Coordinate optimization for generalized fused Lasso

• Published in: Communications in statistics. Theory and methods Vol. 50; no. 24; pp. 5955 - 5973
• Main Authors: Ohishi, M., Fukui, K., Okamura, K., Itoh, Y., Yanagihara, H.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 11.11.2021; Taylor & Francis Ltd
• Subjects: Algorithms; Coordinate descent algorithm; Data analysis; generalized fused Lasso; generalized Lasso; Hierarchies; Kuhn-Tucker method; Optimization
• ISSN: 0361-0926; 1532-415X; 1532-415X
• DOI: 10.1080/03610926.2021.1931888

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.