发表机构
Institute for Financial Studies Shandong University; School of Statistics and Data Science Southeast University; Department of Statistics and Applied Probability National University of Singapore（山东大学金融研究院; 东南大学统计与数据科学学院; 新加坡国立大学统计与应用概率系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出张量TPS-PCA方法，通过分解共享与私有分量实现多视图张量解耦，达到极小极大最优，并在电力、金融和活动识别中验证有效性。
AI 中文摘要
在本工作中，我们通过将每个视图中的潜在信号分解为两个分量来对观测到的多视图张量进行建模：（i）捕获所有视图共同动态的共享分量，以及（ii）解释视图特有变化的私有分量。为了解耦共享分量和私有分量，我们提出了一种新颖的张量Tucker个性化子空间主成分分析（TPS-PCA）方法，该方法具有一步闭式解，并作为我们扩展的张量版本个性化PCA（TP-PCA）的理想替代，后者改编自shi2024personalized的开创性工作。理论分析表明，所提出的TPS-PCA估计器在视图级张量解耦方面达到了极小极大下界，而TP-PCA估计器仅能达到跨视图的平均解耦误差率，该速率仍慢于TPS-PCA估计器。我们在合成数据集和真实数据集上进行了广泛的数值实验，证明了所提方法在电力管理、金融分析和活动识别等领域的广泛适用性。
英文摘要
In this work, we model the observed multi-view tensors by decomposing the underlying signal in each view into two components: (i) the shared component that captures common dynamics across all views, and (ii) the private component that accounts for view-wise unique variations. To decouple the shared and private components, we introduce a novel Tucker personalized subspace principal component analysis (TPS-PCA) approach for tensors, which admits a one-step closed-form solution and serves as an ideal surrogate for our extended tensor-version personalized PCA (TP-PCA), adapted from the seminal work by \cite{shi2024personalized}. The theoretical analysis reveals that the proposed TPS-PCA estimators reach the minimax lower bound in terms of view-wise tensor decoupling, whereas the TP-PCA estimators only achieve a rate of average decoupling error across views, which is still slower than that of the TPS-PCA estimators. Extensive numerical experiments are conducted on synthetic and real datasets, demonstrating the wide applicability of the proposed method in fields including power management, financial analysis, and activity recognition.
