The authors propose Deep Gaussian Processes over directed acyclic graphs (DAGs) to model real-world processes composed of functions along a DAG, addressing challenges in reconstruction and uncertainty propagation with noisy, heterogeneously sampled measurements.
- Theoretical study of prior-collapse behavior and the effect of graph topology on information preservation.
- Derivation of almost-sure lower bounds on the asymptotic frequency of depths where input distinction is preserved.
- Development of a structured variational approximation that retains graph dependencies and captures explaining-away behavior of colliders.
- Empirical validation on latent-collider DAGs, protein signaling networks, and multi-fidelity heavy-ion collision emulation.
The methodology attains state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.