High-Dimensional Additive Modeling

We propose a new sparsity-smoothness penalty for high-dimensional generalized additive models. The combination of sparsity and smoothness is crucial for mathematical theory as well as performance for finite-sample data. We present a computationally efficient algorithm, with provable numerical convergence properties, for optimizing the penalized likelihood. Furthermore, we provide oracle results which yield asymptotic optimality of our estimator for high-dimensional but sparse additive models. Finally, an adaptive version of our sparsity-smoothness penalized approach yields large additional performance gains.