# Decentralized Statistical Inference with Unrolled Graph Neural Networks

arXiv: https://arxiv.org/abs/2104.01555 · HTML: https://mlsanity.com/paper/2104.01555/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 4 Apr 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Graph Neural Networks for Decentralized Multi-Robot Path Planning](https://mlsanity.com/paper/1912.06095/) (2019)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Approximation Ratios of Graph Neural Networks for Combinatorial Problems](https://mlsanity.com/paper/1905.10261/) (2019)
- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [On Nonconvex Decentralized Gradient Descent](https://mlsanity.com/paper/1608.05766/) (2016)
- [COLA: Decentralized Linear Learning](https://mlsanity.com/paper/1808.04883/) (2018)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [The Squared-Error of Generalized LASSO: A Precise Analysis](https://mlsanity.com/paper/1311.0830/) (2013)
- [Graph Neural Networks for Decentralized Controllers](https://mlsanity.com/paper/2003.10280/) (2020)

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

- [Scalable Power Control/Beamforming in Heterogeneous Wireless Networks with Graph Neural Networks](https://mlsanity.com/paper/2104.05463/) (2021)

## Abstract (arXiv)

In this paper, we investigate the decentralized statistical inference problem, where a network of agents cooperatively recover a (structured) vector from private noisy samples without centralized coordination. Existing optimization-based algorithms suffer from issues of model mismatch and poor convergence speed, and thus their performance would be degraded, provided that the number of communication rounds is limited. This motivates us to propose a learning-based framework, which unrolls well-noted decentralized optimization algorithms (e.g., Prox-DGD and PG-EXTRA) into graph neural networks (GNNs). By minimizing the recovery error via end-to-end training, this learning-based framework resolves the model mismatch issue. Our convergence analysis (with PG-EXTRA as the base algorithm) reveals that the learned model parameters may accelerate the convergence and reduce the recovery error to a large extent. The simulation results demonstrate that the proposed GNN-based learning methods prominently outperform several state-of-the-art optimization-based algorithms in convergence speed and recovery error.