This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian frame...

1 In linear regression with fixed design, we propose two procedures that aggregate a datadriven collection of supports. The collection is a subset of the 2 possible supports and both its cardinality and its elements can depend on the data. The procedures satisfy oracle inequalities with no assumption on the design matrix. Then we use these procedures to aggregate the supports that appear on the...

background hospitals are the most costly operational and really important units of health system because they consume about 50%-89% of total health resources. therefore efficient use of resources could help in saving and reallocating the financial and physical resources. objectives the aim of this study was to obtain an overview of hospitals' performance status by applying different techniques,...

When the variable of model is large, the Lasso method and the Adaptive Lasso method can effectively select variables. This paper prediction the rural residents’ consumption expenditure in China, based on respectively using the Lasso method and the Adaptive Lasso method. The results showed that both can effectively and accurately choose the appropriate variable, but the Adaptive Lasso method is ...

We consider the problem of variables selection and estimation in linear regression model in situations where the number of parameters diverges with the sample size. We propose the adaptive Generalized Ridge-Lasso (AdaGril) which is an extension of the the adaptive Elastic Net. AdaGril incorporates information redundancy among correlated variables for model selection and estimation. It combines ...

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints...

The adaptive lasso is a model selection method shown to be both consistent in variable selection and asymptotically normal in coefficient estimation. The actual variable selection performance of the adaptive lasso depends on the weight used. It turns out that the weight assignment using the OLS estimate (OLS-adaptive lasso) can result in very poor performance when collinearity of the model matr...