Abstract
Often in applications like medical imaging, error correction, and sensor networks, one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving such large-scale systems of linear equations Ax=b that are inconsistent due to corruptions in the measurement vector b. With this as our motivating example, we develop several variants of stochastic gradient descent that converge to the solution of the uncorrupted system of equations, even in the presence of large corruptions. We present both theoretical and empirical results that demonstrate the promise of these iterative methods.
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