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：在探索任何因果机制（如大脑因果网络）时，因果充分性假设起着关键作用。值得注意的是，忽略这一假设可能导致显著错误，而这一点在大脑网络的因果分析中常被忽视。本研究提出一种算法化识别方法，用于确定满足因果充分性关键需求的外生节点，以确保在此类研究中遵循该假设。该方法包含三个主要步骤：首先，通过提取Peter-Clark (PC)算法的核心思想，对网络内区域对进行独立性检验，并基于其他网络节点条件化对同一区域对进行检验；其次，利用科尔莫戈罗夫-斯米尔诺夫检验分析条件与非条件结果之间的差异，从而区分候选混淆因子；随后，采用非因子化可识别变分自编码器（NF-iVAE）结合相关系数指标（CCI），识别这些候选节点中的混淆变量。将本方法应用于人类连接组计划（HCP）电影观看任务数据后，我们证明：尽管背侧与腹侧区域之间存在交互作用，但仅背侧区域作为视觉网络的混淆因子，反之亦然。这些发现与神经科学视角下的结论高度一致。最后，通过30次独立运行的NF-iVAE初始化测试，我们验证了结果的可靠性。