Date(s) - 17/12/2019
14 h 00 min - 16 h 00 min
Thi Khuyen LE (I2M, ALEA-SI, Aix-Marseille Université)
Soutenance de thèse
Statistique et optimisation pour l’estimation de covariances et applications à l’imagerie médicale
Statistics and optimization for estimation of covariances and applications to medical imaging
My work is based on high dimensional graphical models, precisely I find the estimation of the precision matrix in high dimension by solving the GLASSO (Graphical Least Adaptive Shrinkage and Selection Operator) problem. Then, I also apply this estimate matrix to study the brain connections of some patient groups such as Alzheimer’s disease, Depression, Fibromyalgia, etc. Besides, the precision matrix obtained by solving GLASSO problem can be applied for improving the Linear Discriminant Analysis in high dimension. In order to improve the performance of the LDA as well as the other classification methods, we propose a variable selection method basing on the connected components of the precision matrix which have the largest capacity for discriminating data. Another important part in my thesis is testing the significance of points in some models such as the Fused GLASSO model (which is a general model of the GLASSO model), the Joint LASSO model and the Fused LASSO model.