Canonical Correlation Analysis (CCA) is a method for analyzing pairs of random vectors; it learns a sequence of paired linear transformations such that the resultant canonical variates are maximally correlated within pairs while uncorrelated across pairs. CCA outputs both canonical correlations as well as the canonical directions which define the transformations. While inference for canonical correlations is well developed, conducting inference for canonical directions is more challenging and not well-studied, but is key to interpretability. We propose a computational bootstrap method (combootcca) for inference on CCA directions. We conduct thorough simulation studies that range from simple and well-controlled to complex but realistic and validate the statistical properties of combootcca while comparing it to several competitors. We also apply the combootcca method to a brain imaging dataset and discover linked patterns in brain connectivity and behavioral scores.

翻译：典型相关分析（CCA）是一种分析随机向量对的方法；它学习一系列配对的线性变换，使得所得到的典型变量在配对内最大化相关，而在跨配对间不相关。CCA输出典型相关性以及定义这些变换的典型方向。尽管典型相关性的推断已发展成熟，但对典型方向进行推断更具挑战性且研究尚不充分，而这正是可解释性的关键。我们提出了一种用于CCA方向推断的计算自举方法（combootcca）。我们进行了从简单可控到复杂真实的全面模拟研究，验证了combootcca的统计特性，并将其与多种竞争方法进行了比较。我们还将combootcca方法应用于脑成像数据集，发现了大脑连接性与行为评分之间的关联模式。