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We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables.
A survey of sampling from contaminated distributions
John W Tukey · 1960
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The future of data analysis
John W Tukey · 1962
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Robust estimation of a location parameter
Peter J. Huber · 1964
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Efficiency in normal samples and tolerance of extreme values for some estimates of location
J. L. Hodges, Jr · 1967
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The behavior of maximum likelihood estimates under nonstandard conditions
Peter J Huber · 1967
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Contribution to the theory of robust estimation
Frank R Hampel · 1968
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A general qualitative definition of robustness
Frank R Hampel · 1971
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Robust estimation: A condensed partial survey
Frank R Hampel · 1973
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Convergence of estimates under dimensionality restrictions
L. Le Cam · 1973
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The influence curve and its role in robust estimation
Frank R Hampel · 1974
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Adress to international congress of mathematicians
J.W. Tukey · 1974
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T6: Order statistics
J.W. Tukey · 1974
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Beyond location parameters: Robust concepts and methods
Frank R Hampel · 1975
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Breakdown of covariance estimators
Werner A Stahel · 1981
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Breakdown properties of multivariate location estimators
David L Donoho · 1982
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Robust regression using repeated medians
Andrew F Siegel · 1982
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The notion of breakdown point
David L Donoho and Peter J Huber · 1983
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Problem complexity and method efficiency in optimization
A. S. Nemirovsky and D. B. Yudin · 1983
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Regression techniques with high breakdown point
Peter J Rousseeuw · 1983
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Robust regression by means of s-estimators
Peter Rousseeuw and Victor Yohai · 1984
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Linear models: robust estimation
Frank R Hampel, Elvezio M Ronchetti, Peter J Rousseeuw, and Werner A Stahel · 1986
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Random generation of combinatorial structures from a uniform distribution
Mark R. Jerrum, Leslie G. Valiant, and Vijay V. Vazirani · 1986
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Asymptotic methods in statistical decision theory
Lucien Le Cam · 1986
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Least median of squares: a robust method for outlier and model error detection in regression and calibration
Desire L Massart, Leonard Kaufman, Peter J Rousseeuw, and Annick Leroy · 1986
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The history of statistics: The measurement of uncertainty before 1900
Stephen M Stigler · 1986
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An introduction to statistical data analysis l1-norm based
Yadolah Dodge · 1987
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Breakdown properties of location estimates based on halfspace depth and projected outlyingness
David L Donoho and Miriam Gasko · 1992
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Aspects of robust linear regression
Patrick L Davies · 1993
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Alternatives to the median absolute deviation
Peter J Rousseeuw and Christophe Croux · 1993
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Outliers in statistical data
Vic Barnett and Toby Lewis · 1994
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The space complexity of approximating the frequency moments
Noga Alon, Yossi Matias, and Mario Szegedy · 1996
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A probabilistic theory of pattern recognition
Luc Devroye, László Györfi, and Gábor Lugosi · 1996
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Statistical learning theory
Vladimir N. Vapnik · 1998
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Decoupling
Víctor H. de la Peña and Evarist Giné · 1999
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Applications of empirical process theory
Sara A. van de Geer · 2000
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The nature of statistical learning theory
Vladimir N. Vapnik · 2000
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Robust logistic regression for binomial responses
M.-P. Victoria-Feser · 2000
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Performance of empirical risk minimization in linear aggregation
Guillaume Lecué and Shahar Mendelson · 2014
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Sparse recovery under weak moment assumptions
Guillaume Lecué and Shahar Mendelson · 2014
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Learning without concentration
Shahar Mendelson · 2014
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A remark on the diameter of random sections of convex bodies
Shahar Mendelson · 2014
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Small ball probabilities for linear images of high dimensional distributions
Mark Rudelson and Roman Vershynin · 2014
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Understanding Machine Learning: From Theory to Algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
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Local Rademacher Complexities and Oracle Inequalities in Risk Minimization
Vladimir Koltchinskii · 2004
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Breakdown and groups
P. Laurie Davies and Ursula Gather · 2005
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Model selection via testing: an alternative to (penalized) maximum likelihood estimators
Lucien Birgé · 2006
Cited alongside, same era.
Robust statistics. Theory and Methods
Ricardo A. Maronna, R. Douglas Martin, and Victor J. Yohai · 2006
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High-dimensional graphs and variable selection with the lasso
Nicolai Meinshausen and Peter Bühlmann · 2006
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Weakly decomposable regularization penalties and structured sparsity
Sara van de Geer · 2014
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On asymptotically optimal confidence regions and tests for high-dimensional models
Sara van de Geer, Peter Bühlmann, Ya’acov Ritov, and Ruben Dezeure · 2014
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Confidence intervals for low dimensional parameters in high dimensional linear models
Cun-Hui Zhang and Stephanie S. Zhang · 2014
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SLOPE—Adaptive variable selection via convex optimization
Małgorzata Bogdan, Ewout van den Berg, Chiara Sabatti, Weijie Su, and Emmanuel J. Candès · 2015
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Empirical risk minimization for heavy-tailed losses
Christian Brownlees, Emilien Joly, and Gábor Lugosi · 2015
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Introduction to high-dimensional statistics
Christophe Giraud · 2015
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Bounding the smallest singular value of a random matrix without concentration
Vladimir Koltchinskii and Shahar Mendelson · 2015
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Bounding the Smallest Singular Value of a Random Matrix Without Concentration
Vladimir Koltchinskii and Shahar Mendelson · 2015
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Learning without concentration
Shahar Mendelson · 2015
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Geometric median and robust estimation in Banach spaces
Stanislav Minsker · 2015
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Choice of
Sylvain Arlot and Matthieu Lerasle · 2016
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Discussion of “Estimating structured high-dimensional covariance and precision matrices: optimal rates and adaptive estimation” [ MR3466172]
Krishnakumar Balasubramanian and Ming Yuan · 2016
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Rho-estimators for shape restricted density estimation
Y. Baraud and L. Birgé · 2016
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Slope meets lasso: Improved oracle bounds and optimality
Pierre Bellec, Guillaume Lecué, and Alexandre Tsybakov · 2016
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Sub-Gaussian mean estimators
Luc Devroye, Matthieu Lerasle, Gabor Lugosi, and Roberto I. Oliveira · 2016
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Regularization and the small-ball method i: sparse recovery
G. Lecué and S. Mendelson · 2016
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Regularization and the small-ball method i: sparse recovery
Guillaume Lecué and Shahar Mendelson · 2016
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On multiplier processes under weak moment assumptions
Shahar Mendelson · 2016
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SLOPE is adaptive to unknown sparsity and asymptotically minimax
Weijie Su and Emmanuel Candès · 2016
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Rho-estimators revisited: General theory and applications
Y. Baraud and L. Birgé · 2017
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A new method for estimation and model selection:
Y. Baraud, L. Birgé, and M. Sart · 2017
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Estimation of high-dimensional mean regression in absence of symmetry and light-tail assumptions
J. Fan, Q. Li, and Y. Wang · 2017
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Learning from mom’s principle : Le cam’s approach
G. Lecué and M. Lerasle · 2017
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Regularization and the small-ball method ii: complexity dependent error rates
G. Lecué and S. Mendelson · 2017
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Adaptive huber regression: Optimality and phase transition
Wen-Xin Zhou Qiang Sun and Jianqing Fan · 2017
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