发表机构
University of Warwick; Unilink Software Ltd（华威大学; Unilink软件有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究有向无环图上函数组合的相关问题，提出深度高斯过程，通过理论研究其行为，给出结构化变分近似，经实证验证，在多个任务中取得先进性能，能恢复低保真贡献并具有模拟器层次结构的可解释性。
AI 中文摘要
许多现实世界的过程可表示为沿有向无环图（DAG）的函数组合，如因果建模、工程和基因调控网络中。这些函数在DAG上部分可观测，测量有噪声且采样不均，给重建、不确定性传播和推理带来挑战。为此提出DAG上的深度高斯过程，研究其先验崩溃行为等。给出结构化变分近似，保留图依赖等。通过实证验证理论结果和方法，在多个任务中取得了先进性能。
英文摘要
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.
Comments75 pages, 14 figures
