在线监督降维与随机特征：诊断与计算权衡
Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs
- School of Statistics（统计学院）
- University of International Business and Economics（对外经济贸易大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究在线核监督主成分分析中，优化精度不等于总体恢复或预测性能，通过诊断和计算权衡分析，揭示终端优化与几何质量及成本间的分离。
AI中文摘要：
监督谱目标函数的精确优化并不一定能产生准确的总体子空间或更好的预测表示。我们针对在线核监督主成分分析（OKSPCA）研究了这些区别，该方法将有限随机特征坐标中的中心化交叉矩与Adam式正交基更新相结合，以优化既定目标。固定映射一致性、集中性和扰动结果描述了估计量及其精确子空间；随后，同目标比较分别评估实际迭代。在六个预测基准上，性能取决于声明的流程：用精确经验目标替换跟踪器，两个回归缺陷基本不变。直接分类秩模型平均捕获了几乎所有终端目标能量，但保存的中间状态表现出显著的几何偏差；一项受控样本量研究进一步将经验准确性与总体恢复区分开来。在不同的数值服务工作负载中，在测试的分类设置中，按需精确计算更快，而Adam相对于测试的完整薄SVD服务，在某些密集宽回归请求上节省了时间，同时存在持续的几何误差。这些诊断限制了仅基于终端优化精度的解释，并将计算成本与质量、秩覆盖和新颖性区分开来；它们既未确立实际跟踪器的收敛性，也未确立基可用性带来的预测或部署优势。
英文摘要：
Accurate optimization of a supervised spectral objective need not produce an accurate population subspace or a better predictive representation. We investigate these distinctions for Online Kernel Supervised Principal Component Analysis (OKSPCA), which combines a centered cross-moment in finite random-feature coordinates with an Adam-style orthonormal basis update for an established objective. Fixed-map consistency, concentration and perturbation results describe the estimator and its exact subspace; same-target comparisons then assess the practical iterate separately. Across six predictive benchmarks, performance depends on the declared pipeline: replacing the tracker with the exact empirical target leaves the two regression deficits largely unchanged. Direct classification-rank models capture nearly all terminal objective energy on average, but a saved intermediate state exhibits substantial geometric deviation; a controlled sample-size study further separates empirical accuracy from population recovery. In distinct numerical-service workloads, exact on-request computation is faster in the tested classification settings, whereas Adam saves time relative to the tested full thin-SVD service for some dense wider-regression requests, alongside persistent geometric error. These diagnostics limit explanations based solely on terminal optimization accuracy and distinguish numerical cost from quality, rank coverage and freshness; they establish neither practical-tracker convergence nor predictive or deployment benefits from basis availability.
