In this talk, we first study the model selection property of Lasso in linear regression models. We show that an Irrepresentable Condition on the design matrix is almost necessary and sufficient for the model selection consistency of Lasso for fixed p and p >> n cases, provided that the true model is sparse. Moreover, we describe the Boosted Lasso (BLasso)algorithm which produces an approximation to the complete regularization path of Lasso. BLasso consists of both a forward step and a backward step. The forward step is similar to Boosting and Forward Stagewise Fitting, but the backward step is new and crucial for BLasso to approximate the Lasso path in all situations. For cases with finite number of base learners, when the step size goes to zero, the BLasso path is shown to converge to the Lasso path. Finally, the Blasso algorithm is extended to give an approximate path for the case of a convex loss function plus a convex penalty.

]]>Industrial and Systems Engineering

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