2020), SIAM/ASA Journal on Uncertainty Quantification, 8 (2), 775-806.
  13. Global optimization for mixed categorical-continuous variables based on Gaussian process models with a randomized categorical space exploration step, Miguel Munoz Zuniga and Delphine Sinoquet (2020), INFOR Journal, 58, 310-341.
  14. Parseval inequalities and lower bounds for variance-based sensitivity indices, O. Roustant, F. Gamboa, B. Iooss (2020), Electronic Journal of Statistics, 14(1), 386-412.
  15. Sequential design of mixture experiments with an empirically determined input domain and an application to burn-up credit penalization of nuclear fuel rods, F. Bachoc, T. Barthe, T. Santner, Y. Richet (2021), to appear in Nuclear Engineering and Design, 374.
  16. Functional principal component analysis for global sensitivity analysis of model with spatial output, T.V.E. Perrin, O. Roustant, J. Rohmer, O. Alata, J.P. Naulin, D. Idier, R. Pedreros, D. Moncoulon, P. Tinard (2020), to appear in Reliability Engineering & System Safety.

Preprints (P)

  1. Some properties of nested Kriging predictors, F. Bachoc, N. Durrande, D. Rullière and C. Chevalier (2017).
  2. Sequential construction and dimension reduction of Gaussian processes under inequality constraints, F. Bachoc, A. F. López-Lopera and O. Roustant (2020).
  3. A sampling criterion for constrained Bayesian optimization with uncertainties, R. El Amri, C. Helbert, C. Blanchet-Scalliet, R. Le Riche, to appear (2021).
  4. Coupling constraints in Bayesian optimization, J. Pelamatti, R. Le Riche, C. Helbert, C. Blanchet-Scalliet, to appear (2021).
  5. Optimization in presence of categorical inputs with latent variables, J. Cuesta-Ramirez, C. Durantin, A. Glière, G. Perrin, R. Le Riche, O. Roustant, to appear (2021).
  6. Set inversion under functional uncertainties with joint meta-models, R. El Amri, C. Helbert, M. Munoz-Zuniga, C. Prieur, D. Sinoquet (2020).
  7. Sequential design for prediction with Gaussian process models, M. Abtini, C. Helbert, F. Musy, L. Pronzato, M.-J. Rendas (2020).
  8. Revealing the dependence structure of scenario-like inputs in numerical environmental simulations using Gaussian Process regression, J. Rohmer, O. Roustant, S. Lecacheux, J.-C. Manceau (2020)
  9. Multi-output Gaussian processes with functional data: a study on coastal flood hazard assessment, A. F. López-Lopera, D. Idier, J. Rohmer, F. Bachoc (2020).

Conference proceedings (C)

  1. Gaussian Processes For Computer Experiments, F. Bachoc, E. Contal, H. Maatouk, and D. Rullière (2017), ESAIM: Proceedings and surveys, proceedings of MAS2016 conference, 60, p. 163-179.
  2. Gaussian Process Modulated Cox Processes under Linear Inequality Constraints, A. F. López-Lopera, S. John, and N. Durrande (2019), PMLR:, proceedings of AISTATS19 conference, 89, p. 1997-2006.
  3. Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC, A. F. López-Lopera, F. Bachoc, N. Durrande, J. Rohmer, D. Idier, and O. Roustant (2019), Monte Carlo and Quasi-Monte Carlo Methods:, proceedings of MCQMC18 conference, p. 363-381.

(*) One of the Chair activities is to develop opensource R packages that are later available on the CRAN archive website.