Least-angle regression

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, least-angle regression (LARS) is an algorithm for fitting <a href="/facts/Linear_regression/5n998IhK">linear regression</a> models to high-dimensional data, developed by <a href="/facts/Bradley_Efron/D0f95TyH">Bradley Efron</a>, <a href="/facts/Trevor_Hastie/9bSQQGo7">Trevor Hastie</a>, <a href="/facts/Iain_Johnstone_(mathematician)/AnH3ejWv">Iain Johnstone</a> and <a href="/facts/Robert_Tibshirani/BIzgnLuo">Robert Tibshirani</a>.
Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients.
Instead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the <a href="/facts/L1_norm/gbad0Rv1">L1 norm</a> of the parameter vector. The algorithm is similar to forward <a href="/facts/Stepwise_regression/nXNsPDvp">stepwise regression</a>, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.

Least-angle regression open-in-new

Least-angle regression