Model selection consistency of Dantzig selector

The Constrained Dantzig Selector with Enhanced Consistency

The Dantzig selector has received popularity for many applications such as compressed sensing and sparse modeling, thanks to its computational efficiency as a linear programming problem and its nice sampling properties. Existing results show that it can recover sparse signals mimicking the accuracy of the ideal procedure, up to a logarithmic factor of the dimensionality. Such a factor has been ...

Multi-Stage Dantzig Selector

We consider the following sparse signal recovery (or feature selection) problem: given a design matrix X ∈ Rn×m (m À n) and a noisy observation vector y ∈ R satisfying y = Xβ∗ + 2 where 2 is the noise vector following a Gaussian distribution N(0, σI), how to recover the signal (or parameter vector) β∗ when the signal is sparse? The Dantzig selector has been proposed for sparse signal recovery w...

The Group Dantzig Selector

We introduce a new method — the group Dantzig selector — for high dimensional sparse regression with group structure, which has a convincing theory about why utilizing the group structure can be beneficial. Under a group restricted isometry condition, we obtain a significantly improved nonasymptotic `2-norm bound over the basis pursuit or the Dantzig selector which ignores the group structure. ...

Discussion of “the Dantzig selector”

The Dantzig Selector : Statistical Estimation

given just a single parameter t. Two active-set methods were described in [11], with some concern about efficiency if p were large, where X is n× p . Later when basis pursuit de-noising (BPDN) was introduced [2], the intention was to deal with p very large and to allow X to be a sparse matrix or a fast operator. A primal–dual interior method was used to solve the associated quadratic program, b...