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We compute approximate solutions to L0 regularized linear regression using L1regularization, also known as the Lasso, as an initialization step. Ouralgorithm, the Lass-0 ("Lass-zero"), uses a computationally efficient stepwisesearch to determine a locally optimal L0 solution given any L1 regularizationsolution. We present theoretical results of consistency under orthogonality andappropriate handling of redundant features. Empirically, we use synthetic datato demonstrate that Lass-0 solutions are closer to the true sparse support thanL1 regularization models. Additionally, in real-world data Lass-0 finds moreparsimonious solutions than L1 regularization while maintaining similarpredictive accuracy.

Lass-0: sparse non-convex regression by local search