# Least angle regression

@article{Efron2004LeastAR, title={Least angle regression}, author={Bradley Efron and Trevor J. Hastie and Iain M. Johnstone and Robert Tibshirani}, journal={Annals of Statistics}, year={2004}, volume={32}, pages={407-499} }

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional…

## 8,226 Citations

### Linear model selection based on extended robust least angle regression

- Computer Science
- 2012

The Extended Robust LARS is proposed by proposing the generalized definitions of correlations which includes the correlations between nominal variables and quantitative variables.

### Efficient least angle regression for identification of linear-in-the-parameters models

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

A detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency, compared with the original approach where the well-known efficient Cholesky decomposition is involved in solving least angle regression.

### Variable Inclusion and Shrinkage Algorithms

- Computer Science
- 2008

It is shown through extensive simulations that VISA significantly outperforms the Lasso and also provides improvements over more recent procedures, such as the Dantzig selector, relaxed Lasso, and adaptive Lasso.

### A Modified Least Angle Regression Algorithm for Hierarchical Interaction

- Computer Science
- 2008

The heredity structure between the main and interaction effect can be considered, algorithms for LASSO with heredITY structure cannot be executed if the number of main effects is high, due to computational burden when thenumber of covariates is large.

### Variable Selection in Linear Regression With Many Predictors

- Mathematics
- 2009

With advanced capability in data collection, applications of linear regression analysis now often involve a large number of predictors. Variable selection thus has become an increasingly important…

### A Survey of Methods in Variable Selection and Penalized Regression

- Computer Science
- 2020

This paper reviews variable selection methods in linear regression, grouped into two categories: sequential methods, such as forward selection, backward elimination, and stepwise regression; and penalized methods, also called shrinkage or regularization methods, including the LASSO, elastic net, and so on.

### Parameter Selection Algorithm For Continuous Variables

- Mathematics
- 2017

In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset…

### Variable Selection Using a Smooth Information Criterion for Distributional Regression Models

- Mathematics
- 2021

Modern variable selection procedures make use of penalization methods to execute simultaneous model selection and estimation. A popular method is the LASSO (least absolute shrinkage and selection…

### Improved variable selection with Forward-Lasso adaptive shrinkage

- Computer Science
- 2011

This work proposes a new approach, "Forward-Lasso Adaptive SHrinkage" (FLASH), which includes the Lasso and Forward Selection as special cases, and can be used in both the linear regression and the Generalized Linear Model domains.

### Robust Model Selection with LARS Based on S-estimators

- MathematicsCOMPSTAT
- 2010

This work introduces outlier robust versions of the LARS algorithm based on S-estimators for regression based on Rousseeuw and Yohai (1984) and shows that this algorithm is computationally efficient and suitable even when the number of variables exceeds the sample size.

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