Lasso performs model selection and is particularly useful to look for a low dimensional structure with high dimensional data. Yet, the selection of its regularization parameter remains an open problem to which cross validation is only sub-optimal in terms of false discovery rate or true positive rate.

We propose a new selection rule for that parameter. We illustrate with two generalized linear models in Cosmology with an Abel and deblurring inverse problem with Poisson noise, and in Cancer research with logistic regression.