Efficient Implementations of the Generalized Lasso Dual Path Algorithm

The generalized lasso problem penalizes the `1 norm of a matrix D times the coefficient vector to be modeled, and has a wide range of applications, dictated by the choice of D. Special cases include the trend filtering and fused lasso problem classes. We consider in this talk highly efficient implementations of the generalized lasso dual path algorithm of Tibshirani and Taylor [1]. This covers both the generic case in which the penalty D is an arbitrary penalty matrix, and two specialized implementations when D corresponds to the trend filtering and fused lasso problem classes, respectively. We find that 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.