Summary
This paper introduces deep Gaussian processes defined over directed acyclic graphs (DAGs), modeling real-world processes as compositions of functions along graph structures. The authors—Federico L. Perlino, Oliver Hamelijnck, Adam M. Johansen, and Theodoros Damoulas—provide theoretical analysis of prior collapse behavior and study how graph topology and intermediate observations affect information retention. They derive an almost-sure lower bound on the depth up to which input distinctness is preserved. The method includes a structured variational approximation that preserves graph dependencies, propagates compositional uncertainty, and captures the explaining-away behavior associated with colliders. Empirically, the proposed model achieves state-of-the-art performance on protein signaling network tasks and multi-fidelity heavy-ion collision simulations. The work is available as arXiv preprint 2607.09645.
Paper Overview
Research Area: Machine Learning
Authors: Federico L. Perlino, Oliver Hamelijnck, Adam M. Johansen, Theodoros Damoulas
Preprint: arXiv:2607.09645
Abstract
Many real-world processes can be represented as compositions of functions along directed acyclic graphs (DAGs). This paper proposes deep Gaussian processes on DAGs.
Key contributions:
- Theoretical analysis: The authors study prior collapse behavior and examine how graph topology and intermediate observations influence information retention through the network.
- Depth guarantee: They derive an almost-sure lower bound on the depth up to which input distinctness is preserved.
- Inference: A structured variational approximation is provided that preserves graph dependencies, propagates compositional uncertainty, and captures the explaining-away behavior characteristic of colliders.
- Empirical results: The model achieves state-of-the-art performance on protein signaling network tasks and multi-fidelity heavy-ion collision simulation benchmarks.
Links
- arXiv: https://arxiv.org/abs/2607.09645
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