# Influence Estimation and Maximization via Neural Mean-Field Dynamics

arXiv: https://arxiv.org/abs/2106.02608 · HTML: https://mlsanity.com/paper/2106.02608/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 60 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Epidemic processes in complex networks](https://mlsanity.com/paper/1408.2701/) (2014)
- [SNAP: A General Purpose Network Analysis and Graph Mining Library](https://mlsanity.com/paper/1606.07550/) (2016)
- [DeepCas: an End-to-end Predictor of Information Cascades](https://mlsanity.com/paper/1611.05373/) (2016)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency](https://mlsanity.com/paper/1404.0900/) (2014)
- [Popularity Prediction on Social Platforms with Coupled Graph Neural Networks](https://mlsanity.com/paper/1906.09032/) (2019)
- [Sketch-based Influence Maximization and Computation: Scaling up with Guarantees](https://mlsanity.com/paper/1408.6282/) (2014)
- [Scalable Influence Estimation in Continuous-Time Diffusion Networks](https://mlsanity.com/paper/1311.3669/) (2013)
- [Multistage Campaigning in Social Networks](https://mlsanity.com/paper/1606.03816/) (2016)
- [Network Diffusions via Neural Mean-Field Dynamics](https://mlsanity.com/paper/2006.09449/) (2020)
- [Outward Influence and Cascade Size Estimation in Billion-scale Networks](https://mlsanity.com/paper/1704.04794/) (2017)
- [Influence Prediction for Continuous-Time Information Propagation on Networks](https://mlsanity.com/paper/1512.05417/) (2015)

## Abstract (arXiv)

We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems on heterogeneous diffusion networks. Our new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution equation of the individual node infection probabilities, which renders a delay differential equation with memory integral approximated by learnable time convolution operators. Directly using information diffusion cascade data, our framework can simultaneously learn the structure of the diffusion network and the evolution of node infection probabilities. Connections between parameter learning and optimal control are also established, leading to a rigorous and implementable algorithm for training NMF. Moreover, we show that the projected gradient descent method can be employed to solve the challenging influence maximization problem, where the gradient is computed extremely fast by integrating NMF forward in time just once in each iteration. Extensive empirical studies show 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.