Preprints

1. F. Bachoc, Nataša Bolić, T. Cesari and R. Colomboni
   "An online learning theory of brokerage"
   [hal]
2. F. Bachoc, A. González-Sanz, J-M. Loubes and Y. Yao
   "Wasserstein spatial depth"
   [arXiv]
3. M. Deronzier, A. F. López-Lopera, F. Bachoc, O. Roustant and J. Rohmer
   "Block-additive Gaussian processes under monotonicity constraints"
   [arXiv]
4. L. Grammont, F. Bachoc and A. F. López-Lopera
   "Error bounds for a kernel-based constrained optimal smoothing approximation"
   [arXiv]
5. A. Barry, F. Bachoc, S. Bouquet, M.Munoz-Zuniga and C. Prieur
   "Optimal design of physical and numerical experiments for computer code calibration"
   [hal]
6. E. Odin, F. Bachoc and A. Lagnoux
   "Contraction rates and projection subspace estimation with Gaussian process priors in high dimension"
   [arXiv]
7. J. Bona-Pellissier, F. Malgouyres and F. Bachoc
   "Geometry-induced implicit regularization in deep ReLU neural networks"
   [hal]

Refereed journal articles

1. F. Bachoc, L. Béthune, A. Gonzalez-Sanz and J-M. Loubes
   "Improved learning theory for kernel distribution regression with two-stage sampling"
   Annals of statistics, forthcoming
   [arXiv] [code]
2. F. Bachoc, C. Maugis-Rabusseau and P. Neuvial
   "Selective inference after convex clustering with l1 penalization"
   ESAIM: probability and statistics, forthcoming
   [arXiv]
3. P-L. Antonsanti, G. Daniel, F. Bachoc and C. Le Loirec
   "Dynamic dose equivalent rate estimation in dismantling: Physic-informed surrogate modelling"
   Nuclear engineering and design, 436 (2025) 113971
   [journal]
4. L. Reding, A. F. López-Lopera and F. Bachoc
   "Covariance parameter estimation of Gaussian processes with approximated functional inputs"
   Journal of multivariate analysis, 205 (2025) 105380
   [arXiv]
5. F. Bachoc and A. Lagnoux
   "Posterior contraction rates for constrained deep Gaussian processes in density estimation and classification"
   Communications in statistics – theory and methods, 54(3) (2025)
   [arXiv]
6. F. Bachoc, T. Cesari, R. Colomboni and A. Paudice
   "A theoretical framework for zeroth-order budget convex optimization"
   Transactions on machine learning research, (2024)
   [arXiv]
7. F. Bachoc, C. Muehlmann, K. Nordhausen and J. Virta
   "Large-sample properties of non-stationary source separation for Gaussian signals"
   Electronic journal of statistics, 18 (2024) 2241-2291
   [arXiv]
8. J. Bétancourt, F. Bachoc, T. Klein, D. Idier, J. Rohmer and Y. Deville
   "funGp: an R package for Gaussian process regression with scalar and functional inputs"
   Journal of statistical software, 109(5) (2024)
   [hal]
9. J. Demange-Chryst, F. Bachoc, J. Morio and T Krauth
   "Variational autoencoder with weighted samples for high-dimensional non-parametric adaptive importance sampling"
   Transactions on machine learning research, (2024)
   [arXiv]
10. C. Muehlmann, F. Bachoc, K. Nordhausen and M. Yi
    "Test of the latent dimension of a spatial blind source separation model"
    Statistica sinica, 34(2) (2024)
    [arXiv]
11. J. Demange-Chryst, F. Bachoc and J. Morio
    "Efficient estimation of multiple expectations with the same sample by adaptive importance sampling and control variates"
    Statistics and computing, 33(103) (2023)
    [arXiv]
12. G. Damblin, F. Bachoc, S. Gazzo, L. Sargentini and A. Ghione
    "A generalization of the CIRCE method for quantifying input model uncertainty in presence of several groups of experiments"
    Nuclear engineering and design, 413 (2023) 112527
    [arXiv]
13. D. Idier, J. Rohmer, R. Pedreros, S. Le Roy, J. Betancourt, F. Bachoc and S. Lecacheux
    "Coastal flood at Gâvres (Brittany, France): a simulated dataset to support risk management and metamodels development"
    Journal of marine science and engineering, 11(7) (2023)
    [journal]
14. J. Bona-Pellissier, F. Bachoc and F. Malgouyres
    "Parameter identifiability of a deep feedforward ReLU neural network"
    Machine learning, 112 (2023) 4431–4493
    [arXiv]
15. F. Bachoc and M. Fathi
    "Bounds in L1 Wasserstein distance on the normal approximation of general M-estimators"
    Electronic journal of statistics, 17(1) (2023) 1457-1491
    [arXiv]
16. F. Bachoc, F. Gamboa, M. Halford, J-M. Loubes and L. Risser
    "Explaining machine learning models using entropic variable projection"
    Information and inference: a journal of the IMA, 12(3) (2023) 1686–1715
    [arXiv]
17. J. Demange-Chryst, F. Bachoc and J. Morio
    "Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling"
    International journal for uncertainty quantification, 13(3) (2023) 1-37
    [arXiv]
18. J. Rohmer, D. Idier, R. Thieblemont, G. Le Cozannet and F. Bachoc
    "Partitioning the uncertainty contributions of dependent offshore forcing conditions in the probabilistic assessment of future coastal flooding at a macrotidal site"
    Natural hazards and earth system sciences, 22(10) (2022) 3167-3182
    [journal]
19. F. Bachoc, A. F. López-Lopera and O. Roustant
    "Sequential construction and dimension reduction of Gaussian processes under inequality constraints"
    SIAM Journal on mathematics of data science, 4(2) (2022) 772-800
    [arXiv]
20. F. Bachoc, A. P. Peron and E. Porcu
    "Multivariate Gaussian random fields over generalized product spaces involving the hypertorus"
    Theory of probability and mathematical statistics, special issue Theory and Applications of Random Fields, 107 (2022)
    [hal]
21. M.T. Vu, F. Bachoc and E. Pauwels
    "Rate of convergence for geometric inference based on the empirical Christoffel function"
    ESAIM: probability and statistics, 26 (2022) 171–207
    [arXiv]
22. C. Muehlmann, F. Bachoc and K. Nordhausen
    "Blind source separation for non-stationary random fields"
    Spatial statistics, 47 (2022) 100574
    [arXiv]
23. B. Broto, F. Bachoc, L. Clouvel and J-M Martinez
    "Block-diagonal covariance estimation and application to the Shapley effects in sensitivity analysis"
    SIAM/ASA Journal on uncertainty quantification, 10(1) (2022) 379-403
    [arXiv]
24. F. Bachoc, N. Durrande, D. Rullière and C. Chevalier
    "Properties and comparison of some Kriging sub-model aggregation methods"
    Mathematical geosciences, 54 (2022) 941-977
    [pdf] [hal] [arXiv]
25. A. F. López-Lopera, D. Idier, J. Rohmer and F. Bachoc
    "Multioutput Gaussian processes with functional data: a study on coastal flood hazard assessment"
    Reliability engineering and system safety, 218(A) (2022) 108139
    [arXiv]
26. F. Bachoc, E. Porcu, M. Bevilacqua, R. Furrer and T. Faouzi
    "Asymptotically equivalent prediction in multivariate geostatistics"
    Bernoulli, 28(4) (2022) 2518-2545
    [arXiv]
27. A. Fradi, C. Samir and F. Bachoc
    "A scalable approximate Bayesian inference for high-dimensional Gaussian processes"
    Communications in statistics - theory and methods, 51(17) (2022) 5937-5956
    [journal]
28. D. Idier, A. Aurouet, F. Bachoc, A. Baills, J. Betancourt, F. Gamboa, T. Klein, A. F. López-Lopera, R. Pedreros, J. Rohmer and A. Thibault
    "A user-oriented local coastal flooding early warning system using metamodelling techniques"
    Journal of marine science and engineering, 9(11) (2021)
    [journal]
29. B. Broto, F. Bachoc, M. Depecker and J.M. Martinez
    "Gaussian linear approximation for the estimation of the Shapley effects"
    SIAM/ASA Journal on uncertainty quantification, 9(3) (2021) 1132-1151
    [hal]
30. F. Bachoc, T. Barthe, T. Santner and Y. Richet
    "Sequential design of mixture experiments with an empirically determined input domain and an application to burn-up credit penalization of nuclear fuel rods"
    Nuclear engineering and design, 374 (2021) 111034
    [arXiv]
31. A. Fradi, Y. Feunteunp, C. Samir, M. Baklouti, F. Bachoc and J-M. Loubes
    "Bayesian regression and classification using Gaussian process priors indexed by probability density functions"
    Information sciences, 548(16) (2021) 56-68
    [journal]
32. J-M. Azais, F. Bachoc, A. Lagnoux and T.M.N. Nguyen
    "Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments"
    ESAIM: probability and statistics, 24 (2020) 842-882
    [arXiv]
33. F. Bachoc, A. Suvorikova, D. Ginsbourger, J-M. Loubes and V. Spokoiny
    "Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding"
    Electronic journal of statistics, 14(2) (2020) 2742-2772
    [arXiv]
34. F. Bachoc, J. Bétancourt, R. Furrer and T. Klein
    "Asymptotic properties of the maximum likelihood and cross validation estimators for transformed Gaussian processes"
    Electronic journal of statistics, 14(1) (2020) 1962-2008
    [arXiv]
35. B. Broto, F. Bachoc and M. Depecker
    "Variance reduction for estimation of Shapley effects and adaptation to unknown input distribution"
    SIAM/ASA Journal on uncertainty quantification, 8(2) (2020) 693-716
    [arXiv]
36. F. Bachoc and A. Lagnoux
    "Fixed-domain asymptotic properties of composite likelihood estimators for Gaussian processes"
    Journal of statistical planning and inference, 209 (2020) 62-75
    [hal] [code]
37. F. Bachoc, C. Helbert and V. Picheny
    "Gaussian process optimization with failures: classification and convergence proof"
    Journal of global optimization, 78 (2020) 483-506
    [pdf] [hal]
38. J. Betancourt, F. Bachoc, T. Klein, D. Idier, R. Pedreros and J. Rohmer
    "Gaussian process metamodeling of functional-input code for coastal flood hazard assessment"
    Reliability engineering and system safety, 198 (2020) 106870
    [hal]
39. F. Bachoc, M. G. Genton, K. Nordhausen, A. Ruiz-Gazen and J. Virta
    "Spatial blind source separation"
    Biometrika, 107(3) (2020) 627-646
    [arXiv]
40. F. Bachoc, B. Broto, F. Gamboa and J-M. Loubes
    "Gaussian processes indexed on the symmetric group: prediction and learning"
    Electronic journal of statistics, 14 (2020) 503-546
    [arXiv]
41. F. Bachoc, D. Preinerstorfer and L. Steinberger
    "Uniformly valid confidence intervals post-model-selection"
    Annals of statistics, 48(1) (2020) 440-463.
    [arXiv] [code]
42. F. Bachoc, A. Lagnoux and A. F. López-Lopera
    "Maximum likelihood estimation for Gaussian processes under inequality constraints"
    Electronic journal of statistics, 13(2) (2019) 2921-2969
    [arXiv]
43. F. Bachoc, M. Bevilacqua and D. Velandia
    "Composite likelihood estimation for a Gaussian process under fixed domain asymptotics"
    Journal of multivariate analysis, 174 (2019)
    [arXiv]
44. M. Ben Salem, F. Bachoc, O. Roustant, F. Gamboa and L. Tomaso
    "Gaussian process based dimension reduction for goal-oriented sequential design"
    SIAM/ASA Journal on uncertainty quantification, 7(4) (2019) 1369-1397
    [hal]
45. B. Broto, F. Bachoc, M. Depecker and J.M. Martinez
    "Sensitivity indices for independent groups of variables"
    Mathematics and computers in simulation, 163 (2019) 19-31
    [arXiv]
46. J. Bect, F. Bachoc and D. Ginsbourger
    "A supermartingale approach to Gaussian process based sequential design of experiments"
    Bernoulli, 25(4A) (2019) 2883-2919
    [hal] [arXiv]
47. F. Bachoc, H. Leeb and B. Pötscher
    "Valid confidence intervals for post-model-selection predictors"
    Annals of statistics, 47(3) (2019) 1475-1504
    [arXiv] [code]
48. F. Bachoc, G. Blanchard and P. Neuvial
    "On the Post Selection Inference constant under Restricted Isometry Properties"
    Electronic journal of statistics, 12(2) (2018) 3736-3757
    [arXiv]
49. A. F. López-Lopera, F. Bachoc, N. Durrande and O. Roustant
    "Finite-dimensional Gaussian approximation with linear inequality constraints"
    SIAM/ASA Journal on uncertainty quantification, 6(3) (2018) 1224-1255.
    [pdf] [arXiv]
50. F. Bachoc, F. Gamboa, J-M. Loubes and N. Venet
    "Gaussian process regression model for distribution inputs"
    IEEE transactions on information theory, 64(10) (2018) 6620-6637
    [pdf] [arXiv] [code]
51. F. Bachoc
    "Asymptotic analysis of covariance parameter estimation for Gaussian processes in the misspecified case"
    Bernoulli 24(2) (2018) 1531-1575
    [pdf] [arXiv] [supplementary material]
52. D. Rullière, N. Durrande, F. Bachoc and C. Chevalier,
    "Nested Kriging predictions for datasets with large number of observations",
    Statistics and computing 28(4) (2018) 849-867
    [pdf], [hal] [arXiv]
53. F. Bachoc, A. Lagnoux and T.M.N. Nguyen,
    "Cross-validation estimation of covariance parameters under fixed-domain asymptotics",
    Journal of multivariate analysis 160 (2017) 42-67
    [pdf] [hal] [arXiv] [code]
54. D. Velandia, F. Bachoc, M. Bevilacqua, X. Gendre, J-M. Loubes
    "Maximum likelihood estimation for a bivariate Gaussian process under fixed domain asymptotics",
    Electronic journal of statistics 11(2) (2017) 2978-3007
    [pdf] [arXiv]
55. F. Bachoc, M. Ehler and M.Gräf
    "Optimal configurations of lines and a statistical application"
    Advances in computational mathematics 43(1) (2017) 113-126
    [pdf] [arXiv]
56. R. Furrer, F. Bachoc and J. Du
    "Asymptotic properties of multivariate tapering for estimation and prediction"
    Journal of multivariate analysis 149 (2016) 177-191
    [pdf] [arXiv]
57. F. Bachoc and Reinhard Furrer
    "On the smallest eigenvalues of covariance matrices of multivariate spatial processes"
    Stat 5 (2016) 102–107
    [pdf] [arXiv]
58. F. Bachoc, K. Ammar and J.M. Martinez
    "Improvement of code behaviour in a design of experiments by metamodeling"
    Nuclear science and engineering 183(3) (2016) 387-406
    [pdf] [arXiv]
59. F. Bachoc
    "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes"
    Journal of multivariate analysis 125 (2014) 1–35
    [pdf] [arXiv] [supplementary material]
60. F. Bachoc, G. Bois, J. Garnier and J.M. Martinez
    "Calibration and improved prediction of computer models by universal Kriging"
    Nuclear science and engineering 176(1) (2014) 81-97
    [pdf] [arXiv]
61. F. Bachoc
    "Cross Validation and Maximum Likelihood estimation of hyper-parameters of Gaussian processes with model misspecification"
    Computational statistics and data analysis 66 (2013) 55–69
    [pdf] [arXiv]

Refereed international conference proceedings

1. F. Bachoc, T. Cesari and R. Colomboni
   "A contextual online learning theory of brokerage"
   ICML, International Conference on Machine Learning, 2025
   [arXiv]
2. F. Bachoc, T. Cesari and R. Colomboni
   "A tight regret analysis of non-parametric repeated contextual brokerage"
   AISTATS, International Conference on Artificial Intelligence and Statistics, 2025
   [arXiv]
3. F. Bachoc, N. Cesa-Bianchi, T. Cesari and R. Colomboni
   "Fair online bilateral trade"
   NeurIPS, Conference on Neural Information Processing Systems, 2024
   [arXiv]
4. F. Bachoc, L. Béthune, A. Gonzalez-Sanz and J-M. Loubes
   "Gaussian processes on distributions based on regularized optimal transport"
   AISTATS, International Conference on Artificial Intelligence and Statistics, 2023
   [arXiv]
5. J. Bona-Pellissier, F. Malgouyres and F. Bachoc
   "Local identifiability of deep ReLU neural networks: the theory"
   NeurIPS, Conference on Neural Information Processing Systems, 2022
   [arXiv]
6. A. F. López-Lopera, F. Bachoc and O. Roustant
   "High-dimensional additive Gaussian processes under monotonicity constraints"
   NeurIPS, Conference on Neural Information Processing Systems, 2022
   [arXiv]
7. F. Bachoc, T. Cesari and S. Gerchinovitz
   "Instance-dependent bounds for zeroth-order Lipschitz optimization with error certificates"
   NeurIPS, Conference on Neural Information Processing Systems, 2021
   [arXiv]
8. F. Bachoc, T. Cesari and S. Gerchinovitz
   "The sample complexity of level set approximation"
   AISTATS - oral presentation, International Conference on Artificial Intelligence and Statistics, 2021
   [arXiv]
9. D. Idier, A. Aurouet, F. Bachoc, A. Baills, J. Betancourt, J. Durand, R. Mouche, J. Rohmer, F. Gamboa, T. Klein, J. Lambert, G. Le Cozannet, S. Le Roy, J. Louisor, R. Pedreros and A-L Véron
   "Toward a user-based, robust and fast running method for coastal flooding forecast, early warning, and risk prevention"
   Journal of coastal research, special issue 95, p. 11-15, proceedings from the International Coastal Symposium (ICS) 2020, forthcoming
   
10. C. Samir, J-M. Loubes, A.-F. Yao and F. Bachoc
    "Learning a Gaussian process model on the Riemannian manifold of non-decreasing distribution functions"
    PRICAI, Pacific Rim International Conference on Artificial Intelligence, Trends in Artificial Intelligence pp 107-120, 2019
    [hal]
11. A. F. López-Lopera, F. Bachoc, N. Durrande, J. Rohmer, D. Idier and O. Roustant
    "Approximating Gaussian process emulators with linear inequality constraints and noisy observations via MC and MCMC"
    MCQMC, Monte Carlo and Quasi-Monte Carlo Methods (2018)
    [arXiv]

Refereed book chapters

1. F. Bachoc
   "Asymptotic analysis of maximum likelihood estimation of covariance parameters for Gaussian processes: an introduction with proofs"
   Advances in Contemporary Statistics and Econometrics (2021) pp 283-303, Festschrift in honor of Christine Thomas Agnan
   [arXiv]
2. F. Bachoc, E. Contal, H. Maatouk and D. Rullière
   "Gaussian processes for computer experiments"
   ESAIM: Proceedings and Surveys 60 (2017) 163 - 179
   [pdf]
3. F. Bachoc, A. Bachouch and L. Lenôtre
   "Hastings-Metropolis algorithm on Markov chains for small-probability estimation"
   ESAIM: Proceedings and Surveys 48 (2015) p.276
   [pdf] [arXiv]

Refereed national conference proceedings

1. A. Barry, F. Bachoc, C. Prieur, S. Bouquet and M. Munoz-Zuniga
   "Plans d’expériences pour la calibration de code de calcul coûteux"
   Proceedings of the 55e Journées de Statistique Bordeaux, May 27-31 2024
   [pdf]
2. D. Idier, A. Aurouet, F. Bachoc, A. Baills, J. Betancourt, F. Gamboa, T. Klein, S. Le Roy, A. López-Lopera, J. Louisor, R. Pedreros, J. Rohmer and A. Thibault
   "Un système local de prévision et alerte des submersions côtières centré sur les besoins des utilisateurs et utilisant des techniques de métamodélisation"
   XVIIèmes Journées Nationales Génie Côtier – Génie Civil Chatou, 2022
   [pdf]
3. F. Bachoc and A. Lagnoux
   "Posterior contraction rates for constrained deep Gaussian processes in density estimation and classification"
   Proceedings of the 53e Journées de Statistique Lyon, June 13-17 2022
   [pdf]
4. F. Bachoc, D. Preinerstorfer and L. Steinberger
   "Uniformly valid confidence intervals post-model-selection"
   Proceedings of the 49e Journées de Statistique Avignon, May 29-June 2 2017
   [pdf]
5. F. Bachoc, F. Gamboa, J-M. Loubes and N. Venet
   "Gaussian process regression model for distribution inputs"
   Proceedings of the 49e Journées de Statistique Avignon, May 29-June 2 2017
   [pdf]
6. F. Bachoc, H. Leeb and B. Pötscher
   "Valid confidence intervals for post-model-selection predictors"
   Proceedings of the 47e Journées de Statistique Lille, 1-5 June 2015
   [pdf]
7. F. Bachoc, J. Garnier and J.M. Martinez
   "Maximum likelihood and cross validation for covariance hyper-parameter estimation for Kriging",
   Proceedings of the 45e Journées de Statistique Toulouse, 27-31 Mai 2013
   [pdf]

Technical reports

1. J.M. Martinez, A. Marrel, N. Gilardi and F. Bachoc,
   "Krigeage par processus gaussiens Librairie gpLib",
   Internal report CEA DEN/DANS/DM2S/STMF/LGLS/RT/12-026/A. 50p. 2012
   Available upon request
2. F. Bachoc, G. Bois and J.M. Martinez
   "Contribution à la validation des codes de calcul par Processus Gaussiens. Application à la calibration du modèle de frottement pariétal de Flica 4",
   Internal report CEA DEN/DANS/DM2S/STMF/LGLS/RT/12-007/A. 42p. 2012
   Available upon request
3. F. Bachoc
   "Calibration de modèles physiques par méthodes probabilistes",
   Internal report CEA DEN/DANS/DM2S/SFME/LGLS/RT/10-015/A. 78p. 2010
   Available upon request

Software

1. J. Betancourt, F. Bachoc, T. Klein, D. Idier and J. Rohmer,
   "funGp: Gaussian process models for scalar and functional inputs",
   R package 2020
   [link]