High-dimensional additive modeling

TL;DR

This paper introduces a novel sparsity-smoothness penalty for high-dimensional generalized additive models, offering an efficient algorithm with proven convergence and asymptotic optimality, along with an adaptive version that enhances performance.

Contribution

It presents a new combined penalty for additive models, along with an efficient optimization algorithm and theoretical guarantees, including an adaptive method for improved results.

Findings

Efficient algorithm with provable convergence.

Asymptotic optimality of the estimator.

Adaptive approach significantly improves performance.

Abstract

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.