# An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability

arXiv: https://arxiv.org/abs/2203.15500 · HTML: https://mlsanity.com/paper/2203.15500/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Deep Decentralized Multi-task Multi-Agent Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/1703.06182/) (2017)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Large-scale kernelized GRANGER causality to infer topology of directed graphs with applications to brain networks](https://mlsanity.com/paper/2011.08261/) (2020)
- [Local Tomography of Large Networks under the Low-Observability Regime](https://mlsanity.com/paper/1805.09081/) (2018)
- [Consistent Tomography under Partial Observations over Adaptive Networks](https://mlsanity.com/paper/1707.06444/) (2017)

## Built on by (most cited first, 4 of 4)

- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [Network Topology Inference from Smooth Signals Under Partial Observability](https://mlsanity.com/paper/2410.05707/) (2024)
- [Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise](https://mlsanity.com/paper/2312.11324/) (2023)

## Abstract (arXiv)

Network topology inference is a fundamental problem in many applications of network science, such as locating the source of fake news, brain connectivity networks detection, etc. Many real-world situations suffer from a critical problem that only a limited part of observed nodes are available. This letter considers the problem of network topology inference under the framework of partial observability. Based on the vector autoregressive model, we propose a novel unbiased estimator for the symmetric network topology with the Gaussian noise and the Laplacian combination rule. Theoretically, we prove that it converges to the network combination matrix in probability. Furthermore, by utilizing the Gaussian mixture model algorithm, an effective algorithm called network inference Gauss algorithm is developed to infer the network structure. Finally, compared with the state-of-the-art methods, numerical experiments demonstrate the proposed algorithm enjoys better performance in the case of small sample sizes.