Dr Bertrand Gauthier
Lecturer
- gauthierb@cardiff.ac.uk
- +44(0)29 2087 5544
- 2.07, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Overview
My research lies at the interface between Mathematics and Data Science, and focuses on the design and analysis of problem-dependent data-driven learning strategies. I am specially interested in the exploration of the connections between Machine Learning and traditional knowledges in Mathematics, with the aim of developing theoretically sound and numerically efficient learning strategies having the ability to tackle large-scale and complex problems.
Biography
Current and past affiliations:
- Cardiff University - School of Mathematics (since January 2017).
- Postdoctoral researcher at KU Leuven (Belgium), ESAT-STADIUS Centre for Dynamical Systems, Signal Processing and Data Analytics, from March 2015 to December 2016.
- Postdoctoral researcher at CNRS - Université de Nice-Sophia Antipolis (France), Laboratoire I3S, from September 2012 to August 2014; and CNRS contract agent on secondment to EDF-Lab Chatou (France), from September to December 2014.
- ATER (temporary research and teaching assistant) at Université de Saint-Étienne (France), Mathematics Department, Institut Camille Jordan, from February 2011 to August 2012.
- PhD student and teaching assistant at École des Mines de Saint-Étienne (France) from October 2007 to January 2011.
Publications
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)
Teaching
I am a Fellow of The Higher Education Academy (since 2019).
Currently taught courses (2020/21):
- Multivariate Data Analysis (Year 3, MA3506)
- Foundations of Statistics and Data Science (MSc, MAT022)
Supervision of project students: Every academic year, I propose and supervise a selection of projects on various topics. If you are currently studying Mathematics at Cardiff University and consider doing a project on a topic related to the Mathematics of Data Science, please feel free to contact me.
To date, my research has focused on the following topics:
- kernel methods,
- random-field models,
- spectral methods in machine learning,
- design of experiments,
- approximation of integral operators,
- sparse approximation,
- kernel discrepancies.
Recent preprints:
- Isometric representation of integral operators with positive-semidefinite kernels; https://hal.archives-ouvertes.fr/hal-03848105.
- Local optimisation of Nyström samples though stochastic gradient descent; with M. Hutchings; https://arxiv.org/abs/2203.13284.
