| 摘要: |
| 切片逆回归是在不损失关键信息的条件下, 通过将高维协变量投影到低维线性空间实现充分降维的重要方法. 针对大样本和数据流场景下经典切片逆回归需要重复计算、计算成本较高, 且现有在线或增量方法在估计稳定性方面仍有改进空间的问题, 本文提出了一种基于奇异值分解更新的在线增量切片逆回归算法(Singular Value Decomposition Updating-based Incremental Sliced Inverse Regression, SVDU-ISIR). 该方法借助奇异值分解更新思想, 对目标子空间相关特征向量进行直接更新, 并显式构造协方差矩阵逆的更新表达式. 在此基础上, 本文给出了所提算法的误差界与计算复杂度分析. 数据模拟和实数据分析结果表明, 与现有在线或增量切片逆回归方法相比, SVDU-ISIR在多数情形下具有更高或更稳定的估计精度, 并显著提高了计算效率, 从而为大样本在线充分降维提供了一种有效方法. |
| 关键词: 切片逆回归 充分降维 奇异值分解 在线更新 |
| DOI： |
| 分类号:O212.4 |
| 基金项目:山西省自然科学基金 |
|
| Incremental Sliced Inverse Regression Based on Singular Value Updates |
|
BaoHaikuan, ZhangJunying
|
|
Taiyuan University of Technology
|
| Abstract: |
| Sliced inverse regression is an important method for sufficient dimension reduction, which projects high-dimensional covariates onto a low-dimensional linear subspace without losing essential information. In large-sample and data-stream settings, the classical sliced inverse regression method requires repeated computations and incurs high computational cost, while existing online or incremental methods still leave room for improvement in estimation stability. To address these issues, this paper proposes an online incremental sliced inverse regression algorithm based on singular value decomposition updating, namely Singular Value Decomposition Updating-based Incremental Sliced Inverse Regression (SVDU-ISIR). The proposed method directly updates the eigenvectors associated with the target subspace by using the idea of singular value decomposition updating, and explicitly constructs the updating expression for the inverse covariance matrix. On this basis, the error bound and computational complexity of the proposed algorithm are established. Simulation studies and real data analysis show that, compared with existing online or incremental sliced inverse regression methods, SVDU-ISIR achieves higher or more stable estimation accuracy in most cases and significantly improves computational efficiency, thus providing an effective approach for online sufficient dimension reduction with large-scale data. |
| Key words: Sliced inverse regression Sufficient dimension reduction Singular value decomposition Online updating |
