# Graph Distribution-valued Signals: A Wasserstein Space Perspective

arXiv: https://arxiv.org/abs/2509.25802 · HTML: https://mlsanity.com/paper/2509.25802/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2305.00139/) (2023)
- [Bayesian Estimation of Graph Signals](https://mlsanity.com/paper/2103.15520/) (2021)
- [Irregularity-Aware Graph Fourier Transforms](https://mlsanity.com/paper/1802.10220/) (2018)
- [A Hilbert Space Theory of Generalized Graph Signal Processing](https://mlsanity.com/paper/1904.11655/) (2019)
- [Graph-signal Reconstruction and Blind Deconvolution for Structured Inputs](https://mlsanity.com/paper/2105.14747/) (2021)
- [Graph Signal Processing over a Probability Space of Shift Operators](https://mlsanity.com/paper/2108.09192/) (2021)
- [Kernel Based Reconstruction for Generalized Graph Signal Processing](https://mlsanity.com/paper/2308.06949/) (2023)
- [A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control](https://mlsanity.com/paper/2408.03142/) (2024)
- [Traffic signal prediction on transportation networks using spatio-temporal correlations on graphs](https://mlsanity.com/paper/2104.13414/) (2021)
- [GSP-Based MAP Estimation of Graph Signals](https://mlsanity.com/paper/2209.11638/) (2022)

## Built on by (most cited first, 1 of 1)

- [Consistent Geometric Deep Learning via Hilbert Bundles and Cellular Sheaves](https://mlsanity.com/paper/2605.06395/) (2026)

## Abstract (arXiv)

We introduce a novel framework for graph signal processing (GSP) that models signals as graph distribution-valued signals (GDSs), which are probability distributions in the Wasserstein space. This approach overcomes key limitations of classical vector-based GSP, including the assumption of synchronous observations over vertices, the inability to capture uncertainty, and the requirement for strict correspondence in graph filtering. By representing signals as distributions, GDSs naturally encode uncertainty and stochasticity, while strictly generalizing traditional graph signals. We establish a systematic dictionary mapping core GSP concepts to their GDS counterparts, demonstrating that classical definitions are recovered as special cases. The effectiveness of the framework is validated through graph filter learning for prediction tasks, supported by experimental results.