MOCHA: Discovering Multi-Order Dynamic Causal Structure in Temporal Point Processes

Modeling event sequences requires understanding when future events will occur and how event types causally influence one another over time. Existing temporal point process (TPP) models typically assume static or first-order dependence structures, which limits their ability to capture the dynamic and multi-order causal mechanisms commonly observed in real-world systems. We propose MOCHA, a Multi-Order Causal Hierarchical Architecture for multivariate TPP that jointly models time-varying causal structure and multi-hop influence propagation in continuous time. MOCHA learns latent dynamic weighted directed acyclic graphs (DAG) over event types, where acyclicity and sparsity constraints promote structurally valid causal graphs. Based on the learned graph, the model decomposes event dynamics into multi-order causal paths, and incorporate both direct influence and indirect propagation into the intensity function. The entire framework is end-to-end differentiable and optimized jointly for event prediction and causal structure discovery. Experiments on seven real-world datasets from different domains show that MOCHA consistently achieves superior negative log-likelihood, while also recovering dynamic causal patterns that align with domain knowledge. These results demonstrate that MOCHA provides an effective framework for dynamic causal structure learning in TPP.