We propose a novel learning framework based on neural mean-field dynamics for
inference and estimation problems of diffusion on networks. Our new framework
is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the
node infection probabilities, which renders a delay differential equation with
memory integral approximated by learnable time convolution operators, resulting
in a highly structured and interpretable RNN. Directly using cascade data, our
framework can jointly learn the structure of the diffusion network and the
evolution of infection probabilities, which are cornerstone to important
downstream applications such as influence maximization. Connections between
parameter learning and optimal control are also established. Empirical study
shows that our approach is versatile and robust to variations of the underlying
diffusion network models, and significantly outperform existing approaches in
accuracy and efficiency on both synthetic and real-world data.

本文提出了一种基于神经平均场动力学的新型学习框架，用于解决网络扩散的推理和估计问题，该框架利用 Mori-Zwanzig 形式主义从节点感染概率的精确演化获得，形 成一个高度结构化和可解释的 RNN，可用于联合学习扩散网络的结构和感染概率的演化，这是影响最大化等重要下游应用的基石。此外，本文还建立了参数学习和最优控制之间的联系。实证研究表明，我们的方法具有多样性和鲁棒性，可以在合成数据和真实世界数据上显著优于现有方法的准确性和效率。