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...

The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals bas...

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...

The literature is replete with variable selection techniques for the classical linear regression model. It is only relatively recently that authors have begun to explore variable selection in fully nonparametric and additive regression models. One such variable selection technique is a generalization of the LASSO called the group LASSO. In this work, we demonstrate a connection between the grou...

Under the background of big data era today, once been widely used method – multiple linear regressions can not satisfy people’s need to handle big data any more because of its bad characteristics such as multicollinearity, instability, subjectivity in model chosen etc. Contrary to MLR, LASSO method has many good natures. it is stable and can handle multicollinearity and successfully select the ...

We develop a unified robust linear regression model and show that it is equivalent to a general regularization framework to encourage sparse-like structure that contains group Lasso and fused Lasso as specific examples. This provides a robustness interpretation of these widely applied Lasso-like algorithms, and allows us to construct novel generalizations of Lasso-like algorithms by considering...

Lasso is a regularization method for parameter estimation in linear models. It optimizes the model parameters with respect to a loss function subject to model complexities. This paper explores the use of lasso for statistical language modeling for text input. Owing to the very large number of parameters, directly optimizing the penalized lasso loss function is impossible. Therefore, we investig...

We describe a fast method to eliminate features (variables) in l1-penalized least-square regression (or LASSO) problems. The elimination of features leads to a potentially substantial reduction in running time, especially for large values of the penalty parameter. Our method is not heuristic: it only eliminates features that are guaranteed to be absent after solving the LASSO problem. The featu...