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We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degr...
We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron,Hastie, Johnstone & Tibshirani (2004) it is proved that the le...
We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm— the ...
We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a ...
In ordinary regression, imposition of a lasso penalty makes continuous model selection straightforward. Lasso penalized regression is particularly advantageous when the number of predictors far exceed...
We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al. (2010) propose “SAFE” rules, based on univariate inner products bet...
The graphical lasso [5] is an algorithm for learning the structure in an undirected Gaussian graphical model, using ℓ1 regularization to control the number of zeros in the precision matrix Θ = Σ...
We propose several methods for estimating edge-sparse and nodesparse graphical models based on lasso and grouped lasso penalties.We develop efficient algorithms for fitting these models when the numbe...
We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter λ. Suppose the sample covariance graph formed by thresholding the entries of the sampl...
We consider the problem of estimating a function $f_{0}$ in logistic regression model. We propose to estimate this function $f_{0}$ by a sparse approximation build as a linear combinaison of elements ...
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not stri...
Abstract: The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows the parametric estimation, inclu...

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