Robust Mean Estimation on Highly Incomplete Data with Arbitrary Outliers
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We study the problem of robustly estimating the mean of a d-dimensional distribution given N examples, where ε N examples may be arbitrarily corrupted and most coordinates of every example may be missing. Assuming each coordinate appears in a constant factor more than ε N examples, we show algorithms that estimate the mean of the distribution with information-theoretically optimal dimension-independent error guarantees in nearly-linear time O(Nd). Our results extend recent work on computationally-efficient robust estimation to a more widely applicable incomplete-data setting.
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