Causal Modeling with Stationary Diffusions
This provides a new paradigm for causal inference that avoids graph-based limitations, potentially benefiting fields like epidemiology or economics.
The authors tackled causal inference by learning stochastic differential equations (SDEs) with stationary densities to model system behavior under interventions, eliminating the need for causal graphs or acyclicity assumptions, and showed that these models often generalize better to unseen interventions than classical approaches.
We develop a novel approach towards 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 generalize to unseen interventions on their variables, often better than classical approaches. Our inference method is based on a new theoretical result that expresses a stationarity condition on the diffusion's generator in a reproducing kernel Hilbert space. The resulting kernel deviation from stationarity (KDS) is an objective function of independent interest.