Generic chaining and the l1-penalty

Sara van de Geer

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arXiv · 1205.3703

Generic chaining and the l1-penalty

Sara van de Geer

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Abstract

We address the choice of the tuning parameter $\lambda$ in $\ell_1$-penalized M-estimation. Our main concern is models which are highly nonlinear, such as the Gaussian mixture model. The number of parameters $p$ is moreover large, possibly larger than the number of observations $n$. The generic chaining technique of Talagrand[2005] is tailored for this problem. It leads to the choice $\lambda \asymp \sqrt {\log p / n}$, as in the standard Lasso procedure (which concerns the linear model and least squares loss).

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Sara van de Geer. 2012-05-16. Generic chaining and the l1-penalty. https://arxiv.org/abs/1205.3703

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