Supplementary Material Additional Notation

A.1 Robust Mean Estimation from Subset Stability The upper bound is always less than null for m n . Let m be the largest value of f (x) for any x T with w ( x) null= 0 . Thus, by the weighted version of Lemma 2.4 of [DK19], we have that nullµ Section B.1, we show a result stating that pre-processing on i.i.d. points yields a set that contains Then, in Section B.2, we use a coupling argument to show a We recall the median of means principle. We now state our main result in this section, proved using minimax duality, that Theorem B.1 implies We first consider the case of i.i.d. In particular, Lemma E.2 shows that we can deterministically round We now prove Theorem 1.7, i.e., stability of a subset after corruption, using Theorem B.2.