摘要：The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables $p$ exceeds the number of observations $n$. But when $p>n$, the lasso criterion is not strictly convex, and hence it may not have a unique minimizer. An important question is: when is the lasso solution well-defined (unique)? We review results from the literature, which show that if the predictor variables are drawn from a continuous probability distribution, then there is a unique lasso solution with probability one, regardless of the sizes of $n$ and $p$. We also show that this result extends easily to $\ell_{1 penalized minimization problems over a wide range of loss functions.
