标题： 相关尖峰模型中的谱阈值和部分最小二乘法的基本极限 显示英文标题

标题： Spectral Thresholds in Correlated Spiked Models and Fundamental Limits of Partial Least Squares

摘要： 我们提供了对spiked cross-covariance模型的严格随机矩阵理论分析，其中两个高维数据通道中的信号部分对齐。这些模型源于多模态学习，并构成了偏最小二乘法（PLS）的标准生成设置，PLS是一种广泛使用但理论发展不足的方法。我们表明样本交叉协方差矩阵的主导奇异值经历了一个Baik-Ben Arous-Peche（BBP）类型的相变，并表征了信息成分出现的精确阈值。我们的结果给出了该情况下PLS信号恢复能力的第一个精确渐近描述，揭示了PLS与贝叶斯最优估计器之间的基本性能差距。特别是，我们确定了PLS无法恢复任何信号的信噪比和相关性范围，尽管原则上检测是可能的。这些发现明确了PLS的理论极限，并为高维中可靠多模态推理方法的设计提供了指导。 显示英文摘要

摘要： We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These models are motivated by multi-modal learning and form the standard generative setting underlying Partial Least Squares (PLS), a widely used yet theoretically underdeveloped method. We show that the leading singular values of the sample cross-covariance matrix undergo a Baik-Ben Arous-Peche (BBP)-type phase transition, and we characterize the precise thresholds for the emergence of informative components. Our results yield the first sharp asymptotic description of the signal recovery capabilities of PLS in this setting, revealing a fundamental performance gap between PLS and the Bayes-optimal estimator. In particular, we identify the SNR and correlation regimes where PLS fails to recover any signal, despite detectability being possible in principle. These findings clarify the theoretical limits of PLS and provide guidance for the design of reliable multi-modal inference methods in high dimensions.