Discussion of ‘Correlated variables in regression_ Clustering and sparse estimation’ by Peter Bühlmann, Philipp Rütimann, Sara van de Geer and Cun-Hui Zhang
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چکیده
We would like to begin by congratulating the authors on their fine paper. Handling highly correlated variables is one of the most important issues facing practitioners in high-dimensional regression problems, and in some ways it is surprising that it has not received more attention up to this point. The authors have made substantial progress towards practical methodological proposals, however, and we are sure that the paper will stimulate considerable future research. In this discussion, we present a possible improvement to the cluster representative Lasso, give some further insights into the cluster group Lasso and conclude with some brief remarks on one possible new direction suggested by the work.
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Discussion of ‘ Correlated variables in regression : clustering and sparse estimation
We would like to begin by congratulating the authors on their fine paper. Handling highly correlated variables is one of the most important issues facing practitioners in highdimensional regression problems, and in some ways it is surprising that it has not received more attention up to this point. The authors have made substantial progress towards practical methodological proposals, however, a...
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I would like to congratulate the authors for this very interesting contribution. The generalization of `1-penalized linear regression to the “mixture-of-Gaussian-regressions” model raises some very interesting questions both from theoretical and algorithmic points of view and the paper offers a variety of powerful tools to attack both problems. In this comment I would like to mention another di...
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We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished in previous work: we prove that restricted eigenvalue conditions (Bickel et al., 2008) are also sufficient for sparse structure estimation.
متن کاملComment to “ Generic chaining and the ` 1 - penalty ” by Sara van de Geer
1 when ✓0 2 ⇥). There are two main steps in the author’s proof. The first one follows from some tricky algebraic arguments and leads to Equation (3) of Theorem 2.1 (Equation (4) in Theorem 2.1 and Theorem 2.2 are similar in nature). Along the lines of this step, the role of the Margin assumption (Condition 2.1 in [9]): for all ✓ 2 ⇥, E(✓; ✓0) := P (⇢✓ ⇢✓0) G(⌧(✓ ✓0)), (1) and the e↵ective spars...
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