Persistence in high-dimensional linear predictor selection and the virtue of overparametrization

Keywords

Mathematics, Lasso (programming language), Independent and identically distributed random variables, Combinatorics, Set (abstract data type)

References

• Lectures on Probability Theory and StatisticsMartin T. Barlow, David Nualart — 2000
• Problem Complexity and Method Efficiency in OptimizationJ. Darzentas — 1983
• Lectures on Probability Theory and Statistics: Ecole d'Ete de Probabilites de Saint-Flour XXVI - 1996Michel Émery, Arkadi Nemirovski, Dan-Virgil Voiculescu — 1997
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrixZhidong Bai, Yanqing Yin — 1993
• The risk inflation criterion for multiple regressionDean P. Foster, Edward I. George — 1994
• Atomic Decomposition by Basis PursuitScott Shaobing Chen, David L. Donoho, Michael A. Saunders — 1998
• How Many Variables Should Be Entered in a Regression EquationLeo Breiman, Darcy A. Freedman — 1983
• Asymptotic Behavior of M-Estimators of p Regression Parameters when p^2/n is Large. I. ConsistencyStephen Portnoy — 1984
• Asymptotic behavior of M-estimators of p regression parameters when pStephen Portnoy — 1985
• Robust Regression: Asymptotics, Conjectures and Monte CarloPeter J. Huber — 1973
• Functional aggregation for nonparametric regressionAnatoli Juditsky, Arkadi Nemirovski — 2000
• The Smallest Eigenvalue of a Large Dimensional Wishart MatrixJack W. Silverstein — 1985
• Some theory for Fisher''s linear discriminant functionPeter J. Bickel, Elizaveta Levina — 2004
• Regression Shrinkage and Selection via the LassoRobert Tibshirani — 1996
• Ideal spatial adaptation by wavelet shrinkageDavid L. Donoho, Iain M. Johnstone — 1994
• Lectures on probability theory and statisticsBoris Tsirelson, Wendelin Werner — 2004
• Asymptotics In StatisticsLucien Le Cam, Grace L. Yang — 1990
• Probability and MeasureLucy Clarke — 1980
• How Many Variables Should be Entered in a Regression Equation?Leo Breiman, Darcy A. Freedman — 1983
• Probability and Measure.PE, P. Billingsley — 1996

Cited by

• On the ℓ 1 -ℓ q Regularized RegressionHan Liu, Jian Zhang — 2008
• Nonconvex selection in nonparametric additive modelsXiangmin Zhang, Dale Zimmerman, Jian Huang — 2014
• Confidence Intervals for Low-Dimensional Parameters With High-Dimensional DataCun‐Hui Zhang, Stephanie S. Zhang — 2011
• Differentially Private Feature Selection via Stability Arguments, and the Robustness of the LassoAbhradeep Thakurta, Adam Smith — 2013
• Maximum likelihood aggregation and misspecified generalized linear modelsPhilippe Rigollet — 2009
• Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsityArnak S. Dalalyan, Alexandre B. Tsybakov — 2008
• Consistent neighbourhood selection for sparse high-dimensional graphs with the LassoNicolai Meinshausen, Peter Bühlmann — 2004
• Functional time series forecastingRob J. Hyndman, Han Lin Shang — 2009
• Consistent Model Selection Criteria on High DimensionsYongdai Kim, Sunghoon Kwon, Hosik Choi — 2012
• Integrated smoothed location model and data reduction approaches for multi variables classificationHamid Hashibah — 2014
• Structured Estimation In High-DimensionsMartin J. Wainwright, Sahand Negahban — 2012
• The Dantzig selector: Statistical estimation when P is much larger than nEmmanuel J. Candès, Terence Tao — 2005
• Quelques questions de sélection de variables autour de l'estimateur LassoMohamed Hebiri — 2009
• A Survey of L1 RegressionDiego Vidaurre, Concha Bielza, Pedro Larrañaga — 2013
• High-dimensional regression problems with special structureLukas Meier — 2008
• Thresholded Lasso for high dimensional variable selectionShuheng Zhou — 2010
• Oracle approach and slope heuristic in context tree estimationAurélien Garivier, Matthieu Lerasle — 2011
• Topics on high dimensional statistical inference and ANOVA for longitudinal dataPing‐Shou Zhong — 2011
• High-dimensional Gaussian and generalized linear mixed modelsJürg Schelldorfer — 2011
• Inverse Optimization with Noisy DataAnil Aswani, Zuo‐Jun Max Shen, Auyon Siddiq — 2015

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