# Distributed Graph Learning with Smooth Data Priors

arXiv: https://arxiv.org/abs/2112.05887 · HTML: https://mlsanity.com/paper/2112.05887/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 11 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [Large Scale Graph Learning from Smooth Signals](https://mlsanity.com/paper/1710.05654/) (2017)
- [Network Topology Inference with Graphon Spectral Penalties](https://mlsanity.com/paper/2010.07872/) (2020)
- [State-Space Network Topology Identification from Partial Observations](https://mlsanity.com/paper/1906.10471/) (2019)
- [Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes](https://mlsanity.com/paper/2007.03266/) (2020)
- [Does the ℓ1-norm Learn a Sparse Graph under Laplacian Constrained Graphical Models?](https://mlsanity.com/paper/2006.14925/) (2020)
- [Consistent Tomography under Partial Observations over Adaptive Networks](https://mlsanity.com/paper/1707.06444/) (2017)
- [Graph topology inference benchmarks for machine learning](https://mlsanity.com/paper/2007.08216/) (2020)
- [FiGLearn: Filter and Graph Learning using Optimal Transport](https://mlsanity.com/paper/2010.15457/) (2020)

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

- [Free Lunch for Privacy Preserving Distributed Graph Learning](https://mlsanity.com/paper/2305.10869/) (2023)

## Abstract (arXiv)

Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely the data that lives on the graph nodes. However, there are settings where data cannot be collected easily or only with a non-negligible communication cost. In such cases, distributed processing appears as a natural solution, where the data stays mostly local and all processing is performed among neighbours nodes on the communication graph. We propose here a novel distributed graph learning algorithm, which permits to infer a graph from signal observations on the nodes under the assumption that the data is smooth on the target graph. We solve a distributed optimization problem with local projection constraints to infer a valid graph while limiting the communication costs. Our results show that the distributed approach has a lower communication cost than a centralised algorithm without compromising the accuracy in the inferred graph. It also scales better in communication costs with the increase of the network size, especially for sparse networks.