Genome-Wide Association Studies, or GWAS, aim at finding Single Nucleotide Polymorphisms (SNPs) that are associated with a phenotype of interest. GWAS are known to suffer from the large dimensionality of the data with respect to the number of available samples. Many challenges limiting the identification of causal SNPs such as dependency between SNPs, due to linkage disequilibrium (LD), the population stratification and the low of statistical of univariate analysis. Machine learning models based on multivariate analysis contribute to advance research in GWAS. Hence, feature selection models reduce the dimensionality of data by keeping only the relevant features associated with disease. However, these methods lack of stability, that is to say, robustness to slight variations in the input dataset. This major issue can lead to false biological interpretation. Hence, we focus in this thesis on evaluating and improving the stability as it is an important indicator to trust feature selection discoveries. In this thesis, we develop two efficient novel methods (multitask group lasso and sparse multitask group lasso) for the multivariate analysis of multi-population GWAS data based on a two multitask group Lasso formulations. Each task corresponds to a subpopulation of the data, and each group to an LD-block. This formulation alleviates the curse of dimensionality, and makes it possible to identify disease LD-blocks shared across populations/tasks, as well as some that are specific to one population task. In addition, we use stability selection to increase the robustness of our approach. Finally, gap safe screening rules speed up computations enough that our method can run at a genome-wide scale. By analyzing several data including breast cancer dataset, the efficiency of the developed models was demonstrated in discovering new risk genes related to disease.