A lower bound for the Lasso

Theme: 
Statistics and Modeling for Complex Data
Speaker: 
VAN DE GEER Sara

In numerical experiments, it has been observed that the Lasso generally selects too many variables, i.e. it yields a large number of false positives. We will con- firm this theoretically by showing in an example that with positive probability, the Lasso satisfies a sparsity oracle inequality while the number of false posi- tives is of larger order than the sparsity index of the underlying true regression. To arrive at this result, we will apply refined concentration inequalities and extreme value theory.