Relaxed Lasso

By Nicolai Meinshausen. 2007

590 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Demography, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Demography

In Statistics and Probability

Citations in the corpus

Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso (2017, positive): “In addition to the lasso estimator, we consider a simplified version of the relaxed lasso estimator as originally defined by Meinshausen (2007).”
Nearly unbiased variable selection under minimax concave penalty (2010, methodology): “14) where θ∗ 1 ≡ ‖Σ−1 Ao sgn(βAo)‖∞ and θ∗ 2 ≡ ‖Σ(Ao)c,AoΣ Ao sgn(βAo)‖∞ [Meinshausen and Buhlmann (2006), Tropp (2006), Zhao and Yu (2006) and Wainwright (2006)].”
High-dimensional additive modeling (2008, methodology): “…properties of penalization approaches like the lasso [28] are now well understood [3, 14, 23, 24, 33] and this knowledge has led to several extensions or alternative approaches like adaptive lasso [34], relaxed lasso [22], sure independence screening [12] and graphical model based methods [6].”
Regression shrinkage and selection via the lasso: a retrospective (2011, unknown): “Two-stage procedures such as the adaptive lasso (Zou, 2006) or the relaxed lasso (Meinshausen, 2007) are very useful.”
Statistical significance in high-dimensional linear models (2012, methodology): “A related procedure to the adaptive Lasso is the relaxed Lasso (Meinshausen, 2007).”
Sparse Modeling of Categorial Explanatory Variables (2011, methodology): “With the introduction of the Lasso, proposed by Tibshirani (1996), sparse modeling in the high-dimensional predictor case with good performance, in terms of identification of relevant variables combined with good performance in predictive power, became possible.”
p-Values for High-Dimensional Regression (2008, background): “Sparse estimators like the Lasso (Tibshirani 1996) and extensions thereof (Zou 2006; Meinshausen 2007) have been shown to be very powerful because they are suitable for high-dimensional data sets and because they lead to sparse, interpretable results.”
Controlling false positive selections in high-dimensional regression and causal inference (2013, methodology): “A lot of work has been done in the past for variable selection in high-dimensional (generalized) regression [24, 7, 31, 18, 30, 29, 17, 32, 28, 2] while the counterpart for causal or interventional analysis based on observational data is much less developed [16].”
Lasso adjustments of treatment effect estimates in randomized experiments (2015, methodology): “See [22–25] for statistical properties of Lasso+OLS estimator in linear regression model.”
Scaling and evaluating sparse autoencoders (2024, unknown): “15 This refinement method has been proposed multiple times such as in k -SVD [Aharon et al., 2006], the relaxed Lasso [Meinshausen, 2007], or ITI [Maleki, 2009].”
The adaptive and the thresholded Lasso for potentially misspecified models (and a lower bound for the Lasso) (2011, background): “A discussion can be found in [39], and [22].”
SLOPE—ADAPTIVE VARIABLE SELECTION VIA CONVEX OPTIMIZATION (2014, methodology): “, Meinshausen (2007)], can be thought of as an extreme case of reweighting, where the selected variables are not penalized while those that are not selected receive an infinite penalty.”
A Selective Overview of Variable Selection in High Dimensional Feature Space (2009, result): “Meinshausen (2007) presents similar results for the LASSO for dimensionality of exponential growth and ﬁnite nonsparsity size, but its persistency rate is slower than that of a relaxed LASSO.”
Improved variable selection with Forward-Lasso adaptive shrinkage (2011, background): “A few examples include SCAD [Fan and Li (2001)], the Elastic Net [Zou and Hastie (2005)], the Adaptive Lasso [Zou (2006)], the Dantzig selector [Candes and Tao (2007)], the Relaxed Lasso [Meinshausen (2007)], VISA [Radchenko and James (2008)] and the Double Dantzig [James and Radchenko (2009)].”
Spectral Deconfounding and Perturbed Sparse Linear Models (2018, methodology): “Using other methods, such as OLS, in combination with the Lasso is common in practice [19].”
The joint graphical lasso for inverse covariance estimation across multiple classes (2011, methodology): “When simultaneous edge selection and estimation are desired, it may be useful to run FGL or GGL once and then to re-run them with smaller penalties on the selected edges, as in Meinshausen (2007).”