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

Presented by: 
Andreas Elsener
Thursday 18th January 2018 - 14:45 to 15:30
INI Seminar Room 1
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. 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons