Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.

翻译：利用多元函数数据发现因果关系近期受到了广泛关注。本文提出了一种函数线性结构方程模型，用于在涉及多元函数的潜在图可能包含环的情况下进行因果结构学习。为增强可解释性，我们的模型引入了一个低维因果嵌入空间，使得多元函数数据中所有相关的因果信息均被保留在该低维子空间中。我们证明了在因果发现文献中常采用的标准假设下，所提模型具有因果可识别性。为进行模型推断，我们开发了一个完整的贝叶斯框架，包含合适的先验设定以及通过后验摘要实现的不确定性量化。通过大量模拟研究，我们展示了本方法在因果图估计方面优于现有方法的性能。我们还利用一个脑电图数据集验证了所提方法的有效性。