# Causality inference in stochastic systems from neurons to currencies: Profiting from small sample size

## TL;DR

This paper introduces a novel data-driven statistical physics method for causality inference in stochastic systems, demonstrating superior performance with small datasets in fields like neuroscience and finance.

## Contribution

The authors develop a free energy minimization approach for model inference that outperforms traditional methods in small sample scenarios, applicable to complex systems like neural and currency networks.

## Key findings

- Effective inference of neural connectivity networks from limited data.
- Successful modeling of currency exchange networks with small samples.
- Scalable approach applicable to large systems.

## Abstract

Success in modeling complex phenomena such as human perception hinges critically on the availability of data and computational power. Significant progress has been made in modeling such phenomena using probabilistic methods, particularly in image analysis and speech recognition. Maximum Likelihood Estimation (MLE) combined with Bayesian model selection is the basis of much of this progress, as MLE converges to the true model with copious data. In the sciences, large enough datasets are rarae aves, so alternatives to MLE must be developed for small sample size. We introduce a data-driven statistical physics approach to model inference based on minimizing a free energy of data and show superior model recovery for small sample sizes. We demonstrate coupling strength inference in non-equilibrium kinetic Ising models, including in the difficult large coupling variability regime, and show scaling to systems of arbitrary size. As applications, we infer a functional connectivity network in the salamander retina and a currency exchange rate network from time-series data of neuronal spiking and currency exchange rates, respectively. Accurate small sample size inference is critical for devising a profitable currency hedging strategy.