The Lasso
Strong convergence of a modified proximal algorithm for solving the lasso
... As is well known the proximal iterative method can be used to solve the lasso of Tibshirani (J. R. Stat. Soc., Ser. B 58:267-288, 1996). In this paper, we first propose a modified proximal iterative method based on ...
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A Comparison of the Lasso and Marginal Regression
... We now investigate how well these expectations are met. For each combination of these parame- ters, we generate data and compare the Hamming errors of the lasso and marginal regression, where for each method, the ...
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On the Degrees of Freedom of the Lasso
... regularized Lasso (λ = 0) corresponds to Ordinary Least Squares (OLS); while the most regularized Lasso uses λ = ∞ , yielding a constant ...the Lasso shrinkage is not very clear except for these two ...
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On Tight Bounds for the Lasso
... We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order ...
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Adaptive-LASSO for Cox's proportional hazards model
... the LASSO applies the same penalty to all the ...adaptive LASSO improves the LASSO by using the data-driven penalties and hence achieves the theoretical properties of the ...
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Sparse Matrix Inversion with Scaled Lasso
... the Lasso is applied to estimate the columns of the target matrix under the assumption of equal diagonal, and the estimation error is studied in the Frobenius norm for p = n ν ...
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Lasso Screening Rules via Dual Polytope Projection
... the Lasso problem, it is unclear if there exists a sequential version of ...of Lasso problems to determine an appropriate parameter value (Tibshirani et ...
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A Multi-Stage Framework for Dantzig Selector and LASSO
... The main contributions of this paper lie in the theoretical analysis of the proposed method. Specifically, we show: 1) the proposed method can improve the estimation bound of the standard Dantzig selector approximately ...
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The Doubly Adaptive LASSO Methods for Time Series Analysis
... The LASSO methodology is successful and popular in statistical modeling, especially in high dimensional data analysis, due to the fact that it performs model selection and parameter esti- mation ...the ...
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On the distribution of the adaptive LASSO estimator
... the LASSO estimator (and of Bridge estimators more gener- ally) when the tuning parameter governing the influence of the penalty term is chosen in such a way that the LASSO acts as a conservative model ...
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LASSO-Driven Inference in Time and Space
... the LASSO tuning parameter selection requires characterizing the asymptotic distribution of the maximum of a high dimensional random ...our LASSO estimation is with random design for dependent data; ...
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Consistency of the Group Lasso and Multiple Kernel Learning
... one, where it is commonly referred to as the Lasso. In this paper, we study the asymptotic group selection consistency of the group Lasso. We derive necessary and sufficient conditions for the consistency ...
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Variable selection by lasso-type methods
... as lasso. The theoretical properties of lasso-type methods are well studied in the past ...for lasso-type methods. The lasso can do consistent model selection if it satisfies a necessary ...
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Lasso Factorial Design Quantile Regression Model with Application
... the lasso methods which were proposed by Tibshirani (1996). The lasso method has some advantages: firstly, it does not need a long time for performing variable selection and secondly it improves predictive ...
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Sparsity via new Bayesian Lasso
... Ridge, Lasso, Bayesian Lasso, and New Bayesian Lasso (R, L, BL, NBL) regression methods through the prediction accuracy using the bias of the estimates with different sample sizes, bias indicates ...
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Bayesian lasso binary quantile regression
... In this section, we extend Bayesian lasso quantile regression as reported in Li et al. (2010) in two ways. First, we consider Bayesian lasso quantile regres- sion for dichotomous response data, i.e. the ...
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Approximation Lasso Methods for Language Modeling
... (Zhao and Yu 2004) provides theoretical justi- fications for BLasso. It has been proved that (1) it guarantees that it is safe for BLasso to start with an initial α which is the largest α that would allow an ε step away ...
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Detecting disease causing genes by LASSO Patternsearch algorithm
... the LASSO penalty to select SNPs, gene × gene interactions, and gene × environmental ...the LASSO [5] was proposed as a variant of linear least- squares ridge ...penalties. LASSO-Patternsearch ...
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Prediction of Rural Residents’ Consumption Expenditure Based on Lasso and Adaptive Lasso Methods
... Adaptive Lasso method is more close to the real value than the Lasso method, proves the estimate effect of the model of Adaptive Lasso method is better than the Lasso ...
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Adaptive Lasso and group-Lasso for functional Poisson regression
... the Lasso estimator but also its extension, the group-Lasso proposed by Yuan and Lin (2006), which is relevant when the set of parameters can be par- titioned into ...the Lasso, generalizing the ...
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