[论文解读] Deep Probabilistic Spatial Modeling for Multivariate Mixed-Type Responses

Yeseul Jeon, Kyeong Eun Lee+1 more|arXiv (Cornell University)|Mar 7, 2026

Soil Geostatistics and Mapping被引用 0

一句话总结

我们提出 MultiDeepGP，这是一个可扩展的框架，通过共享潜在空间分量对多变量混合型时空结果进行联合建模，并利用蒙特卡罗 dropout 实现连贯的不确定性量化。

ABSTRACT

Many scientific applications involve mixed spatially indexed outcomes of heterogeneous types that are driven by shared latent mechanisms. Modeling such data is challenging due to complex, nonlinear, and potentially nonstationary spatial dependence, as well as the need for coherent joint inference across mixed outcome distributions. Existing multivariate mixed outcome models often rely on restrictive linear assumptions, while recent deep learning approaches emphasize predictive flexibility but typically lack coherent joint modeling and uncertainty quantification for spatial data. We develop MultiDeepGP, a scalable and statistically principled framework for joint modeling of multivariate mixed outcomes in spatial settings. The proposed approach introduces a shared latent spatial component that governs cross-outcome dependence while allowing outcome-specific distributions. Spatial dependence and nonlinear structure are captured through a deep latent representation, and uncertainty quantification is enabled via an efficient Monte Carlo-based inference strategy. This construction balances modeling flexibility with probabilistic interpretability and computational feasibility. The proposed method is evaluated through simulation studies designed to reflect key challenges in mixed outcome spatial modeling, as well as an application to georeferenced environmental and public health data from the African Great Lakes region. The results demonstrate that the proposed framework provides accurate joint prediction and reliable uncertainty quantification in complex spatial settings.

研究动机与目标

• 促使需要对具有共享潜在结构的混合型时空数据进行联合建模的动机。
• 开发一个灵活的、非线性的共享表示，捕捉复杂的时空依赖。
• 允许结果特定的分布，同时通过共同的潜在时空过程将它们联系起来。
• 为跨多个结果的联合预测提供可扩展的不确定性量化。

提出的方法

• 引入一个共同的潜在时空过程 H(s)，通过结果特异的似然来控制跨结果的相关性。
• 通过深度神经网络对 H(s) 进行参数化，以捕捉非线性和非平稳的时空结构。
• 通过具有适当链接的结果特异头，将共享表示与结果特异的自然参数相联系。
• 将神经网络解释为深度高斯过程，以实现概率推断。
• 使用蒙特卡罗 dropout 作为近似变分推断策略来计算预测分布和不确定性。
• 通过最小化带有层级权重衰减的正则化负对数似然进行训练，然后进行 MC dropout 以进行预测和不确定性量化。

实验结果

研究问题

• RQ1 如何通过一个共享的潜在时空分量在多变量混合型时空数据中引入跨结果的相关性？
• RQ2 在允许结果特定分布的同时，深度潜在表示是否能捕捉非线性和非平稳的时空依赖？
• RQ3 MC dropout 是否能够为异质结果的联合预测提供可靠、可扩展的不确定性量化？
• RQ4 与确定性 DNN 和传统克里金相比，MultiDeepGP 在预测性能和经校准的不确定性方面有何差异？

主要发现

• 该框架能够在混合型时空结果之间实现准确的联合预测。
• 通过 MC dropout 的不确定性量化在复杂时空情境中产生了很好校准的预测分布。
• 仿真研究显示对非线性和非平稳时空结构以及跨结果相关性的鲁棒性。
• 应用于来自非洲大湖区的地理参考环境与公共卫生数据，展示了实际应用性和一致的联合推断。