Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes
This addresses causal discovery for stochastic processes, which is incremental as it builds on existing methods but extends them to handle SDE models with both fully and partially observed data.
The paper tackles the problem of inferring causal structure from observational data of stochastic dynamical systems, developing a sound and complete causal discovery algorithm that uniquely recovers the underlying graph and outperforms existing approaches in benchmarks.
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 conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.