Coordinate descent algorithm of generalized fused Lasso logistic regression for multivariate trend filtering

Generalized fused Lasso (GFL) is an extension of fused Lasso and performs multivariate trend filtering based on adjacent information among parameters. This paper deals with an optimization problem for GFL logistic regression. Model parameters for the generalized linear model including the logistic regression model are usually optimized by minimizing a linear approximation of an objective function because the minimizer of the objective function cannot be obtained in closed form. In this paper, we propose an algorithm for solving the optimization problem for GFL logistic regression without approximating the objective function, for the purpose of optimizing fast and accurately. Specifically, we derive update equations of a coordinate descent algorithm for solving the optimization problem in closed form. Moreover, we show an example for spatio-temporal data analysis.