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.

通过对观测节点的时间序列数据进行特征嵌入和聚类，解决了具有噪声相关性和部分可观测性的线性网络动力系统中隐藏因果网络的学习问题。

学习具有潜在节点和结构噪声的网络动力系统的因果结构