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• W100695655 abstract "Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. Worse yet, even estimating statistics of the noise (the noise covariance) can be a central challenge. In this paper we develop a simple variant of orthogonal matching pursuit (OMP) for precisely this setting. We show that without knowledge of the noise covariance, our algorithm recovers the support, and we provide matching lower bounds that show that our algorithm performs at the minimax optimal rate. While simple, this is the first algorithm that (provably) recovers support in a noise-distribution-oblivious manner. When knowledge of the noise-covariance is available, our algorithm matches the best-known l2-recovery bounds available. We show that these too are min-max optimal. Along the way, we also obtain improved performance guarantees for OMP for the standard sparse regression problem with Gaussian noise." @default.
• W100695655 created "2016-06-24" @default.
• W100695655 creator A5053978837 @default.
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• W100695655 date "2013-06-16" @default.
• W100695655 modified "2023-09-29" @default.
• W100695655 title "Noisy and Missing Data Regression: Distribution-Oblivious Support Recovery" @default.
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