Nonconvex Regularized Robust Regression with Oracle Properties in Polynomial Time

9 Jul 2019Xiaoou PanQiang SunWen-Xin Zhou

This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear models have only bounded second moment, our results suggest that adaptive Huber regression with nonconvex regularization yields statistically optimal estimators that satisfy oracle properties as if the true underlying support set were known beforehand... (read more)

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