Fused Lasso Additive Model
This provides an interpretable method for high-dimensional prediction, but it is incremental as it builds on existing additive and lasso models.
The authors tackled the problem of predicting an outcome with flexible and interpretable fits by proposing the fused lasso additive model (FLAM), which estimates piecewise constant additive functions with adaptively-chosen knots, and demonstrated its performance in simulations and on two datasets.
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.