将不完整观测融入高斯过程网络，提升复杂系统建模精度。
Partially Observable Gaussian Process Network and Doubly Stochastic Variational Inference
- 构建部分可观测高斯过程网络，融合多源间接观测
- 在基准测试中提升整体预测性能，优于传统方法
- 适合处理传感器数据不全的工业系统建模
为缓解高斯过程（GP）的维度灾难，可将其分解为低维耦合子过程的高斯过程网络（GPN）。现实中，子过程间常存在间接、噪声大且不完整的中间观测。本文提出部分可观测高斯过程网络（POGPN）以建模真实过程网络。通过联合建模子过程的潜在函数，并利用所有子过程的观测进行推断，将观测透镜（观测似然）引入深度高斯过程的成熟推断框架。提出两种训练方法，使基于节点观测即可对全网络进行推断。在基准问题上的应用表明，在训练与推断中引入部分观测能显著提升整体网络预测性能，展现出良好的实际应用前景。
原文摘要 · Abstract (English)
To reduce the curse of dimensionality for Gaussian processes (GP), they can be decomposed into a Gaussian Process Network (GPN) of coupled subprocesses with lower dimensionality. In some cases, intermediate observations are available within the GPN. However, intermediate observations are often indirect, noisy, and incomplete in most real-world systems. This work introduces the Partially Observable Gaussian Process Network (POGPN) to model real-world process networks. We model a joint distribution of latent functions of subprocesses and make inferences using observations from all subprocesses. POGPN incorporates observation lenses (observation likelihoods) into the well-established inference method of deep Gaussian processes. We also introduce two training methods for POPGN to make inferences on the whole network using node observations. The application to benchmark problems demonstrates how incorporating partial observations during training and inference can improve the predictive performance of the overall network, offering a promising outlook for its practical application.
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