Network Inference in Stochastic Systems

Introduction

We developed a data-driven approach for network inference in stochastic systems, Free Energy Minimazation (FEM). From data comprising of configurations of variables, we determine the interactions between them in order to infer a predictive stochastic model. FEM outperforms other existing methods such as variants of mean field approximations and Maximum Likelihood Estimation (MLE), especially in the regimes of large coupling variability and small sample sizes. Besides better performance, FEM is parameter-free and significantly faster than MLE.

Interactive notebook

Use Binder to run our code online. You are welcome to change the parameters and edit the jupyter notebooks as you want.

Links

Code Documentation

https://nihcompmed.github.io/network-inference

Code Source

https://github.com/nihcompmed/network-inference

Reference

Danh-Tai Hoang, Juyong Song, Vipul Periwal, and Junghyo Jo, “Causality inference in stochastic systems from neurons to currencies: Profiting from small sample size”, arXiv:1705.06384.

Table of Contents

• Model
• Method: Free Energy Minimization
  • Small coupling variability \((g = 2)\)
  • Large coupling variability \((g=4)\)
• Other methods
  • Naive Mean-Field approximation
  • Thouless-Anderson-Palmer mean field approximation
  • Exact mean field approximation
  • Maximum Likelihood Estimation
• Comparison: MLE vs. FEM
  • Small coupling variability
  • Large coupling variability
• Non-linear interactions
• Conclusion