Efficient List-Decodable Regression using Batches. (arXiv:2211.12743v1 [cs.LG])

We begin the study of list-decodable linear regression using batches. In this
setting only an $\alpha \in (0,1]$ fraction of the batches are genuine. Each
genuine batch contains $\ge n$ i.i.d. samples from a common unknown
distribution and the remaining batches may contain arbitrary or even
adversarial samples. We derive a polynomial time algorithm that for any $n\ge
\tilde \Omega(1/\alpha)$ returns a list of size $\mathcal O(1/\alpha^2)$ such
that one of the items in the list is close to the …

arxiv decodable list regression