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DOI: 10.4230/LIPIcs.ITCS.2018.45
URN: urn:nbn:de:0030-drops-83687
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8368/
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Steinhardt, Jacob ; Charikar, Moses ; Valiant, Gregory

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

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LIPIcs-ITCS-2018-45.pdf (0.6 MB)


Abstract

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 p-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.

BibTeX - Entry

@InProceedings{steinhardt_et_al:LIPIcs:2018:8368,
  author =	{Jacob Steinhardt and Moses Charikar and Gregory Valiant},
  title =	{{Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{45:1--45:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Anna R. Karlin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8368},
  URN =		{urn:nbn:de:0030-drops-83687},
  doi =		{10.4230/LIPIcs.ITCS.2018.45},
  annote =	{Keywords: robust learning, outliers, stochastic block models, p-norm estimation}
}

Keywords: robust learning, outliers, stochastic block models, p-norm estimation
Seminar: 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Issue Date: 2018
Date of publication: 05.01.2018


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