An Outer-Product-of-Gradient Approach to Dimension Reduction and its Application to Classification in High Dimensional Space

• 成果类型: Article
• 署名作者: Cai, Zhibo; Xia, Yingcun; Hang, Weiqiang
• 署名单位: National University of Singapore; University of Electronic Science & Technology of China
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.2003202
• 发表日期: 2023
• 页码: 1671-1681
• 关键词: sliced inverse regression; SPARSE

摘要

Sufficient dimension reduction (SDR) has progressed steadily. However, its ability to improve general function estimation or classification has not been well received, especially for high-dimensional data. In this article, we first devise a local linear smoother for high dimensional nonparametric regression and then utilise it in the outer-product-of-gradient (OPG) approach of SDR. We call the method high-dimensional OPG (HOPG). To apply SDR to classification in high-dimensional data, we propose an ensemble classifier by aggregating results of classifiers that are built on subspaces reduced by the random projection and HOPG consecutively from the data. Asymptotic results for both HOPG and the classifier are established. Superior performance over the existing methods is demonstrated in simulations and real data analyses. Supplementary materials for this article are available online.