We study the problem of robustly estimating the mean of a d-dimensional distribution given N examples, where \varepsilon 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 \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.
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.
D
\varepsilon N examples may be arbitrarily corrupted and
A
and \varepsilon N examples may be arbitrarily corrupted