Split Regularized Regression

TL;DR: In this article, the benefits of splitting variables variables for reducing the variance of linear functions of the regression coefficient estimate was studied. And they showed that splitting combined with shrinkage can result in estimators with smaller mean squared error compared to popular shrinkage estimators such as Lasso, ridge regression and garrote.

TL;DR: An elastic net (EN) as discussed by the authors is an algorithm for fitting penalized regression models using a convex combination of the LASSO and ridge penalty norms, which takes advantage of both the sparsity property of the lasso and variable grouping property of ridge, making it a natural choice for model selection.

TL;DR: In this article, a multi-model penalized regression (MMPR) method is proposed to identify multiple models with different subsets of covariates that explain a single type of response.

TL;DR: In this paper , the performance of seven previously proposed group variable selection methods; the group Lasso estimates, the group lasso net, the sparse group LASSO estimate, group scad estimates, scad scad net estimates, group mcp estimates, and the group gel estimate via a simulation study is compared.

TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.

TL;DR: A general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion, and specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification.

TL;DR: It is shown that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation, and an algorithm called LARS‐EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lamba.

TL;DR: In comparative timings, the new algorithms are considerably faster than competing methods and can handle large problems and can also deal efficiently with sparse features.