# Learning Graph ARMA Processes from Time-Vertex Spectra

arXiv: https://arxiv.org/abs/2302.06887 · HTML: https://mlsanity.com/paper/2302.06887/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [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)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Reconstruction of Time-varying Graph Signals via Sobolev Smoothness](https://mlsanity.com/paper/2207.06439/) (2022)
- [Adaptive Least Mean Squares Estimation of Graph Signals](https://mlsanity.com/paper/1602.05703/) (2016)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs](https://mlsanity.com/paper/1612.03615/) (2016)
- [Semi-supervised Learning in Network-Structured Data via Total Variation Minimization](https://mlsanity.com/paper/1901.09838/) (2019)
- [Greedy Sampling of Graph Signals](https://mlsanity.com/paper/1704.01223/) (2017)
- [Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies](https://mlsanity.com/paper/1709.03726/) (2017)
- [Stationary time-vertex signal processing](https://mlsanity.com/paper/1611.00255/) (2016)
- [Space-Time Graph Neural Networks with Stochastic Graph Perturbations](https://mlsanity.com/paper/2210.16270/) (2022)
- [Sampling and Reconstruction of Signals on Product Graphs](https://mlsanity.com/paper/1807.00145/) (2018)
- [Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach](https://mlsanity.com/paper/1404.1361/) (2014)
- [Towards stationary time-vertex signal processing](https://mlsanity.com/paper/1606.06962/) (2016)

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

- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)

## Abstract (arXiv)

The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time instants. In this study, we propose an algorithm for computing graph autoregressive moving average (graph ARMA) processes based on learning the joint time-vertex power spectral density of the process from its incomplete realizations for the task of signal interpolation. Our solution relies on first roughly estimating the joint spectrum of the process from partially observed realizations and then refining this estimate by projecting it onto the spectrum manifold of the graph ARMA process through convex relaxations. The initially missing signal values are then estimated based on the learnt model. Experimental results show that the proposed approach achieves high accuracy in time-vertex signal estimation problems.