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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Sparsity considerations for dependent observations
2011-02-08 · via math.ST updates on arXiv.org

The aim of this paper is to provide a comprehensive introduction for the study of L1-penalized estimators in the context of dependent observations. We define a general $\ell_{1}$-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study our estimator under various dependence assumptions.

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