2011

Scaled Sparse Linear Regression

Sun, Tingni, Zhang, Cun-Hui

Understand

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model.

It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level.
The iterative algorithm costs little beyond the computation of a path or grid of the sparse regression estimator for penalty levels above a proper threshold.
For the scaled lasso, the algorithm is a gradient descent in a convex minimization of a penalized joint loss function for the regression coefficients and noise level.

Variable selection via nonconcave penalized likelihood and its oracle properties
2001
Earlier work this paper cites.
Least angle regression (with discussion)
2004
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On non-concave penalized likelihood with diverging number of parameters
2004
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Persistence in high–dimensional linear predictor selection and the virtue of overparametrization
2004
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Best subset selection, persistence in high-dimensional statistical learning and optimization under
2006
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High-dimensional graphs and variable selection with the lasso
2006
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Regulation of gene expression in the mammalian eye and its relevance to eye disease
2006
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On model selection consistency of lasso
2006
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Sparsity oracle inequalities for the lasso
2007
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The Dantzig selector: statistical estimation when
2007
Earlier work this paper cites.

Adaptive lasso for sparse high-dimensional regression models
2008
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High–dimensional generalized linear models and the lasso
2008
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The sparsity and bias of the lasso selection in high-dimensional linear regression
2008
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Simultaneous analysis of lasso and Dantzig selector
2009
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Robust Statistics
2009
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Lasso-type recovery of sparse representations for high-dimensional data
2009
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On the conditions used to prove oracle results for the lasso
2009
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Some sharp performance bounds for least squares regression with
2009
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Comments on:
2010
Cited alongside, same era.
A new approach to variable selection in least squares problems
Cited in the paper.
On the lasso and its dual
Cited in the paper.

Stability selection (with discussion)
2010
Later among the works it cites.
ℓ 1 \ell_{1} -penalization for mixture regression models (with discussion)
2010
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Comments on:
2010
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Rate minimaxity of the lasso and Dantzig selector for the
2010
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Nearly unbiased variable selection under minimax concave penalty
2010
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Square-root lasso: Pivotal recovery of sparse signals via conic programming
2011
Closest in time.
Nuclear norm penalization and optimal rates for noisy low rank matrix completion
2011
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Outlier detection using nonconvex penalized regression
2011
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Variance estimation using refitted cross-validation in ultrahigh dimensional regression
2012
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