稀疏典型相关估计的贝叶斯方法
A Bayesian Methodology for Estimation for Sparse Canonical Correlation
AI总结：
本文提出一种新的贝叶斯结构化稀疏CCA方法，通过贝叶斯无限因子模型、乘性半柯西先验和图马蹄先验在载荷矩阵与协方差矩阵两个层面鼓励稀疏性，并在模拟和乳腺癌多组学数据上验证了其稳健估计性能。
摘要：
对参与联合研究的每个受试者从不同实验中获取的多视图高维数据进行综合统计分析可能具有挑战性。典型相关分析（CCA）是一种用于识别此类数据集之间关系的统计方法。在这一背景下，结构化稀疏CCA（ScSCCA）是一个快速兴起的方法学领域，其目标是通过假设相应的CCA方向向量是稀疏的，从而对不同数据模态之间的相互关系进行稳健建模。尽管该统计方法学发展领域正在迅速增长，但仍需要在贝叶斯范式下发展相关方法。在本文中，我们提出了一种新的ScSCCA方法，其中采用贝叶斯无限因子模型，并旨在通过在建模框架的两个不同层次上鼓励稀疏性来实现稳健估计。首先，我们利用乘性半柯西过程先验在潜变量载荷矩阵层面鼓励稀疏性。此外，我们通过使用图马蹄先验或对角结构在协方差矩阵中进一步促进稀疏性。我们进行了多次模拟，将所提方法与其他常用CCA方法的性能进行比较，并将所开发的方法应用于分析来自一项乳腺癌研究的多组学数据。
英文摘要：
It can be challenging to perform an integrative statistical analysis of multi-view high-dimensional data acquired from different experiments on each subject who participated in a joint study. Canonical Correlation Analysis (CCA) is a statistical procedure for identifying relationships between such data sets. In that context, Structured Sparse CCA (ScSCCA) is a rapidly emerging methodological area that aims for robust modeling of the interrelations between the different data modalities by assuming the corresponding CCA directional vectors to be sparse. Although it is a rapidly growing area of statistical methodology development, there is a need for developing related methodologies in the Bayesian paradigm. In this manuscript, we propose a novel ScSCCA approach where we employ a Bayesian infinite factor model and aim to achieve robust estimation by encouraging sparsity in two different levels of the modeling framework. Firstly, we utilize a multiplicative Half-Cauchy process prior to encourage sparsity at the level of the latent variable loading matrices. Additionally, we promote further sparsity in the covariance matrix by using graphical horseshoe prior or diagonal structure. We conduct multiple simulations to compare the performance of the proposed method with that of other frequently used CCA procedures, and we apply the developed procedures to analyze multi-omics data arising from a breast cancer study.
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