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We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $\eta$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type.
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Peter J. Huber · 1964
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John W. Tukey · 1974
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Robust m m -estimators of multivariate location and scatter
Ricardo Antonio Maronna · 1976
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J. R. Kettenring S. J. Devlin, R. Gnandesikan · 1981
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Breakdown Properties of Multivariate Location Estimators
David L. Donoho · 1982
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Christopher G Small · 1990
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David L. Donoho and Miriam Gasko · 1992
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Bias-robust estimators of multivariate scatter based on projections
Ricardo A. Maronna, Werner A. Stahel, and Victor J. Yohai · 1992
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Sanjoy Dasgupta · 1999
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Sanjeev Arora and Ravi Kannan · 2001
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Independent Component Analysis
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A spectral algorithm for learning mixture models
Santosh Vempala and Grant Wang · 2004
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Robust statistics
RARD Maronna, Douglas Martin, and Victor Yohai · 2006
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A probabilistic analysis of EM for mixtures of separated, spherical Gaussians
Sanjoy Dasgupta and Leonard Schulman · 2007
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Isotropic PCA and affine-invariant clustering
S Charles Brubaker and Santosh S Vempala · 2008
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Kamalika Chaudhuri and Satish Rao · 2008
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Principal component analysis based on l1-norm maximization
Nojun Kwak · 2008
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Robust principal component analysis?
Emmanuel J. Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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Rank-sparsity incoherence for matrix decomposition
Venkat Chandrasekaran, Sujay Sanghavi, Pablo A Parrilo, and Alan S Willsky · 2011
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Robust statistics: the approach based on influence functions
Frank R Hampel, Elvezio M Ronchetti, Peter J Rousseeuw, and Werner A Stahel · 2011
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International Encyclopedia of Statistical Science
Peter J. Huber · 2011
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Two proposals for robust pca using semidefinite programming
Michael McCoy, Joel A Tropp, et al · 2011
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Provable ICA with unknown gaussian noise, with implications for gaussian mixtures and autoencoders
Sanjeev Arora, Rong Ge, Ankur Moitra, and Sushant Sachdeva · 2012
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Spectral Algorithms
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Handbook of Blind Source Separation
Pierre Comon and Christian Jutten, editors · 2010
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Robust estimates of location and dispersion for high-dimensional datasets
Ricardo A Maronna and Ruben H Zamar · 2012
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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Uniqueness of tensor decompositions with applications to polynomial identifiability
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Blind signal separation in the presence of Gaussian noise
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Learning mixtures of spherical Gaussians: moment methods and spectral decompositions
Daniel Hsu and Sham M. Kakade · 2013
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Fourier pca and robust tensor decomposition
Navin Goyal, Santosh Vempala, and Ying Xiao · 2014
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Robust Covariance Matrix Estimation via Matrix Depth
M. Chen, C. Gao, and Z. Ren · 2015
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Max vs min: Tensor decomposition and ICA with nearly linear sample complexity
Santosh Vempala and Ying Xiao · 2015
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Robust estimators in high dimensions without the computational intractability
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