  Sparse additive modeling is a class of effective methods for performing
high-dimensional nonparametric regression. In this work we show how shape
constraints such as convexity/concavity and their extensions, can be integrated
into additive models. The proposed sparse difference of convex additive models
(SDCAM) can estimate most continuous functions without any a priori smoothness
assumption. Motivated by a characterization of difference of convex functions,
our method incorporates a natural regularization functional to avoid
overfitting and to reduce model complexity. Computationally, we develop an
efficient backfitting algorithm with linear per-iteration complexity.
Experiments on both synthetic and real data verify that our method is
competitive against state-of-the-art sparse additive models, with improved
performance in most scenarios.
