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Estimation with Norm Regularization
Arindam Banerjee · Sheng Chen · Farideh Fazayeli · Vidyashankar Sivakumar

Wed Dec 10 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None

Analysis of estimation error and associated structured statistical recovery based on norm regularized regression, e.g., Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise vector. This paper presents generalizations of such estimation error analysis on all four aspects, compared to the existing literature. We characterize the restricted error set, establish relations between error sets for the constrained and regularized problems, and present an estimation error bound applicable to {\em any} norm. Precise characterizations of the bound are presented for a variety of noise vectors, design matrices, including sub-Gaussian, anisotropic, and dependent samples, and loss functions, including least squares and generalized linear models. Gaussian widths, as a measure of size of suitable sets, and associated tools play a key role in our generalized analysis.

Author Information

Arindam Banerjee (University of Minnesota, Twin Cities)

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.

Sheng Chen (University of Minnesota)
Farideh Fazayeli (University of Minnesota-Twin Cities)
Vidyashankar Sivakumar (UNIVERSITY OF MINNESOTA, TC)

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