Pairwise Fused Lasso

Abstract

In the last decade several estimators have been proposed that enforce the grouping property. A regularized estimate exhibits the grouping property if it selects groups of highly correlated predictor rather than selecting one representative. The pairwise fused lasso is related to fusion methods but does not assume that predictors have to be ordered. By penalizing parameters and differences between pairs of coefficients it selects predictors and enforces the grouping property. Two methods how to obtain estimates are given. The first is based on LARS and works for the linear model, the second is based on quadratic approximations and works in the more general case of generalized linear models. The method is evaluated in simulation studies and applied to real data sets.