Group LASSO is widely used to enforce the structural sparsity, which achieves the sparsity at the inter-group level. In this paper, we propose a new formulation called “exclusive group LASSO”, which brings out sparsity at intra-group level in the context of feature selection. The proposed exclusive group LASSO is applicable on any feature structures, regardless of their overlapping or non-overl...

Identifying homogeneous subgroups of variables can be challenging in high dimensional data analysis with highly correlated predictors. The generalized fused lasso has been proposed to simultaneously select correlated variables and identify them as predictive clusters. In this article, we study several properties of generalized fused lasso. First, we present a geometric interpretation of the gen...

Background: Two main issues that challenge model building are number of Events Per Variable and multicollinearity among exploratory variables. Our aim is to review statistical methods that tackle these issues with emphasize on penalized Lasso regression model.  The present study aimed to explain problems of traditional regressions due to small sample size and m...

Abstract: We study the asymptotic properties of Lasso+mLS and Lasso+ Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we propose a valid inference procedure for parameter estimation based on parametric residual bootstrap after Lasso+ mLS and Lasso+Ridge. Second, we der...

We propose a novel group regularization which we call exclusive lasso. Unlike the group lasso regularizer that assumes covarying variables in groups, the proposed exclusive lasso regularizer models the scenario when variables in the same group compete with each other. Analysis is presented to illustrate the properties of the proposed regularizer. We present a framework of kernel based multi-tas...

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero (i.e., the solution is sparse). Moreover, statistical properties of high-dimensional lasso estimators are often proved under the assumption that the correlation between the predictors is bounded. In this vein, coordinatewise methods, the most ...

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a characteristic feature of several real-world applications. Previous work on sparse Poisson inverse problems encountered several limiting technical hurdles. Thi...

Previous genome-wide association study (GWAS) focused on low-order interactions between pairwise single-nucleotide polymorphisms (SNPs) with significant main effects. Little is known how high-order interactions effect, especially one among the SNPs without main effects regulates quantitative traits.Within the frameworks of linear model and generalized linear model, the LASSO with coordinate des...