论文标题
当输出受到对抗污染时，用拉索进行了稳健的估计
Robust estimation with Lasso when outputs are adversarially contaminated
论文作者
论文摘要
当输出受到对抗污染时，我们考虑强大的估计。 Nguyen和Tran（2012）提出了一个扩展的拉索，以进行鲁棒参数估计，然后显示了估计误差的收敛速率。最近，Dalalyan和Thompson（2019）给出了一些有用的不平等现象，然后它们的收敛速度比Nguyen和Tran（2012）更快。他们专注于这样一个事实，即扩展的拉索的最小化问题可以成为受$ l_1 $罚款的罚款Huber损失功能的事实。区分点是，Huber损耗函数包括一个额外的调整参数，该参数与常规方法不同。我们给出证明，这与Dalalyan和Thompson（2019）不同，然后我们给出了与Dalalyan和Thompson（2019）相同的收敛速度。我们证明的意义是使用Huber函数的某些特定属性。在过去的证明中，这种技术尚未使用。
We consider robust estimation when outputs are adversarially contaminated. Nguyen and Tran (2012) proposed an extended Lasso for robust parameter estimation and then they showed the convergence rate of the estimation error. Recently, Dalalyan and Thompson (2019) gave some useful inequalities and then they showed a faster convergence rate than Nguyen and Tran (2012). They focused on the fact that the minimization problem of the extended Lasso can become that of the penalized Huber loss function with $L_1$ penalty. The distinguishing point is that the Huber loss function includes an extra tuning parameter, which is different from the conventional method. We give the proof, which is different from Dalalyan and Thompson (2019) and then we give the same convergence rate as Dalalyan and Thompson (2019). The significance of our proof is to use some specific properties of the Huber function. Such techniques have not been used in the past proofs.
