# A Full Bayesian Approach to Sparse Network Inference using Heterogeneous Datasets

## TL;DR

This paper introduces a Bayesian network inference method using reversible jump MCMC and dynamical structure functions, significantly improving accuracy over existing kernel-based approaches in biological and engineering networks.

## Contribution

It presents a novel data-driven Bayesian inference approach with reversible jump MCMC for more accurate sparse network topology detection, outperforming previous methods like KEB and iCheMA.

## Key findings

- The proposed method yields more accurate network reconstructions than KEB.
- Simulations show superior performance over iCheMA in synthetic biological networks.
- The approach is applicable to diverse fields such as control, diagnostics, and therapy development.

## Abstract

Network inference has been attracting increasing attention in several fields, notably systems biology, control engineering and biomedicine. To develop a therapy, it is essential to understand the connectivity of biochemical units and the internal working mechanisms of the target network. A network is mainly characterized by its topology and internal dynamics. In particular, sparse topology and stable system dynamics are fundamental properties of many real-world networks. In recent years, kernel-based methods have been popular in the system identification community. By incorporating empirical Bayes, this framework, which we call KEB, is able to promote system stability and impose sparse network topology. Nevertheless, KEB may not be ideal for topology detection due to local optima and numerical errors. Here, therefore, we propose an alternative, data-driven, method that is designed to greatly improve inference accuracy, compared with KEB. The proposed method uses dynamical structure functions to describe networks so that the information of unmeasurable nodes is encoded in the model. A powerful numerical sampling method, namely reversible jump Markov chain Monte Carlo (RJMCMC), is applied to explore full Bayesian models effectively. Monte Carlo simulations indicate that our approach produces more accurate networks compared with KEB methods. Furthermore, simulations of a synthetic biological network demonstrate that the performance of the proposed method is superior to that of the state-of-the-art method, namely iCheMA. The implication is that the proposed method can be used in a wide range of applications, such as controller design, machinery fault diagnosis and therapy development.