We consider (nonparametric) sparse additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso and more general sparse group Slope-type penalties on the coefficients of univariate components' expansions in orthonormal series (e.g., Fourier or wavelets). The resulting classifiers are inherently adaptive to the unknown sparsity and smoothness. We show that under certain sparse group restricted eigenvalue condition the sparse group Lasso classifier is nearly-minimax (up to log-factors) within the entire range of analytic, Sobolev and Besov classes while the sparse group Slope classifier achieves the exact minimax order (without the extra log-factors) for sparse and moderately dense setups. The performance of the proposed classifier is illustrated on the real-data example.

翻译：我们考虑了分类问题中的（非参数）稀疏加性模型（SpAM）。该稀疏加性模型分类器的设计基于最小化逻辑损失，并采用稀疏组Lasso及更一般的稀疏组Slope型惩罚项，作用于单变量分量在正交基（如傅里叶或小波）展开中的系数。所得分类器对未知的稀疏性和光滑性具有内在自适应性。我们证明，在满足特定稀疏组限制特征值条件的情况下，稀疏组Lasso分类器在解析类、Sobolev类及Besov类的整个范围内几乎达到极小极大最优（仅含对数因子）；而稀疏组Slope分类器在稀疏和中等稠密情形下则精确达到极小极大最优阶（无需额外对数因子）。最后，通过实际数据案例展示了所提分类器的性能。