Probabilistic theory and differential equation are powerful tools for the interpretability and guidance of the design of machine learning models, especially for illuminating the mathematical motivation of learning latent variable from observation. Subspace learning maps high-dimensional features on low-dimensional subspace to capture efficient representation. Graphs are widely applied for modeling latent variable learning problems, and graph neural networks implement deep learning architectures on graphs. Inspired by probabilistic theory and differential equations, this paper conducts notes and proposals about graph neural networks to solve subspace learning problems by variational inference and differential equation. Source code of this paper is available at https://github.com/zshicode/Latent-variable-GNN.

翻译：概率论与微分方程为机器学习模型的设计可解释性和指导提供了强大工具，尤其揭示了从观测中学习潜变量的数学动机。子空间学习将高维特征映射至低维子空间以捕获高效表示。图被广泛用于建模潜变量学习问题，而图神经网络则在图上实现了深度学习架构。受概率论与微分方程启发，本文通过变分推断与微分方程，对图神经网络求解子空间学习问题进行了探讨与建议。本文源代码见https://github.com/zshicode/Latent-variable-GNN。