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For high dimensional supervised learning problems, often using problem specific assumptions can lead to greater accuracy. For problems with grouped covariates, which are believed to have sparse effect...
A framework to characterize performance of LASSO algorithms
Noisy linear systems of equations LASSO SOCP ℓ 1 -optimization compressed sensing
2013/5/2
In this paper we consider solving \emph{noisy} under-determined systems of linear equations with sparse solutions. A noiseless equivalent attracted enormous attention in recent years, above all, due t...
The Lasso is a popular statistical tool invented by Robert Tibshirani for linear regression when the number of covariates is greater than or comparable to the number of observations. The validity of t...
Pivotal Estimation of Nonparametric Functions via Square-root Lasso
pLASSO Pivotal Estimation Square-root Lasso
2011/6/16
In a nonparametric linear regression model we study a variant of LASSO,
called pLASSO, which does not require the knowledge of the scaling parameter σ of the
noise or bounds for it. This work derive...
The LASSO for generic design matrices as a function of the relaxation parameter
linear regression LASSO relaxation parameter
2011/6/16
The LASSO is a variable subset selection procedure in statistical
linear regression based on ℓ1 penalization of the least-squares
operator. Its behavior crucially depends, both in practice and...
The Lasso under Heteroscedasticity
Lasso Poisson-like Model Sign Consistency Heteroscedas-ticity
2010/11/9
The performance of the Lasso is well understood under the assumptions of the standard linear model with homoscedastic noise. However, in several appli-cations, the standard model does not describe the...