# Forecasting Graph Signals with Recursive MIMO Graph Filters

arXiv: https://arxiv.org/abs/2210.15258 · HTML: https://mlsanity.com/paper/2210.15258/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 11 of 11)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Evaluating time series forecasting models: An empirical study on performance estimation methods](https://mlsanity.com/paper/1905.11744/) (2019)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs](https://mlsanity.com/paper/1612.03615/) (2016)
- [Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies](https://mlsanity.com/paper/1709.03726/) (2017)
- [Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes](https://mlsanity.com/paper/2007.03266/) (2020)
- [Forecasting Multi-Dimensional Processes over Graphs](https://mlsanity.com/paper/2004.08260/) (2020)
- [Social Network Analysis: From Graph Theory to Applications with Python](https://mlsanity.com/paper/2102.10014/) (2021)
- [MIMO Graph Filters for Convolutional Neural Networks](https://mlsanity.com/paper/1803.02247/) (2018)

## Abstract (arXiv)

Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product graphs to combine this multidimensional information, at the expense of creating a larger graph. In this paper, we show the limitations of such approaches, and propose extensions to tackle them. Then, we propose a recursive multiple-input multiple-output graph filter which encompasses many already existing models in the literature while being more flexible. Numerical simulations on a real world data set show the effectiveness of the proposed models.