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.

本研究解决了高斯过程的维数灾难问题，通过引入部分可观察的高斯过程网络（POGPN）来应对真实世界系统中的间接、噪声和不完整的中间观测。该方法利用所有子过程的观测数据建模潜在函数的联合分布，显著提高了整体网络的预测性能，展现了其在实际应用中的良好前景。

部分可观察的高斯过程网络与双重随机变分推理