Adaptive ridge is a special form of ridge regression, balancing the quadratic penalization on each parameter of the model. This paper shows the equivalence between adaptive ridge and lasso (least absolute shrinkage and selection operator). This equivalence states that both procedures produce

Adaptive Ridge is a special form of Ridge regression, balancing the quadratic penalization on each parameter of the model. It was shown to be equivalent to Lasso (least absolute shrinkage and selection operator), in the sense that both procedures produce the same estimate. Lasso can thus be viewed

The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the ℓ2data error objective and the ℓ1-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection process with sparsity models has been precisely

We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients

Abstract: The Lasso, the Forward Stagewise regression and the Lars are closely related procedures recently proposed for linear regression problems. Each of them can produce sparse models and can be used both for estimation and variable selection. In practical implementations these algorithms are typically tuned to achieve optimal prediction accuracy. We show that, when the prediction accuracy is used as the criterion to choose the tuning parameter, in general these procedures are not consistent in terms of variable selection. That is, the sets of variables selected are not consistently the true set of important variables. In particular, we show that for any sample size n, when there are superfluous variables in the linear regression model and the design matrix is orthogonal, the probability that these procedures correctly identify the true set of important variables is less than a constant (smaller than one) not depending on n. This result is also shown to hold for two-dimensional problems with general correlated design matrices. The results indicate that in problems where the main goal is variable selection, prediction-accuracy-based criteria alone are not sufficient for this purpose. Adjustments will be discussed to make the Lasso and related procedures useful/consistent for variable selection.

Purpose: The aim of this study was to develop a multivariate logistic regression model with least absolute shrinkage and selection operator (LASSO) to make valid predictions about the incidence of moderate-to-severe patient-rated xerostomia among head and neck cancer (HNC) patients treated

sparseness-inducing (ℓ1) regularization term.Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution, and compressed sensing are a few well-known examples of this approach. This paper proposes gradient projection (GP) algorithms for the bound

Finding sparse approximate solutions to large underdetermined linear systems of equations is a common problem in signal/image processing and statistics. Basis pursuit, the least absolute shrinkage and selection operator (LASSO), wavelet-based deconvolution and reconstruction, and compressed sensing

Proposed by Tibshirani (1996), the LASSO (least absolute shrinkage and selection operator) estimates a vector of regression coe#cients by minimising the residual sum of squares subject to a constraint on the l 1 -norm of coe#cient vector. The LASSO estimator typically has one or more zero

LASSO (Least Absolute Shrinkage and Selection Operator) is a useful tool to achieve the shrinkage and variable selection simultaneously.