- Master 2 Data Sciences from Ecole Polytechnique
- Master in Statistics and Economics from ENSAE
- MsC in Management from ESSEC Business School
Multivariate quantile normalization and applications to machine learning.
Quantile renormalization is a fundamental tool in statistics. It allows univariate data to be modified so that they follow a predetermined distribution (i.e. Gaussian) by means of a monotonic transformation. This normalization has several practical virtues, notably that of removing extreme values and facilitating the training of the parameters of learning models based on these data. The context in which this renormalization is applied is therefore most often static, in the sense that the distribution towards which data are transformed is most often chosen a priori. Recent work  has shown that it is possible to make this operation differentiable, and thus to be able to adapt the final distribution as needed in order to improve, in an integrated way, the final result of learning methods. The aim of this thesis is to study theoretically and numerically multi-variate extensions of this approach, with possible applications in genomics.