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Generalized Dantzig Selector: Application to the k-support norm
Soumyadeep Chatterjee · Sheng Chen · Arindam Banerjee

Mon Dec 08 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D

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.

Author Information

Soumyadeep Chatterjee (Quora Inc.)
Sheng Chen (University of Minnesota)
Arindam Banerjee (University of Illinois Urbana-Champaign)

Arindam Banerjee is a Professor at the Department of Computer & Engineering and a Resident Fellow at the Institute on the Environment at the University of Minnesota, Twin Cities. His research interests are in machine learning, data mining, and applications in complex real-world problems in different areas including climate science, ecology, recommendation systems, text analysis, and finance. He has won several awards, including the NSF CAREER award (2010), the IBM Faculty Award (2013), and six best paper awards in top-tier conferences.

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