title: Multinomial least angle regression.
abstract: Keerthi and Shevade (2007) proposed an efficient algorithm for constructing an approximate least angle regression least absolute shrinkage and selection operator solution path for logistic regression as a function of the regularization parameter. In this brief, their approach is extended to multinomial regression. We show that a brute-force approach leads to a multivariate approximation problem resulting in an infeasible path tracking algorithm. Instead, we introduce a noncanonical link function thereby: 1) repeatedly reusing the univariate approximation of Keerthi and Shevade, and 2) producing an optimization objective with a block-diagonal Hessian. We carry out an empirical study that shows the computational efficiency of the proposed technique. A MATLAB implementation is available from the author upon request.
authors.forename: Ilya
authors.initials: I
authors.lastname: Gluhovsky