Abstract

Fused Lasso is one of extensions of Lasso to shrink differences of parameters. We focus on a general form of it called generalized fused Lasso (GFL). The optimization problem for GFL can be came down to that for generalized Lasso and can be solved via a path algorithm for generalized Lasso. Moreover, the path algorithm is implemented via the genlasso package in R. However, the genlasso package has some computational problems. Then, we apply a coordinate descent algorithm (CDA) to solve the optimization problem for GFL. We give update equations of the CDA in closed forms, without considering the Karush-Kuhn-Tucker conditions. Furthermore, we show an application of the CDA to a real data analysis.

摘要

Fused Lasso 是 Lasso 的一种扩展，用于缩小参数差异。我们专注于它的一般形式，称为广义融合套索（GFL）。GFL的优化问题可以归结为广义套索的优化问题，可以通过广义套索的路径算法解决。此外，路径算法是通过 R 中的 genlasso 包实现的。然而，genlasso 包有一些计算问题。然后，我们应用坐标下降算法 (CDA) 来解决 GFL 的优化问题。我们以闭合形式给出 CDA 的更新方程，不考虑 Karush-Kuhn-Tucker 条件。此外，我们展示了 CDA 在实际数据分析中的应用。