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Structured Matrix Recovery via the Generalized Dantzig Selector
Sheng Chen · Arindam Banerjee

Tue Dec 06 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #46

In recent years, structured matrix recovery problems have gained considerable attention for its real world applications, such as recommender systems and computer vision. Much of the existing work has focused on matrices with low-rank structure, and limited progress has been made on matrices with other types of structure. In this paper we present non-asymptotic analysis for estimation of generally structured matrices via the generalized Dantzig selector based on sub-Gaussian measurements. We show that the estimation error can always be succinctly expressed in terms of a few geometric measures such as Gaussian widths of suitable sets associated with the structure of the underlying true matrix. Further, we derive general bounds on these geometric measures for structures characterized by unitarily invariant norms, a large family covering most matrix norms of practical interest. Examples are provided to illustrate the utility of our theoretical development.

Author Information

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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