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Transductive versions of the LASSO and the Dantzig Selector (2009)
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BibTeX
@MISC{Alquier09transductiveversions,
author = {Pierre Alquier and Mohamed Hebiri},
title = {Transductive versions of the LASSO and the Dantzig Selector},
year = {2009}
}
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Abstract
We consider the linear regression problem, where the number p of covariates is possibly larger than the number n of observations (xi, yi)i≤i≤n, under sparsity assumptions. On the one hand, several methods have been successfully proposed to perform this task, for example the LASSO in [Tib96] or the Dantzig Selector in [CT07]. On the other hand, consider new values (xi)n+1≤i≤m. If one wants to estimate the corresponding yi’s, one should think of a specific estimator devoted to this task, referred in [Vap98] as a ”transductive ” estimator. This estimator may differ from an estimator designed to the more general task ”estimate on the whole domain”. In this work, we propose a generalized version both of the LASSO and the Dantzig Selector, based on the geometrical remarks about the LASSO in [Alq08, AH08]. The ”usual ” LASSO and Dantzig Selector, as well as new estimators interpreted as transductive versions of the LASSO, appear as special cases. These estimators are interesting at least from a
