Research work

I am currently working for EDF China in Beijing and preparing in parallel the defense of my Phd thesis under the supervision of Romain Couillet (GIPSA-lab) and Mohamed Tamaazousti (CEA). The goal of my thesis is to employ the Theory of Random Matrices to predict the performances of machine learning algorithms like Ridge regression, robust regression, kernel methods, ELM, transfer learning, softmax classification… The theory of random matrices becomes essential when one studies data with high dimension (like images or sounds for instance). My personal contribution is to start from a Concentration of Measure hypothesis on the data following the theory initiated by Milman in the 70s. The concentration of measure hypothesis is a flexible property valid for a wide range of random vectors, possibly having complex dependencies between the entries (like images or sounds). It allows us to obtain precise convergence results on the performances. Besides, the validity of this assumption has been justified for artificial images provided by GANs (generative adversarial neural networks), as they are Lipschitz transformation of a Gaussian vector. Our practical experiments tend to show that this hypothesis is also true for most real data.

I provide on this website my articles and some of the Julia scripts to validate the theory with experimental results.