Efficient Implementations of the Generalized Lasso Dual Path Algorithm

We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani &amp; Taylor (2011). We first describe a generic approach that covers any penalty matrix <i>D</i> and any (full column rank) matrix <i>X</i> of predictor variables. We then describe fast implementations for the special cases of trend filtering problems, fused lasso problems, and sparse fused lasso problems, both with <i>X</i> = <i>I</i> and a general matrix <i>X</i>. These specialized implementations offer a considerable improvement over the generic implementation, both in terms of numerical stability and efficiency of the solution path computation. These algorithms are all available for use in the genlasso R package, which can be found in the CRAN repository.