AI Insight
This paper introduces a theoretical framework for Deep Gaussian Processes structured along directed acyclic graphs (DAGs), enabling modeling of complex systems where functions compose hierarchically with partial observations at different nodes. The authors establish mathematical bounds on how information propagates through network depths, identify conditions under which input distinctions are preserved, and develop a variational inference method that maintains graph dependencies and uncertainty quantification. Applications demonstrate improved performance on protein signaling networks, multi-fidelity physics simulations, and causal modeling tasks while providing interpretable hierarchical structure.
Why it matters
This framework addresses critical challenges in modeling real-world systems with hierarchical structure and sparse observations, including causal inference, multi-scale scientific simulations, and gene regulatory networks. The theoretical guarantees and practical methodology enable more reliable uncertainty quantification in complex systems where traditional models struggle with compositional effects and heterogeneous data.
Understand the Science
arXiv:2607.09645v1 Announce Type: cross
Abstract: Many real-world processes can be represented as compositions of functions along a directed acyclic graph (DAG). In causal modelling, these correspond to the underlying mechanisms; in engineering, to multiple fidelity levels; and in gene-regulatory networks, to transcription factors. These functions are partially observed across the DAG, with noisy and heterogeneously sampled measurements, posing significant challenges for reconstruction, uncertainty propagation, and inference. To tackle these challenges, we place priors over functions and naturally arrive at Deep Gaussian Processes over DAGs. We theoretically study their prior-collapse behaviour, and the effect of graph topology and intermediate observations on the preservation of information. We obtain almost-sure lower bounds on the asymptotic frequency of depths at which the distinction between inputs is preserved, identify broad kernel classes for which these hold, and prove an observation by cite{dunlop2018} on the role of input connections. We offer a structured variational approximation that retains graph dependencies, preserves compositional uncertainty, and captures the explaining-away behaviour of colliders. Finally, we empirically validate our theoretical results and our methodology, and model a latent-collider DAG, a protein signalling network, and a multi-fidelity heavy-ion collision emulation task, attaining state-of-the-art performance while recovering low-fidelity contributions and yielding interpretability of the simulator hierarchy.