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The LASSO risk: asymptotic results and real world examples
Coefficient vector linear observation construct sparse the lasso matrix sequence
2015/8/21
We consider the problem of learning a coefficient vector x0 ∈ RN from noisy linear observation y = Ax0 + w ∈ Rn. In many contexts (ranging from model
selection to image processing) it is desirable to...
ON THE “DEGREES OF FREEDOM” OF THE LASSO
Degrees of freedom LARS algorithm lasso model selection SURE unbiased estimate
2015/8/21
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...
Sparse inverse covariance estimation with the lasso
Sparse inverse covariance estimation the lasso
2015/8/21
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 ...
Genomewide Association Analysis by Lasso Penalized Logistic Regression
Genomewide Association Analysis Lasso Penalized Logistic Regression
2015/8/21
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...
Strong Rules for Discarding Predictors in Lasso-type Problems
Strong Rules Discarding Predictors Lasso-type Problems
2015/8/21
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:New insights and alternatives
Graphical lasso sparse inverse covariance selection precision matrix convex analysis/optimization positive definite matrices sparsity semidefinite programming
2015/8/21
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...
Applications of the lasso and grouped lasso to the estimation of sparse graphical models
lasso and grouped lasso sparse graphical models
2015/8/21
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...
Exact Covariance Thresholding into Connected Components for Large-Scale Graphical Lasso
sparse inverse covariance selection sparsity graphical lasso Gaussian graphical models graph connected components concentration graph large scale covariance estimation
2015/8/21
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...
The LASSO risk for gaussian matrices
Noisy linear observation vector image processing the matrix sequence
2015/8/20
We consider the problem of learning a coecient vector x0 2 R N from noisy linear observation y = Ax0 + w 2 R n. In many contexts (ranging from model selection to image processing) it is desirable to ...
We also
study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the
lasso and forward stagewise pro...
Proximal methods for the latent group lasso penalty
Structured sparsity proximal methods regularization
2012/11/23
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to over...
Non-asymptotic Oracle Inequalities for the Lasso and Group Lasso in high dimensional logistic model
Logistic model Lasso Group Lasso High-dimensional
2012/6/19
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...