Activity Number:
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314
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Learning and Data Science
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Abstract #320069
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Title:
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CoCoLasso for High-Dimensional Error-in-Variables Regression
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Author(s):
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Abhirup Datta* and Hui Zou
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Companies:
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University of Minnesota and University of Minnesota
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Keywords:
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Error-in-variables ;
High-dimensional regression ;
Lasso
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Abstract:
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We often face corrupted high dimensional data in many applications where missing data and measurement errors cannot be ignored. We propose a new method named CoCoLasso that is convex and can handle a general class of corrupted datasets including the cases of additive measurement error and random missing data. CoCoLasso can be reformulated as a modified Lasso problem and automatically enjoys the benefits of convexity for high-dimensional regression. Theoretically, we establish that the error bounds of CoCoLasso are comparable to those of the Lasso. We also derive finite sample and asymptotic sign-consistent selection property without requiring any specification of the type of measurement error. We elucidate how standard cross validation techniques may be inefficient in presence of measurement error and develop a novel cross-validation technique for choosing tuning parameter for CoCoLasso. We demonstrate the superior performance of our method over the non-convex approach by simulation studies.
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Authors who are presenting talks have a * after their name.