# Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers

arXiv: https://arxiv.org/abs/1703.04940 · HTML: https://mlsanity.com/paper/1703.04940/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2017.

## Built on by (most cited first, 30 of 43)

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## Abstract (arXiv)

We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a weaker condition than most other properties considered so far in the literature, and yet enables robust estimation in a broader variety of settings. We provide new information-theoretic results on robust distribution learning, robust estimation of stochastic block models, and robust mean estimation under bounded kth moments. We also provide new algorithmic results on robust distribution learning, as well as robust mean estimation in ℓp-norms. Among our proof techniques is a method for pruning a high-dimensional distribution with bounded 1st moments to a stable "core" with bounded 2nd moments, which may be of independent interest.