Bolasso: model consistent Lasso estimation through the bootstrap

Understand

We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso.

• In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso.
• For various decays of the regularization parameter, we compute asymptotic equivalents of the probability of correct model selection (i.e., variable selection).
• For a specific rate decay, we show that the Lasso selects all the variables that should enter the model with probability tending to one exponentially fast, while it selects all other variables with strictly positive probability.