高维分类中基于非参数选择的特征增强算法（FANS）
Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification
摘要：
我们提出了一个高维分类方法，涉及非参数特征增强。知道边际密度比是最强大的单变量分类器，我们使用比估计来转换原始特征测量。随后，调用惩罚的逻辑斯谛回归，将新变换或增强的特征作为输入。该过程训练具有局部复杂性和全局简单性的模型，从而避免维数灾难，同时创建灵活的非线性决策边界。由此产生的方法被称为通过非参数化和选择的特征增强（FANS）。我们激励FANS通过推广朴素贝叶斯模型，将联合密度的对数比作为边际密度的线性组合。它与广义可加模型有关，但具有更好的可解释性和可计算性。为FANS制定了风险界限。在数值分析中，将FANS方法与其它方法进行了比较，为FANS方法的最佳应用领域提供了指导。真实数据分析表明，FANS在基准电子邮件垃圾和基因表达数据集上表现得非常有竞争力。此外，FANS是通过并行计算的一个非常快速的算法实现。
英文摘要：
We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.
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