There are several issues with causal discovery from fMRI. First, the sampling frequency is so low that the time-delayed dependence between different regions is very small, making time-delayed causal relations weak and unreliable. Moreover, the complex correspondence between neural activity and the BOLD signal makes it difficult to formulate a causal model to represent the effect as a function of the cause. Second, the fMRI experiment may last a relatively long time period, during which the causal influences are likely to change along with certain unmeasured states (e.g., the attention) of the subject which can be written as a function of time, and ignoring the time-dependence will lead to spurious connections. Likewise, the causal influences may also vary as a function of the experimental condition (e.g., health, disease, and behavior). In this paper we aim to develop a principled framework for robust and time- or condition-specific causal discovery, by addressing the above issues. Motivated by a simplified fMRI generating process, we show that the time-delayed conditional independence relationships at the proper causal frequency of neural activities are consistent with the instantaneous conditional independence relationships between brain regions in fMRI recordings. Then we propose an enhanced constraint-based method for robust discovery of the underlying causal skeletons, where we include time or condition as an additional variable in the system; it helps avoid spurious causal connections between brain regions and discover time- or condition-specific regions. It also has additional benefit in causal direction determination. Experiments on both simulated fMRI data and real data give encouraging results.

本文提出了一个有原则的框架来处理非平稳数据，并开发了一些方法来处理三个重要问题：检测局部机制不平稳的变量以及恢复观测变量之间的因果结构，通过利用变化分布所携带的信息确定某些因果方向，以及开发可视化因果模块的非平稳方法。作者通过各种合成和真实世界数据集的实验结果来展示这些方法的有效性。

非定态因果模型的发现和可视化