We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least-squares problems. Thereaft...

We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of randomly selected covariates. A measure of importance is yielded from this step for each covariate. In step 2, a similar procedure to the first step is implem...

Kernelized LASSO (Least Absolute Selection and Shrinkage Operator) has been investigated in two separate recent papers [Gao, J., Antolovich, M., & Kwan, P. H. (2008). L1 LASSO and its Bayesian inference. In W. Wobcke, & M. Zhang (Eds.), Lecture notes in computer science: Vol. 5360 (pp. 318-324); Wang, G., Yeung, D. Y., & Lochovsky, F. (2007). The kernel path in kernelized LASSO. In Internationa...

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...