Robust Multi-task Regression with Grossly Corrupted Observations
Huan Xu, Chenlei Leng ; JMLR W&CP 22: 1341-1349, 2012.
We consider the multiple-response regression problem, where the response is subject to *sparse gross errors*, in the high-dimensional setup. We propose a tractable regularized M-estimator that is robust to such error, where the sum of two individual regularization terms are used: the first one encourages row-sparse regression parameters, and the second one encourages a sparse error term. We obtain non-asymptotical estimation error bounds of the proposed method. To the best of our knowledge, this is the first analysis of the robust multi-task regression problem with gross errors.