Variable selection in genome-wide association studies can be a daunting task and statistically challenging because there are more variables than subjects. We propose an approach that uses principal-component analysis (PCA) and least absolute shrinkage and selection operator (LASSO) to identify gene-gene interaction in genome-wide association studies. A PCA was used to first reduce the dimension...

In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping variables and then pursuing model fitting is widely accepted. When the dimension is very high, finding an appropriate group structure is as difficult as the ori...

The Lasso is a popular and computationally efficient procedure for automatically performing both variable selection and coefficient shrinkage on linear regression models. One limitation of the Lasso is that the same tuning parameter is used for both variable selection and shrinkage. As a result, it typically ends up selecting a model with too many variables to prevent over shrinkage of the regr...

Given n noisy samples with p dimensions, where n ≪ p, we show that the multi-step thresholding procedure based on the Lasso – we call it the Thresholded Lasso, can accurately estimate a sparse vector β ∈ R in a linear model Y = Xβ + ǫ, where Xn×p is a design matrix normalized to have column l2 norm √ n, and ǫ ∼ N(0, σ2In). We show that under the restricted eigenvalue (RE) condition (Bickel-Rito...

Mining of gene expression data to identify genes associated with patient survival is an ongoing problem in cancer prognostic studies using microarrays in order to use such genes to achieve more accurate prognoses. The least absolute shrinkage and selection operator (lasso) is often used for gene selection and parameter estimation in high-dimensional microarray data. The lasso shrinks some of th...

Lasso is a popular method for high-dimensional variable selection, but it hinges on a tuning parameter that is difficult to calibrate in practice. In this study, we introduce TREX, an alternative to Lasso with an inherent calibration to all aspects of the model. This adaptation to the entire model renders TREX an estimator that does not require any calibration of tuning parameters. We show that...

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The largesample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the ...

In variable or graph selection problems, finding a right-sized model or controlling the number of false positives is notoriously difficult. Recently, a meta-algorithm called Stability Selection was proposed that can provide reliable finite-sample control of the number of false positives. Its benefits were demonstrated when used in conjunction with the lasso and orthogonal matching pursuit algor...

The Lasso is a cornerstone of modern multivariate data analysis, yet its performance suffers in the common situation in which covariates are correlated. This limitation has led to a growing number of Preconditioned Lasso algorithms that pre-multiply X and y by matrices PX , Py prior to running the standard Lasso. A direct comparison of these and similar Lasso-style algorithms to the original La...