标题： 高维非线性分类的创新交互筛选 显示英文标题

标题： Innovated interaction screening for high-dimensional nonlinear classification

摘要： 本文研究了高维情况下交互作用筛选和非线性分类的问题。 我们提出了一种两步法，即IIS-SQDA，在第一步中，基于变换原始的$p$维特征向量，提出了一个创新的交互作用筛选（IIS）方法；在第二步中，提出了稀疏二次判别分析（SQDA），用于进一步选择重要的交互作用和主要效应，并同时进行分类。 我们的IIS方法通过检查$p$个特征而不是所有$O(p^2)$阶的两两交互作用来筛选重要的交互作用。 我们的理论表明，所提出的方法在样本数量的指数增长的高维$p$情况下具有确定性筛选性质。 在选择和分类步骤中，我们对QDA的估计系数向量建立了一个稀疏不等式，并证明了我们的方法的分类误差可以被上界为Oracle分类误差加上一些较小阶数项。 大量的模拟研究和真实数据分析显示，我们的提议方法在交互作用选择和高维分类方面优于现有方法。 显示英文摘要

摘要： This paper is concerned with the problems of interaction screening and nonlinear classification in a high-dimensional setting. We propose a two-step procedure, IIS-SQDA, where in the first step an innovated interaction screening (IIS) approach based on transforming the original $p$-dimensional feature vector is proposed, and in the second step a sparse quadratic discriminant analysis (SQDA) is proposed for further selecting important interactions and main effects and simultaneously conducting classification. Our IIS approach screens important interactions by examining only $p$ features instead of all two-way interactions of order $O(p^2)$. Our theory shows that the proposed method enjoys sure screening property in interaction selection in the high-dimensional setting of $p$ growing exponentially with the sample size. In the selection and classification step, we establish a sparse inequality on the estimated coefficient vector for QDA and prove that the classification error of our procedure can be upper-bounded by the oracle classification error plus some smaller order term. Extensive simulation studies and real data analysis show that our proposal compares favorably with existing methods in interaction selection and high-dimensional classification.