Generalized Dantzig Selector: Application to the k-support norm
By Soumyadeep Chatterjee, Sheng Chen, Arindam Banerjee. 2014
38 citations recorded by the source corpus.
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian widths of the unit norm ball and the error set. Further, we consider a non-trivial example of the GDS using k-support norm. We derive an efficient method to compute the proximal operator for k-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the k-support norm. The experimental results confirm our theoretical analysis.
Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Vipin Kumar
- Michael S. Steinbach
- Anuj Karpatne
- Nagiza F. Samatova
- Arindam Banerjee
- Shashi Shekhar
- Auroop Ratan Ganguly
- James H. Faghmous
In Computational Mechanics
- Arindam Banerjee
- Michael S. Steinbach
- Vipin Kumar
- François Laviolette
- Pascal Germain
- Yevgeny Seldin
- Naftali Tishby
- Noah A. Smith
In Statistics and Probability
- Vipin Kumar
- Auroop Ratan Ganguly
- Arindam Banerjee
- Shashi Shekhar
- Michael S. Steinbach
- Nagiza F. Samatova
- James H. Faghmous
- Anuj Karpatne
Citations in the corpus
- Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, methodology): “The Gaussian widths of such sub-spaces can be used as a regularization term in techniques such as the generalized Dantzig selector [60], [61].”
- Spectral k-Support Norm Regularization (2014, unknown): “Further Work I Statistical bounds on the performance of the norms: various results known [Chatterjee, Chen & Banerjee 2014, Maurer & Pontil 2012, Richard, Obozinksi & Vert 2014] I Infimum formulation of (k , p)-support norm: known for p ∈ [1, 2], unclear for p ∈ (2,∞].”