Beyond Sub-Gaussian Measurements: High-Dimensional Structured Estimation with Sub-Exponential Designs

NeurIPS 2015 Vidyashankar SivakumarArindam BanerjeePradeep K. Ravikumar

We consider the problem of high-dimensional structured estimation with norm-regularized estimators, such as Lasso, when the design matrix and noise are drawn from sub-exponential distributions.Existing results only consider sub-Gaussian designs and noise, and both the sample complexity and non-asymptotic estimation error have been shown to depend on the Gaussian width of suitable sets. In contrast, for the sub-exponential setting, we show that the sample complexity and the estimation error will depend on the exponential width of the corresponding sets, and the analysis holds for any norm... (read more)

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