# High Precision Variational Bayesian Inference of Sparse Linear Networks

## TL;DR

This paper introduces a variational Bayesian inference method using Gaussian processes to accurately infer sparse networks with near-perfect precision, even with noisy data, without needing full-state measurements.

## Contribution

It presents a novel approach that achieves extremely high precision in network inference and promotes sparsity and stability without requiring full-state data.

## Key findings

- Achieves 100% or near 100% precision in network inference.
- Effectively promotes network sparsity and stability.
- Works well even with noisy data.

## Abstract

Sparse networks can be found in a wide range of applications, such as biological and communication networks. Inference of such networks from data has been receiving considerable attention lately, mainly driven by the need to understand and control internal working mechanisms. However, while most available methods have been successful at predicting many correct links, they also tend to infer many incorrect links. Precision is the ratio between the number of correctly inferred links and all inferred links, and should ideally be close to 100%. For example, 50% precision means that half of inferred links are incorrect, and there is only a 50% chance of picking a correct one. In contrast, this paper develops a method, based on variational Bayesian inference and Gaussian processes, that focuses on inferring links with very high precision. In addition, our method does not require full-state measurements and effectively promotes both system stability and network sparsity. Monte Carlo simulations illustrate that our method has 100% or nearly 100% precision, even in the presence of noise. The method should be applicable to a wide range of network inference contexts, including biological networks and power systems.