Research focus in a few words
I am a mathematical engineer, endeavouring to solve practical problems by possibly new theories with deep impact beyond the original issue. In the industry, I dealt with signal processing applications (radar, speech, electronic warfare) involving so much uncertainty that “even if the model is reasonably good, our knowledge of the parameters in it, [...] may not be enough to justify a direct numerical evaluation of formulas derived from the model.” [Kailath, 1999]. Encountering the same issue in biomedical engineering during my academic career, my main research focus since 2009 has been on the optimal testing of signals in noise, regardless and with prior knowledge of their distributions. I introduced two theoretical frameworks with PhD students and collaborators.
1) Via the weak notion of sparseness, random signals separate from noise in a suitable transform domain, as the wavelet transform domain. This led to a new robust noise estimator outperforming standard ones.
2) The Random Distortion Testing (RDT) framework is an alternative to likelihood theory when too much uncertainty prevents the use of the latter. By visiting Prof. Pramod K. Varshney at Syracuse University (2015, 2016, 2017), and receiving his PhD student Prashant Khandury (2017, 2019), we moved to sequential RDT, which outperforms the celebrated SPRT when signals are affected by unknown distortions.
Since 2016, I have started working on the hybridization of Statistical Hypothesis Testing and Category Theory. Specifically, as part of Erwan Beurier’s PhD and in collaboration with David Spivak (MIT), a first-class expert in Category Theory whom I visited in 2016 and 2017 and received in 2016, we proved that any discrete automaton can be synthesized by wiring memoryless Boolean automata such as statistical tests. With Prof. Andrée Ehresmann (University of Picardie), world-wide known for her contributions to Category Theory, we proved that optimal likelihood ratio and RDT tests satisfy the Multiplicity Principle (a formalization of Edelman’s concept of degeneracy) for detecting signals in noise. A network of sensors to detect signals in noise must thus involve RDT and likelihood ratio tests, robustness of the former making up for fragility of the latter in case of uncertainties.
Teaching activities in a nutschell
I am also strongly involved in teaching activities, considering that education and research are indivisible. I strive to give students the opportunity to keep in touch with the most advanced achievements in my domain and to hone their critical sense by confronting usual concepts to new ones. I published Probabilités pour l’ingénieur: des fondements aux calculs théoriques, co-authored with Christophe Sintes, Hermes Science Publications, 2014. I am a member of the teaching team of the MOOC "Statistiques pour l’ingénieur". I am co-head of the new curriculum "Mathematical and Computational Engineering” (MCE) at IMT Atlantique, as well as of the MCE new core course “Introduction to Machine Learning”.