Classification by sparse generalized additive models

TL;DR

This paper introduces a sparse generalized additive model (SpAM) classifier for nonparametric classification, which adapts to unknown sparsity and smoothness, and achieves near-minimax performance under certain conditions.

Contribution

The paper develops a novel SpAM classifier using group penalties on orthonormal series expansions, with theoretical guarantees and practical illustrations.

Findings

Nearly-minimax optimality across various function classes

Adaptive to unknown sparsity and smoothness

Validated on simulated and real datasets

Abstract

We consider (nonparametric) sparse (generalized) additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso/Slope-type penalties on the coefficients of univariate additive components' expansions in orthonormal series (e.g., Fourier or wavelets). The resulting classifier is inherently adaptive to the unknown sparsity and smoothness. We show that under certain sparse group restricted eigenvalue condition it is nearly-minimax (up to log-factors) simultaneously across the entire range of analytic, Sobolev and Besov classes. The performance of the proposed classifier is illustrated on a simulated and a real-data examples.