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Well-Conditioned Methods for Ill-Conditioned Systems: Linear Regression with Semi-Random Noise

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 نشر من قبل Kevin Tian
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
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Classical iterative algorithms for linear system solving and regression are brittle to the condition number of the data matrix. Even a semi-random adversary, constrained to only give additional consistent information, can arbitrarily hinder the resulting computational guarantees of existing solvers. We show how to overcome this barrier by developing a framework which takes state-of-the-art solvers and robustifies them to achieve comparable guarantees against a semi-random adversary. Given a matrix which contains an (unknown) well-conditioned submatrix, our methods obtain computational and statistical guarantees as if the entire matrix was well-conditioned. We complement our theoretical results with preliminary experimental evidence, showing that our methods are effective in practice.



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