Robust Mean Estimation on Highly Incomplete Data with Arbitrary Outliers

Abstract

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