# Inferring Diffusion Structures of Heterogeneous Network Cascade

arXiv: https://arxiv.org/abs/2506.19142 · HTML: https://mlsanity.com/paper/2506.19142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 42 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Builds on (most cited first, 6 of 6)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Regularized EM Algorithms: A Unified Framework and Statistical Guarantees](https://mlsanity.com/paper/1511.08551/) (2015)
- [Modeling Information Propagation with Survival Theory](https://mlsanity.com/paper/1305.3616/) (2013)
- [Scalable Influence Estimation in Continuous-Time Diffusion Networks](https://mlsanity.com/paper/1311.3669/) (2013)
- [High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality](https://mlsanity.com/paper/1412.8729/) (2014)
- [Estimation of a Low-rank Topic-Based Model for Information Cascades](https://mlsanity.com/paper/1709.01919/) (2017)

## Abstract (arXiv)

Network cascade refers to diffusion processes in which outcome changes within part of an interconnected population trigger a sequence of changes across the entire network. These cascades are governed by underlying diffusion networks, which are often latent. Inferring such networks is critical for understanding cascade pathways, uncovering Granger causality of interaction mechanisms among individuals, and enabling tasks such as forecasting or maximizing information propagation. In this project, we propose a novel double mixture directed graph model for inferring multi-layer diffusion networks from cascade data. The proposed model represents cascade pathways as a mixture of diffusion networks across different layers, effectively capturing the strong heterogeneity present in real-world cascades. Additionally, the model imposes layer-specific structural constraints, enabling diffusion networks at different layers to capture complementary cascading patterns at the population level. A key advantage of our model is its convex formulation, which allows us to establish both statistical and computational guarantees for the resulting diffusion network estimates. We conduct extensive simulation studies to demonstrate the model's performance in recovering diverse diffusion structures. Finally, we apply the proposed method to analyze cascades of research topics in the social sciences across U.S. universities, revealing the underlying diffusion networks of research topic propagation among institutions.