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Abstract:
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The lasso is famous for its ability to automatically produce a sparse subset model. The LARS algorithm further facilitates the applications of the lasso in practice. The lasso method now seems to become the default choice for building a sparse model. In this talk, we first show a necessary condition for the lasso variable selection to be consistent. We present some examples in which the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the lasso penalty. We show that the adaptive lasso is consistent in variable selection, and in addition, it possesses the oracle properties.
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