This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates spurious associations across pairs of nodes, rendering the problem much harder. To address the challenge of noise correlation and partial observability, we assign to each pair of nodes a feature vector computed from the time series data of observed nodes. The feature embedding is engineered to yield structural consistency: there exists an affine hyperplane that consistently partitions the set of features, separating the feature vectors corresponding to connected pairs of nodes from those corresponding to disconnected pairs. The causal inference problem is thus addressed via clustering the designed features. We demonstrate with simple baseline supervised methods the competitive performance of the proposed causal inference mechanism under broad connectivity regimes and noise correlation levels, including a real world network. Further, we devise novel technical guarantees of structural consistency for linear NDS under the considered regime.

翻译：本文考虑从部分节点的时间序列数据（即部分可观测性）中学习线性网络化动力系统（NDS）的隐式因果网络。该NDS的动态由有色噪声驱动，会在节点对之间产生虚假关联，使得问题更加复杂。为应对噪声相关性和部分可观测性的挑战，我们为每对节点分配一个从观测节点时间序列数据计算得出的特征向量。该特征嵌入被设计为具有结构一致性：存在一个仿射超平面能够一致地划分特征集，将相连节点对对应的特征向量与不相连节点对对应的特征向量分离。因此，因果推断问题通过聚类所设计的特征来解决。我们利用简单的基线监督方法展示了所提出的因果推断机制在广泛连接模式和噪声相关水平（包括真实世界网络）下的竞争性能。此外，我们为所考虑场景下的线性NDS提供了结构一致性的新颖技术保障。