论文标题
多类分类通过稀疏的多项式逻辑回归
Multiclass classification by sparse multinomial logistic regression
论文作者
论文摘要
在本文中，我们考虑通过稀疏的多项式逻辑回归来考虑高维多类分类。我们首先提出一个基于受惩罚最大似然的特征选择程序，对模型大小的复杂性惩罚，并得出未分类的分类分类器的非隔离范围。我们还通过得出相应的极小下限来建立它们的紧密度。特别是，我们表明存在两个与小型类别相对应的制度。在额外的低噪声条件下可以减少边界。但是，要找到具有复杂性惩罚的惩罚最大似然解决方案，需要对所有可能的模型进行组合搜索。为了在计算高维数据的计算上设计功能选择程序，我们提出了多项式逻辑群体套索和斜率分类器，并表明它们也达到了最小订单。
In this paper we consider high-dimensional multiclass classification by sparse multinomial logistic regression. We propose first a feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the nonasymptotic bounds for misclassification excess risk of the resulting classifier. We establish also their tightness by deriving the corresponding minimax lower bounds. In particular, we show that there exist two regimes corresponding to small and large number of classes. The bounds can be reduced under the additional low noise condition. To find a penalized maximum likelihood solution with a complexity penalty requires, however, a combinatorial search over all possible models. To design a feature selection procedure computationally feasible for high-dimensional data, we propose multinomial logistic group Lasso and Slope classifiers and show that they also achieve the minimax order.
