Non-Stationary Causal Learning via Hierarchical Modeling

Causal discovery in time-varying environments requires methods that accommodate changes in the underlying causal mechanisms while retaining computational tractability. Classical approaches impose a stationarity assumption that forces all observations to share a single directed acyclic graph (DAG), an assumption that fails in many real systems. Modern differentiable causal discovery frameworks address the static problem through continuous optimization but provide limited support for non-stationary settings. This paper introduces a hierarchical framework for non-stationary causal discovery based on an unconstrained parameterization of DAGs. A stochastic-process prior on the sequence of latent potentials restricts the temporal evolution of the graphs and permits smooth, abrupt, or locally adaptive structural changes. Random-walk, Gaussian-process, and switching-state priors arise as special cases. The resulting formulation produces a fully differentiable objective that incorporates data fit, sparsity, and temporal structure. Experiments under linear structural equation models show that appropriate temporal regularization improves the recovery of time-varying causal relationships relative to stationary estimators. The proposed framework, therefore, provides a flexible and computationally efficient approach to causal identification in non-stationary time series.