Coordinate descent algorithm for generalized group fused Lasso

We deal with a model with discrete varying coefficients to consider modeling for heterogeneity and clustering for homogeneity, and estimate the varying coefficients by generalized group fused Lasso (GGFL). GGFL allows homogeneous groups to be joined together based on one-to-many relationships among groups. This makes GGFL a powerful technique, but to date there has been no effective algorithm for obtaining the solutions. Here we propose an algorithm for obtaining a GGFL solution based on the coordinate descent method, and show that a solution for each coordinate direction converges to the optimal solution. In a simulation, we show our algorithm is superior to ADMM, which is one of the popular algorithms. We also present an application to a spatial data analysis.