Robust linear regression: optimal rates in polynomial time

  title={Robust linear regression: optimal rates in polynomial time},
  author={Ainesh Bakshi and Adarsh Prasad},
  journal={Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing},
  • Ainesh Bakshi, A. Prasad
  • Published 29 June 2020
  • Mathematics, Computer Science
  • Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a k-hypercontractive distribution and an є-fraction is adversarially corrupted. We then describe an estimator that converges to the optimal least-squares minimizer for the true distribution at a rate proportional to є2−2/k, when the noise is independent of the… 

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