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Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious adversary.
Rejection of outliers
Frank J Anscombe · 1960
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A survey of sampling from contaminated distributions
J.W. Tukey · 1960
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Robust estimation of a location parameter
Peter J Huber · 1964
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Mathematics and the picturing of data
John W Tukey · 1975
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The densest hemisphere problem
David S Johnson and Franco P Preparata · 1978
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Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
William B Johnson, Gideon Schechtman, and Joel Zinn · 1985
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On the learnability of discrete distributions
Michael Kearns, Yishay Mansour, Dana Ron, Ronitt Rubinfeld, Robert E Schapire, and Linda Sellie · 1994
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Robust estimators are hard to compute
Thorsten Bernholt · 2006
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New results for learning noisy parities and halfspaces
Vitaly Feldman, Parikshit Gopalan, Subhash Khot, and Ashok Kumar Ponnuswami · 2006
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On basing lower-bounds for learning on worst-case assumptions
Benny Applebaum, Boaz Barak, and David Xiao · 2008
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Hardness of learning halfspaces with noise
Venkatesan Guruswami and Prasad Raghavendra · 2009
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On lattices, learning with errors, random linear codes, and cryptography
Oded Regev · 2009
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Graph expansion and the unique games conjecture
Prasad Raghavendra and David Steurer · 2010
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On the complexity of unique games and graph expansion
David Steurer · 2010
Cited alongside, same era.
Subexponential algorithms for d-to-1 two-prover games and for certifying almost perfect expansion
David Steurer · 2010
Cited alongside, same era.
Hypercontractivity, sum-of-squares proofs, and their applications
Boaz Barak, Fernando G. S. L. Brandão, Aram Wettroth Harrow, Jonathan A. Kelner, David Steurer, and Yuan Zhou · 2012
Cited alongside, same era.
Hypercontractivity, sum-of-squares proofs, and their applications
Boaz Barak, Fernando G. S. L. Brandão, Aram Wettroth Harrow, Jonathan A. Kelner, David Steurer, and Yuan Zhou · 2012
Cited alongside, same era.
Computational bounds on statistical query learning
Vitaly Feldman and Varun Kanade · 2012
Cited alongside, same era.
Reductions between expansion problems
Learning from untrusted data
Moses Charikar, Jacob Steinhardt, and Gregory Valiant · 2017
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Being robust (in high dimensions) can be practical
Ilias Diakonikolas, Gautam Kamath, Daniel M Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2017
Later among the works it cites.
Being robust (in high dimensions) can be practical
Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2017
Later among the works it cites.
Statistical query lower bounds for robust estimation of high-dimensional gaussians and gaussian mixtures
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2017
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Resilience: A criterion for learning in the presence of arbitrary outliers
Jacob Steinhardt, Moses Charikar, and Gregory Valiant · 2017
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Prasad Raghavendra, David Steurer, and Madhur Tulsiani · 2012
Cited alongside, same era.
Algorithms and hardness for robust subspace recovery
Moritz Hardt and Ankur Moitra · 2013
Cited alongside, same era.
Sum of squares upper bounds, lower bounds, and open questions
Boaz Barak · 2014
Cited alongside, same era.
Embedding hard learning problems into gaussian space
Adam R. Klivans and Pravesh Kothari · 2014
Cited alongside, same era.
Order-revealing encryption and the hardness of private learning
Mark Bun and Mark Zhandry · 2016
Cited alongside, same era.
Robust estimators in high dimensions without the computational intractability
Ilias Diakonikolas, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart · 2016
Cited alongside, same era.
Agnostic estimation of mean and covariance
Kevin A. Lai, Anup B. Rao, and Santosh Vempala · 2016
Cited alongside, same era.
Sébastien Bubeck, Yin Tat Lee, Eric Price, and Ilya Razenshteyn · 2018
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List-decodable robust mean estimation and learning mixtures of spherical gaussians
Ilias Diakonikolas, Daniel M Kane, and Alistair Stewart · 2018
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Mixture models, robustness, and sum of squares proofs
Samuel B Hopkins and Jerry Li · 2018
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Robust moment estimation and improved clustering via sum of squares
Pravesh K Kothari, Jacob Steinhardt, and David Steurer · 2018
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Principled Approaches to Robust Machine Learning and Beyond
Jerry Li · 2018
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Robust Learning: Information Theory and Algorithms
Jacob Steinhardt · 2018
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Talk at stoc 2018 workshop on computational phase transitions
Jacob Steinhardt · 2018
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Efficient algorithms and lower bounds for robust linear regression
Ilias Diakonikolas, Weihao Kong, and Alistair Stewart · 2019
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