Robust estimation with Lasso when outputs are adversarially contaminated

Understand

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.