Signature Kernel Conditional Independence Tests in Causal Discovery for
  Stochastic Processes
Georg Manten Cecilia Casolo Emilio Ferrucci Søren Wengel Mogensen Cristopher Salvi Niki Kilbertus
Inferring the causal structure underlying stochastic dynamical systems from
observational data holds great promise in domains ranging from science and
health to finance. Such processes can often be accurately modeled via
stochastic differential equations (SDEs), which naturally imply causal
relationships via "which variables enter the differential of which other
variables". In this paper, we develop a kernel-based test of conditional
independence (CI) on "path-space" -- solutions to SDEs -- by leveraging recent
advances in signature kernels. We demonstrate strictly superior performance of
our proposed CI test compared to existing approaches on path-space. Then, we
develop constraint-based causal discovery algorithms for acyclic stochastic
dynamical systems (allowing for loops) that leverage temporal information to
recover the entire directed graph. Assuming faithfulness and a CI oracle, our
algorithm is sound and complete. We empirically verify that our developed CI
test in conjunction with the causal discovery algorithm reliably outperforms
baselines across a range of settings.