Tommaso D’Orsi

Consistent regression when oblivious outliers overwhelm

We consider a robust linear regression model $y=X\beta^* + \eta$, where an adversary oblivious to the design $X\in \mathbb{R}^{n\times d}$ may choose $\eta$ to corrupt all but an $\alpha$ fraction of the observations $y$ in an arbitrary way. Prior to our work, even for Gaussian $X$, no estimator for…