An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability

TL;DR

This paper introduces an unbiased symmetric matrix estimator for network topology inference under partial observability, leveraging a vector autoregressive model and Gaussian mixture algorithms, with proven convergence and superior performance in small samples.

Contribution

It presents a novel unbiased estimator for network topology under partial observability, with theoretical convergence guarantees and an effective inference algorithm.

Findings

Estimator converges to the network matrix in probability

Proposed algorithm outperforms state-of-the-art methods with small samples

Effective for networks with Gaussian noise and Laplacian structure

Abstract

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.