  We consider the problem of predicting an outcome variable using $p$
covariates that are measured on $n$ independent observations, in the setting in
which flexible and interpretable fits are desirable. We propose the fused 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 the 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.
