English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We propose a Generalized Dantzig Selector (GDS) for linear models, in whichany norm encoding the parameter structure can be leveraged for estimation. Weinvestigate both computational and statistical aspects of the GDS. Based onconjugate proximal operator, a flexible inexact ADMM framework is designed forsolving GDS, and non-asymptotic high-probability bounds are established on theestimation error, which rely on Gaussian width of unit norm ball and suitableset encompassing estimation error. Further, we consider a non-trivial exampleof the GDS using $k$-support norm. We derive an efficient method to compute theproximal operator for $k$-support norm since existing methods are inapplicablein this setting. For statistical analysis, we provide upper bounds for theGaussian widths needed in the GDS analysis, yielding the first statisticalrecovery guarantee for estimation with the $k$-support norm. The experimentalresults confirm our theoretical analysis.

Generalized Dantzig Selector: Application to the k-support norm