Learning Causal Structure from Undersampled Time Series

Even if one can experiment on relevant factors, learning the causal structure of a dynamical system can be quite difficult if the relevant measurement processes occur at a much slower sampling rate than the “true” underlying dynamics. This problem is exacerbated if the degree of mismatch is unknown. This paper gives a formal characterization of this learning problem, and then provides two sets of results. First, we prove a set of theorems characterizing how causal structures change under undersampling. Second, we develop an algorithm for inferring aspects of the causal structure at the “true” timescale from the causal structure learned from the undersampled data. Research on causal learning in dynamical contexts has largely ignored the challenges of undersampling, but this paper provides a framework and foundation for learning causal structure from this type of complex time series data.