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تسجيل مستخدم جديدRobust 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 most coordinates of every example may be missing and $varepsilon N$ examples may be arbitrarily corrupted. Assuming each coordinate appears in a constant factor more than $varepsilon N$ examples, we show algorithms that estimate the mean of the distribution with information-theoretically optimal dimension-independent error guarantees in nearly-linear time $widetilde O(Nd)$. Our results extend recent work on computationally-efficient robust estimation to a more widely applicable incomplete-data setting.
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