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Sharp oracle inequalities for stationary points of nonconvex penalised M-estimators

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STSW01 - Theoretical and algorithmic underpinnings of Big Data

Co-author: Sara van de Geer (ETH Zurich)

Nonconvex loss functions are used in several areas of statistics and machine learning. They have several appealing properties as in the case of robust regression. We propose a general framework to derive sharp oracle inequalities for stationary points of penalised M-estimators with nonconvex loss. The penalisation term is assumed to be a weakly decomposable norm. We apply the general framework to sparse (additive) corrected linear regression, sparse PCA , and sparse robust regression. Finally, a new estimator called “robust SLOPE ” is proposed to illustrate how to apply our framework to norms different from the l1-norm. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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