Jérémy Guérin works under the direction of Pavlo Mozharovskyi on the topic of data depth. My PhD will begin on April 2022 but I work on the subject since November 2021. This subject uses different courses I took during my studies : high dimensional statistics and optimisation. Data depth allows to quantify the centrality of a datapoint inside of a multivariate dataset. I try to prove the existence of algorithms able to compute the depth for datasets of large dimension so that they can be used in practice.

Keywords: data depth, machine learning, optimisation, robustness, computational statistics.