title: Fused Lasso Additive Model.
abstract: We consider the problem of predicting an outcome variable usingpcovariates that are measured onnindependent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose thefused lasso additive model(FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively-chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two data sets. Supplemental materials are available online, and the R package flam is available on CRAN.
authors.affiliation: Department of Biostatistics, University of Washington, Seattle WA 98195.
authors.forename: Ashley
authors.initials: A
authors.lastname: Petersen
authors.affiliation: Department of Biostatistics, University of Washington, Seattle WA 98195.
authors.forename: Daniela
authors.initials: D
authors.lastname: Witten
authors.affiliation: Department of Biostatistics, University of Washington, Seattle WA 98195.
authors.forename: Noah
authors.initials: N
authors.lastname: Simon
keywords: additive model; feature selection; high-dimensional; non-parametric regression; piecewise constant; sparsity