  We compute approximate solutions to L0 regularized linear regression using L1
regularization, also known as the Lasso, as an initialization step. Our
algorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwise
search to determine a locally optimal L0 solution given any L1 regularization
solution. We present theoretical results of consistency under orthogonality and
appropriate handling of redundant features. Empirically, we use synthetic data
to demonstrate that Lass-0 solutions are closer to the true sparse support than
L1 regularization models. Additionally, in real-world data Lass-0 finds more
parsimonious solutions than L1 regularization while maintaining similar
predictive accuracy.
