A geometrical stopping criterion for the LAR algorithm

Abstract

In this paper a geometrical stopping criterion for the Least Angle Regression (LAR) algorithm is proposed based on the angles between each coefficient data vector and the residual error. Taking into account the most correlated coefficients one by one, the LAR algorithm can be interrupted to estimate a given number of non-zero coefficients. However, if the number of coefficients is not known a priori, defining when to stop the LAR algorithm is an important issue, specially when the number of coefficients is large and the system is sparse. The proposed scheme is validated employing the LAR algorithm with a Volterra filter to identify nonlinear systems of third and fifth orders. Results are compared with three other criteria: Akaike Information, Schwarz's Bayesian Information, and Mallows Cp.