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A Full Bayesian Approach to Sparse Network Inference using Heterogeneous Datasets

Junyang Jin, Ye Yuan, Jorge Goncalves

TL;DR

This work presents a full Bayesian framework that combines Dynamical Structure Functions with Reversible Jump MCMC to infer sparse, stable networks while accounting for unmeasured nodes. By using kernel-based priors with ARD and trans-dimensional moves, the method jointly infers topology and impulse responses, often outperforming empirical Bayes approaches and state-of-the-art methods in synthetic biological networks. The approach demonstrates strong topology recovery and predictive performance across random, ring, and circadian-clock-inspired networks, even under partial observability and varying noise levels. However, the method incurs substantial computational cost and relies on adequate sampling frequency for continuous-time extensions, suggesting avenues for scalable implementation and extension to stochastic differential dynamics.

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.

A Full Bayesian Approach to Sparse Network Inference using Heterogeneous Datasets

TL;DR

This work presents a full Bayesian framework that combines Dynamical Structure Functions with Reversible Jump MCMC to infer sparse, stable networks while accounting for unmeasured nodes. By using kernel-based priors with ARD and trans-dimensional moves, the method jointly infers topology and impulse responses, often outperforming empirical Bayes approaches and state-of-the-art methods in synthetic biological networks. The approach demonstrates strong topology recovery and predictive performance across random, ring, and circadian-clock-inspired networks, even under partial observability and varying noise levels. However, the method incurs substantial computational cost and relies on adequate sampling frequency for continuous-time extensions, suggesting avenues for scalable implementation and extension to stochastic differential dynamics.

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.

Paper Structure

This paper contains 18 sections, 1 theorem, 37 equations, 4 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Overview of Markov Chain Monte Carlo
  3. MH-within-PCG Sampler
  4. Reversible Jump Markov Chain Monte Carlo
  5. Model Specification
  6. The dynamical structure function
  7. The likelihood distribution
  8. The prior distributions
  9. The posterior distributions
  10. Network Inference using RJMCMC
  11. Sampler with fixed topology
  12. Sampler with unknown topology
  13. Detection of topology and estimation of model parameters
  14. Simulation
  15. Random DSF networks
  16. ...and 3 more sections

Key Result

Proposition 1

Given a $p\times (m+q)$ transfer matrix $G=[G_u, G_e]$, the corresponding DSF is unique if and only if $p-1$ elements in each column of $[Q, P, H]'$ are known, which uniquely specifies the component of $(Q,P,H)$ in the null space of $[G', I]$.

Figures (4)

  • Figure 1: The structure of a randomly generated network. Solid lines with arrows represent links. Red circles denote nodes.
  • Figure 2: Prediction of randomly generated networks.
  • Figure 3: A network with the ring structure. Symbol '$\sim$' denotes the input signals.
  • Figure 4: Prediction of ring networks.

Theorems & Definitions (1)

  • Proposition 1: Identifiability of DSF networks qpmodel