Least Angle Regression

Details Least Angle Regression Least Angle Regression

2004-06-23

arxiv.org/abs/math/0406456v2

Annals of Statistics 2004, Vol. 32, No. 2, 407-451

Mathematics

Statistics Theory

This paper discussed in: math.ST/0406463, math.ST/0406467, math.ST/0406468, math.ST/0406469, math.ST/0406470, math.ST/0406471,

Scientific paper

10.1214/009053604000000067

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 forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising new model selection method;

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