Perlino et al. pioneer Deep Gaussian Processes on DAGs, beating state-of-the-art in emulation

Federico L. Perlino, Oliver Hamelijnck, Adam M. Johansen, and Theodoros Damoulas have introduced Deep Gaussian Processes on Directed Acyclic Graphs (DGPs on DAGs), a rigorous framework for modeling processes that can be represented as compositions of functions along DAGs—common in causal modeling, multi-fidelity engineering, and gene-regulatory networks. The paper tackles the challenge of partially observed, noisy, and heterogeneously sampled measurements across the graph. The authors theoretically analyze prior-collapse behavior and the effect of graph topology and intermediate observations on information preservation. They derive almost-sure lower bounds on the asymptotic frequency of depths at which input distinctions are preserved, identify broad kernel classes satisfying these bounds, and confirm a conjecture by Dunlop (2018) on the role of input connections.

To enable practical inference, the team proposes a structured variational approximation that retains dependencies across the DAG, preserves compositional uncertainty, and captures the explaining-away behavior of colliders. Empirically, the method is validated on three diverse tasks: a latent-collider DAG, a protein signaling network, and a multi-fidelity heavy-ion collision emulation problem. In all cases, DGPs on DAGs achieve state-of-the-art performance while providing interpretability of the simulator hierarchy and recovering low-fidelity contributions. The 75-page paper, available on arXiv, spans theoretical machine learning, statistics, and applications in computational science.