![Bertrand Gauthier](https://profiles-cardiff.imgix.net/attachments/176?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Dr Bertrand Gauthier
- Available for postgraduate supervision
Teams and roles for Bertrand Gauthier
Lecturer
Overview
I am a menber of the Statistics and Data Science Research Group.
My research lies at the interface between mathematics and data science, and focuses on the design and analysis of data-driven, problem-dependent learning and modelling strategies. I am particularly interested in exploring the connections between statistical learning, approximation theory and computational mathematics, with the aim of developing theoretically sound and numerically efficient approaches to tackling complex problems.
Publication
2025
- Boucher, A., Beevers, C., Gauthier, B. and Roldan, A. 2025. Machine learning force field for optimization of isolated and supported transition metal particles. Journal of Chemical Theory and Computation 21(5), pp. 2626-2637. (10.1021/acs.jctc.4c01606)
2024
- Hutchings, M. and Gauthier, B. 2024. Energy-based sequential sampling for low-rank PSD-matrix approximation. SIAM Journal on Mathematics of Data Science 6(4), pp. 1055-1077. (10.1137/23M162449X)
- Gauthier, B. 2024. Kernel embedding of measures and low-rank approximation of integral operators. Positivity 28, article number: 29. (10.1007/s11117-024-01041-8)
2023
- Hutchings, M. and Gauthier, B. 2023. Local optimisation of Nyström samples through stochastic gradient descent. Presented at: The 8th International Online & Onsite Conference on Machine Learning, Optimization, and Data Science, Siena, Italy, September 18 – 22, 2022. Vol. 13810. Springer pp. 123-140., (10.1007/978-3-031-25599-1_10)
2018
- Gauthier, B. and Suykens, J. A. K. 2018. Optimal quadrature-sparsification for integral operator approximation. SIAM Journal on Scientific Computing 40(5), pp. A3636-A3674. (10.1137/17M1123614)
2017
- Gauthier, B. and Pronzato, L. 2017. Convex relaxation for IMSE optimal design in random-field models. Computational Statistics and Data Analysis 113, pp. 375-394. (10.1016/j.csda.2016.10.018)
2016
- Gauthier, B. and Pronzato, L. 2016. Approximation of IMSE-optimal designs via quadrature rules and spectral decomposition. Communications in Statistics - Simulation and Computation 45(5), pp. 1600-1612. (10.1080/03610918.2014.972518)
- Gauthier, B. and Pronzato, L. 2016. Optimal design for prediction in random field models via covariance kernel expansions. In: Kunert, J., Muller, C. H. and Atkinson, A. C. eds. mODa 11 - Advances in Model-Oriented Design and Analysis: Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016. Springer, pp. 103-111., (10.1007/978-3-319-31266-8_13)
2014
- Gauthier, B. and Pronzato, L. 2014. Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models. SIAM/ASA Journal on Uncertainty Quantification 2(1), pp. 805-825. (10.1137/130928534)
2012
- Gauthier, B. and Bay, X. 2012. Spectral approach for kernel-based interpolation. Annales de la faculté des sciences de Toulouse Mathématiques 21(3), pp. 439-479. (10.5802/afst.1341)
Articles
- Boucher, A., Beevers, C., Gauthier, B. and Roldan, A. 2025. Machine learning force field for optimization of isolated and supported transition metal particles. Journal of Chemical Theory and Computation 21(5), pp. 2626-2637. (10.1021/acs.jctc.4c01606)
- Hutchings, M. and Gauthier, B. 2024. Energy-based sequential sampling for low-rank PSD-matrix approximation. SIAM Journal on Mathematics of Data Science 6(4), pp. 1055-1077. (10.1137/23M162449X)
- Gauthier, B. 2024. Kernel embedding of measures and low-rank approximation of integral operators. Positivity 28, article number: 29. (10.1007/s11117-024-01041-8)
- Gauthier, B. and Suykens, J. A. K. 2018. Optimal quadrature-sparsification for integral operator approximation. SIAM Journal on Scientific Computing 40(5), pp. A3636-A3674. (10.1137/17M1123614)
- Gauthier, B. and Pronzato, L. 2017. Convex relaxation for IMSE optimal design in random-field models. Computational Statistics and Data Analysis 113, pp. 375-394. (10.1016/j.csda.2016.10.018)
- Gauthier, B. and Pronzato, L. 2016. Approximation of IMSE-optimal designs via quadrature rules and spectral decomposition. Communications in Statistics - Simulation and Computation 45(5), pp. 1600-1612. (10.1080/03610918.2014.972518)
- Gauthier, B. and Pronzato, L. 2014. Spectral approximation of the IMSE criterion for optimal designs in kernel-based interpolation models. SIAM/ASA Journal on Uncertainty Quantification 2(1), pp. 805-825. (10.1137/130928534)
- Gauthier, B. and Bay, X. 2012. Spectral approach for kernel-based interpolation. Annales de la faculté des sciences de Toulouse Mathématiques 21(3), pp. 439-479. (10.5802/afst.1341)
Book sections
- Gauthier, B. and Pronzato, L. 2016. Optimal design for prediction in random field models via covariance kernel expansions. In: Kunert, J., Muller, C. H. and Atkinson, A. C. eds. mODa 11 - Advances in Model-Oriented Design and Analysis: Proceedings of the 11th International Workshop in Model-Oriented Design and Analysis held in Hamminkeln, Germany, June 12-17, 2016. Springer, pp. 103-111., (10.1007/978-3-319-31266-8_13)
Conferences
- Hutchings, M. and Gauthier, B. 2023. Local optimisation of Nyström samples through stochastic gradient descent. Presented at: The 8th International Online & Onsite Conference on Machine Learning, Optimization, and Data Science, Siena, Italy, September 18 – 22, 2022. Vol. 13810. Springer pp. 123-140., (10.1007/978-3-031-25599-1_10)
Research
My research focuses on the following themes:
- sampling-based approximation in statistical learning and stochastic modelling,
- numerical strategies for large-scale machine learning and approximate linear algebra,
- reproducing kernel Hilberts spaces,
- spectral methods in statistical learning,
- particle-flow methods in statistical learning,
- sparse approximation and graphical modelling.
Teaching
Current modules:
- Multivariate Data Analysis (Year 3, MA3506)
- Computational Statistics (Year 2, MA2502)
Past modules (at Cardiff University):
- Foundations of Statistics and Data Science (MSc, MAT022)
Final-year projects:
- Every year, I propose a selection of projects on various topics. If you are studying mathematics at Cardiff University and are interested in doing a project related to the mathematics of data science, feel free to contact me.
I am a Fellow of The Higher Education Academy.
Biography
Current and past affiliations:
- Cardiff University - School of Mathematics, since 2017.
- Postdoctoral researcher at KU Leuven (Belgium), ESAT-STADIUS Centre for Dynamical Systems, Signal Processing and Data Analytics, 2015-2016.
- Postdoctoral researcher at CNRS - Université de Nice-Sophia Antipolis (France), Laboratoire I3S, 2012-2014
- Research and teaching assistant at Université de Saint-Étienne (France), Mathematics Department, Institut Camille Jordan, 2011-2012.
- PhD student and teaching assistant at École des Mines de Saint-Étienne (France), 2007-2011.
Supervisions
Current supervision
Past projects
Supervision:
- Matthew Hutchings, Energy-based sampling strategies for the low-rank approximation of positive semidefinite matrices, 2024 (with Kirstin Strokorb).
Second or co-supervision:
- Michela Corradini, Stochastic ordering and sparse approximation of multivariate extremal dependence, 2024 (first supervisor: Kirstin Strokorb).
- Zeljka Salinger, Stochastic models for increments of EEG recordings using heavy-tailed and multimodal diffusions, 2023 (first supervisor: Nikolai Leonenko).
- Alya Alzahrani, Envelope-based support vector machines classification, 2022 (first supervisor: Andreas Artemiou).
Contact Details
GauthierB@cardiff.ac.uk
+44 29208 75544
Abacws, Room 2.07, Senghennydd Road, Cathays, Cardiff, CF24 4AG
+44 29208 75544
Abacws, Room 2.07, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Research themes
Specialisms
- Computational statistics
- Machine learning
- Numerical and computational mathematics