Simultaneous analysis of Lasso and Dantzig selector
نویسندگان
چکیده
منابع مشابه
Simultaneous Analysis of Lasso and Dantzig
We exhibit an approximate equivalence between the Lasso es-timator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparamet-ric regression model, as well as bounds on the p estimation loss for 1 ≤ p ≤ 2 in the linear model when the number of variables can be much larger than the sample size.
متن کاملTransductive versions of the LASSO and the Dantzig Selector
Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transduct...
متن کاملA Remark on the Lasso and the Dantzig Selector
This article investigates a new parameter for the high-dimensional regression with noise: the distortion. This latter has attracted a lot of attention recently with the appearance of new deterministic constructions of “almost”-Euclidean sections of the L1-ball. It measures how far is the intersection between the kernel of the design matrix and the unit L1-ball from an L2-ball. We show that the ...
متن کاملDASSO: Connections Between the Dantzig Selector and Lasso
We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the LARS algorithm that is used to compute the Lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to LARS. Comparison of the two algorithms sheds new light on the question of how ...
متن کاملA Multi-Stage Framework for Dantzig Selector and LASSO
We consider the following sparse signal recovery (or feature selection) problem: given a design matrix X ∈ Rn×m (m ≫ n) and a noisy observation vector y ∈ Rn satisfying y = Xβ∗ + ε where ε is the noise vector following a Gaussian distribution N(0,σ2I), how to recover the signal (or parameter vector) β∗ when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2009
ISSN: 0090-5364
DOI: 10.1214/08-aos620