Chair of applied mathematics OQUAIDO

Optimization and uncertainty quantification for expensive data

Cross classification scientific production
Inversion /
Categorical inputs S1 S4 P2
Stochastic codes
Functional inputs/outputs
High number of inputs
J7 J10 J7 J10 J2 J5 J10
Specific constraints S2 J6 J8 C2 C3
High number of data S3 J3 J4 P1
Other topics J1 J1 J9 S1 J11 C1

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. mixgp: Kriging models with both discrete and continuous input variables. Will be 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 (2019), Statistics and Computing, online publication on Sept. 13.
  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, online version in January.
  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), to appear in SIAM/ASA Journal on Uncertainty Quantification.
  11. Karhunen-Loève decomposition of Gaussian measures on Banach spaces, X. Bay and J.C. Croix (2019), to appear in Probability and Mathematical Statistics.

Preprints (P)

  1. Some properties of nested Kriging predictors, F. Bachoc, N. Durrande, D. Rullière and C. Chevalier (2017).
  2. Group kernels for Gaussian process metamodels with categorical inputs, O. Roustant, E. Padonou, Y. Deville, A. Clément, G. Perrin, J. Giorla and H. Wynn (2018).

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), to appear in Monte Carlo and Quasi-Monte Carlo Methods:, proceedings of MCQMC18 conference, 13, p. 355-371.

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