We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1 ≤ p ≤ 2 in the linear model when

Abstract—Recovery of sparse signals from noisy observations is a problem that arises in many information processing contexts. LASSO and the Dantzig selector (DS) are two well-known schemes used to recover high-dimensional sparse signals from linear observations. This paper presents some results

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

is the intersection between the kernel of the design matrix and the unit L1-ball from an L2-ball. We show that the distortion holds enough information to derive oracle inequalities (i.e. a comparison to an ideal situation where one knows the s largest coefficients of the target) for the lasso and the Dantzig selector

We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the least angle regression algorithm that is used to compute the lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex

The Dantzig selector (Candes and Tao, 2007) is a new approach that has been proposed for performing variable selection and model fitting on linear regression models. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso

vector) β ∗ when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery with strong theoretical guarantees. In this paper, we propose a multi-stage Dantzig selector method, which iteratively refines the target signal β ∗. We show that if X obeys a certain condition

study the sta-bility of two algorithms, namely LASSO and Dantzig selec-tor. We demonstrate that for a given stability parameter (noise sensitivity), there exits a minimum undersampling ratio above which the recovery algorithms are guaranteed to be stable.

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. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis