Efficient Implementations of the Generalized Lasso Dual Path Algorithm
This work provides incremental improvements for researchers and practitioners in statistics and machine learning who use the generalized lasso for tasks like signal processing and data analysis.
The paper tackles the problem of efficiently computing solution paths for the generalized lasso, a statistical method for regularization, by developing specialized implementations for trend filtering, fused lasso, and sparse fused lasso cases, resulting in improved numerical stability and computational efficiency compared to a generic approach.
We consider efficient implementations of the generalized lasso dual path algorithm of Tibshirani and 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.