Causal Modeling with Stationary Diffusions

We develop a new model and learning algorithm for causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These stationary diffusion models do not require the formalism of causal graphs, let alone the common assumption of acyclicity. We show that in several cases, they still allow generalizing to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a novel theoretical result that translates a stationarity condition on the diffusion's generator into reproducing kernel Hilbert spaces. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.