In the investigation of any causal mechanisms, such as the brain's causal networks, the assumption of causal sufficiency plays a critical role. Notably, neglecting this assumption can result in significant errors, a fact that is often disregarded in the causal analysis of brain networks. In this study, we propose an algorithmic identification approach for determining essential exogenous nodes that satisfy the critical need for causal sufficiency to adhere to it in such inquiries. Our approach consists of three main steps: First, by capturing the essence of the Peter-Clark (PC) algorithm, we conduct independence tests for pairs of regions within a network, as well as for the same pairs conditioned on nodes from other networks. Next, we distinguish candidate confounders by analyzing the differences between the conditional and unconditional results, using the Kolmogorov-Smirnov test. Subsequently, we utilize Non-Factorized identifiable Variational Autoencoders (NF-iVAE) along with the Correlation Coefficient index (CCI) metric to identify the confounding variables within these candidate nodes. Applying our method to the Human Connectome Projects (HCP) movie-watching task data, we demonstrate that while interactions exist between dorsal and ventral regions, only dorsal regions serve as confounders for the visual networks, and vice versa. These findings align consistently with those resulting from the neuroscientific perspective. Finally, we show the reliability of our results by testing 30 independent runs for NF-iVAE initialization.

翻译：在任何因果机制（如大脑的因果网络）的研究中，因果充分性假设起着关键作用。值得注意的是，忽视这一假设可能导致重大错误，这一事实在大脑网络的因果分析中常被忽略。在本研究中，我们提出了一种算法识别方法，用于确定必要的外生节点，以满足此类研究中遵循因果充分性的关键需求。我们的方法包含三个主要步骤：首先，通过捕捉Peter-Clark（PC）算法的精髓，我们对网络内区域对进行独立性检验，并对以其他网络节点为条件的相同区域对进行条件独立性检验。其次，通过分析条件结果与无条件结果之间的差异，利用Kolmogorov-Smirnov检验区分候选混淆变量。随后，我们采用非分解可识别变分自编码器（NF-iVAE）及相关系数指标（CCI）度量，识别这些候选节点中的混淆变量。将我们的方法应用于人类连接组计划（HCP）电影观看任务数据，我们证明：尽管背侧与腹侧区域之间存在交互作用，但只有背侧区域是视觉网络的混淆变量，反之亦然。这些发现与神经科学视角的结果一致。最后，通过30次独立运行的NF-iVAE初始化测试，我们展示了结果的可靠性。