Section: New Results
The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning
This is a joint work with Andrea Montanari.
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters
Here, we consider a standard random design model and prove exponential concentration of
its empirical distribution around the prediction provided by the Gaussian denoising model. Crucially, our results are uniform with respect to
Our proofs make use of Gaussian comparison inequalities, and in particular of a version of Gordon's minimax theorem developed by Thrampoulidis, Oymak, and Hassibi, which controls the optimum value of the Lasso optimization problem. Crucially, we prove a stability property of the minimizer in Wasserstein distance, that allows to characterize properties of the minimizer itself.