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Many models for sparse regression typically assume that the covariates are known completely, and without noise.
Measurement error models
W. A. Fuller · 1987
Earlier work this paper cites.
Greed is good: Algorithmic results for sparse approximation
J. A. Tropp · 2004
Earlier work this paper cites.
Measurement error in nonlinear models: a modern perspective
R. J. Carroll · 2006
Earlier work this paper cites.
Stable recovery of sparse overcomplete representations in the presence of noise
D. L. Donoho, M. Elad, and V. N. Temlyakov · 2006
Earlier work this paper cites.
Signal recovery from random measurements via orthogonal matching pursuit
J. A. Tropp and A. C. Gilbert · 2007
Earlier work this paper cites.
Covariate selection for linear errors-in-variables regression models
Q. Xu and J. You · 2007
Earlier work this paper cites.
Orthogonal matching pursuit from noisy measurements: A new analysis
A. K. Fletcher and S. Rangan · 2009
Cited alongside, same era.
Lasso-type recovery of sparse representations for high-dimensional data
N. Meinshausen and B. Yu · 2009
Cited alongside, same era.
Analysis of orthogonal matching pursuit using the restricted isometry property
M. A. Davenport and M. B. Wakin · 2010
Cited alongside, same era.
Sparse recovery under matrix uncertainty
M. Rosenbaum and A. B. Tsybakov · 2010
Cited alongside, same era.
Missing values: sparse inverse covariance estimation and an extension to sparse regression
N. Städler and P. Bühlmann · 2010
Cited alongside, same era.
Orthogonal matching pursuit for sparse signal recovery with noise
T. T. Cai and L. Wang · 2011
Later among the works it cites.
Orthogonal matching pursuit with replacement
P. Jain, A. Tewari, and I. S. Dhillon · 2011
Later among the works it cites.
High-dimensional regression with noisy and missing data: Provable guarantees with non-convexity
P. L. Loh and M. J. Wainwright · 2011
Later among the works it cites.
Improved matrix uncertainty selector
M. Rosenbaum and A. B. Tsybakov · 2011
Later among the works it cites.
Corrupted and missing predictors: Minimax bounds for high-dimensional linear regression
P. L. Loh and M. J. Wainwright · 2012
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