这篇论文把深度高斯过程自然地拓展到有向无环图，理论证明很漂亮，而且在蛋白网络和重离子碰撞模拟上跑赢了现有方法，值得搞因果建模或不确定性量化的朋友细读。
该论文提出将深度高斯过程（DGP）扩展到有向无环图（DAG）上，用于建模函数组合结构。理论分析了DGP的先前塌缩行为，并证明在图深度渐近频率中输入区分性保持的几乎必然下界，适用于宽核类。提出了保持图依赖和组合不确定性的结构化变分近似，能捕捉碰撞器的解释性效应。在蛋白信号网络、多保真重离子碰撞模拟等任务上达到SOTA，同时恢复低保真贡献并实现模拟器层次的可解释性。
Deep Gaussian Processes on Directed Acyclic Graphs
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.