Multinomial Least Angle Regression with Application to Web Personalization

Keerthi and Shevade (2007) proposed an efficient algorithm for constructing an approximate LARS solution path for logistic regression as a function of the regularization parameter. In this paper we extend their approach 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 non-canonical link function thereby a) repeatedly reusing the univariate approximation of Keerthi and Shevade and b) producing an optimization objective with a block-diagonal Hessian. We carry out a simulation study that shows the computational efficiency of the proposed technique. A Matlab implementation is available from the author upon request. We apply this technique to a web personalization problem in corporate marketing.