Canonical Correlation Analysis as Reduced Rank Regression in High Dimensions
高维典型相关分析的降秩回归表述AI 解读 ↓
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高维典型相关分析的降秩回归表述
- 研究问题
- 论文研究一组数据高维、另一组低维时如何估计典型方向，重点应对稀疏典型相关方法在扩展规模与适应结构方面的困难。
- 方法与思路
- 作者将典型方向估计改写为降秩回归问题，利用高维回归方法容纳结构先验，并通过模拟和三个真实数据集考察表现。
- 材料陈述的贡献
- 摘要称该方法兼顾计算效率与精度，在模拟中比既有方法更准确，并在真实数据中发现具有科学意义的变量关联。
- 阅读关注点
- 应核对降秩回归与典型方向的对应条件、稀疏及其他先验的实现、比较方法的调参公平性和真实数据关联的解释依据。
- 阅读边界
- 这是所给 arXiv v2 预印本摘要，不能据此声称已同行评审或期刊接收；具体精度增益、理论条件和应用细节未说明。
原文摘要
Canonical correlation analysis is a widespread technique for discovering linear relationships between two sets of variables. In high dimensions, however, standard estimates of the canonical directions cease to be consistent without assuming further structure. In this setting, a possible solution consists in leveraging the presumed sparsity of the solution: only a subset of the covariates span the canonical directions. While the last decade has seen a proliferation of sparse canonical correlation analysis methods, practical challenges regarding the scalability and adaptability of these methods still persist. To circumvent these issues, this paper suggests an alternative strategy that uses reduced rank regression to estimate the canonical directions when one of the datasets is high-dimensional while the other remains low-dimensional. By casting the problem of estimating the canonical direction as a regression problem, our estimator is able to leverage the rich statistics literature on high-dimensional regression and is easily adaptable to accommodate a wider range of structural priors. Our proposed solution maintains computational efficiency and accuracy, even in the presence of very high-dimensional data. We demonstrate the advantages of our approach through a series of simulated experiments, achieving a substantial increase in accuracy compared to existing methods. Additionally, we highlight its practical utility by applying it to three real-world datasets, where we show that our method is able to uncover scientifically meaningful associations between variables.