Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise
This addresses the problem of causal inference in complex systems with hidden nodes and noise for researchers in network science and machine learning, representing an incremental improvement over existing methods.
The paper tackles learning causal networks from partially observed time series data in linear networked dynamical systems with correlated noise, proposing a feature-based clustering method that achieves competitive performance across various connectivity and noise conditions, including a real-world network.
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.