Causal Learning through Deliberate Undersampling

Domain scientists interested in causal mechanisms are usually limited by the frequency at which they can collect the measurements of social, physical, or biological systems. A common and plausible assumption is that higher measurement frequencies are the only way to gain more informative data about the underlying dynamical causal structure. This assumption is a strong driver for designing new, faster instruments, but such instruments might not be feasible or even possible. In this paper, we show that this assumption is incorrect: there are situations in which we can gain additional information about the causal structure by measuring more slowly than our current instruments. We present an algorithm that uses graphs at multiple measurement timescales to infer underlying causal structure, and show that inclusion of structures at slower timescales can nonetheless reduce the size of the equivalence class of possible causal structures. We provide simulation data about the probability of cases in which deliberate undersampling yields a gain, as well as the size of this gain.