Efficient Implementations of the Generalized Lasso Dual Path Algorithm

We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani & Taylor (2011). We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X 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 X = I and a general matrix X. 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.