论文标题
多类稀疏线性分类器的概括误差界限
Generalization Error Bounds for Multiclass Sparse Linear Classifiers
论文作者
论文摘要
我们通过稀疏的多项式逻辑回归来考虑高维多类分类。与二进制分类不同，在多类设置中，人们可以考虑与回归系数矩阵上不同结构假设相关的稀疏性概念的整个范围。我们提出了一个基于惩罚最大似然的计算可行特征选择程序，并捕获了特定类型的稀疏性。特别是，我们考虑全局稀疏性，双行稀疏性和低率稀疏性，并表明，使用正确选择的调谐参数，派生的插件分类器在多级稀疏类稀疏类别的稀有类别中，达到了Minimax概括误差范围（在错误分类过剩的风险方面）。开发的方法是一般的，也可以适应其他类型的稀疏性。
We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with different structural assumptions on the regression coefficients matrix. We propose a computationally feasible feature selection procedure based on penalized maximum likelihood with convex penalties capturing a specific type of sparsity at hand. In particular, we consider global sparsity, double row-wise sparsity, and low-rank sparsity, and show that with the properly chosen tuning parameters the derived plug-in classifiers attain the minimax generalization error bounds (in terms of misclassification excess risk) within the corresponding classes of multiclass sparse linear classifiers. The developed approach is general and can be adapted to other types of sparsity as well.
