# Graph Mixture Density Networks

arXiv: https://arxiv.org/abs/2012.03085 · HTML: https://mlsanity.com/paper/2012.03085/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2020.

## Built on by (most cited first, 9 of 9)

- [Graph-Guided Network for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2110.05357/) (2021)
- [Uncertainty Estimation for Molecules: Desiderata and Methods](https://mlsanity.com/paper/2306.14916/) (2023)
- [Mixture Density Networks for Classification with an Application to Product Bundling](https://mlsanity.com/paper/2402.05428/) (2024)
- [Learnable Kernel Density Estimation for Graphs and Its Application to Graph-Level Anomaly Detection](https://mlsanity.com/paper/2505.21285/) (2025)
- [Multi-Task Mixture Density Graph Neural Networks for Predicting Cu-based Single-Atom Alloy Catalysts for CO2 Reduction Reaction](https://mlsanity.com/paper/2209.07300/) (2022)
- [Bayesian Deep Learning for Graphs](https://mlsanity.com/paper/2202.12348/) (2022)
- [Transformer-based few-shot learning for modeling Electricity Consumption Profiles with minimal data across thousands of domains](https://mlsanity.com/paper/2408.08399/) (2024)
- [Information propagation dynamics in Deep Graph Networks](https://mlsanity.com/paper/2410.10464/) (2024)
- [Nash: Neural Adaptive Shrinkage for Structured High-Dimensional Regression](https://mlsanity.com/paper/2505.11143/) (2025)

## Abstract (arXiv)

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.