In this paper, we study problem of estimating a sparse regression vector with correct support in the presence of outlier samples. The inconsistency of lasso-type methods is well known in this scenario. We propose a combinatorial version of outlier-robust lasso which also identifies clean samples. Subsequently, we use these clean samples to make a good estimation. We also provide a novel invex relaxation for the combinatorial problem and provide provable theoretical guarantees for this relaxation. Finally, we conduct experiments to validate our theory and compare our results against standard lasso.

翻译：在本文中，我们研究了在存在离群样本的情况下，估计具有正确支撑集的稀疏回归向量的问题。众所周知，在该场景下，lasso类方法存在不一致性。我们提出了一种组合版本的离群点鲁棒lasso，该方法还能识别干净样本。随后，我们利用这些干净样本进行良好估计。我们还为该组合问题提出了一种新颖的invex松弛，并为该松弛提供了可证明的理论保证。最后，我们进行了实验以验证我们的理论，并将我们的结果与标准lasso进行了比较。