# Using Machine Learning to Assess Short Term Causal Dependence and Infer Network Links

arXiv: https://arxiv.org/abs/1912.02721 · HTML: https://mlsanity.com/paper/1912.02721/

## Key facts

- Cited by 10 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 10 of 10)

- [Parallel Machine Learning for Forecasting the Dynamics of Complex Networks](https://mlsanity.com/paper/2108.12129/) (2021)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events](https://mlsanity.com/paper/2106.08968/) (2021)
- [Time Shifts to Reduce the Size of Reservoir Computers](https://mlsanity.com/paper/2205.02267/) (2022)
- [Characterizing control between interacting subsystems with deep Jacobian estimation](https://mlsanity.com/paper/2507.01946/) (2025)
- [Suppressing unknown disturbances to dynamical systems using machine learning](https://mlsanity.com/paper/2307.03690/) (2023)
- [Backpropagation on Dynamical Networks](https://mlsanity.com/paper/2207.03093/) (2022)
- [Detecting disturbances in network-coupled dynamical systems with machine learning](https://mlsanity.com/paper/2307.12771/) (2023)
- [Machine learning of network inference enhancement from noisy measurements](https://mlsanity.com/paper/2309.02050/) (2023)
- [Distinguishing indistinguishable attractors: Unsupervised anomaly detection with reservoir computers](https://mlsanity.com/paper/2606.21322/) (2026)

## Abstract (arXiv)

We introduce and test a general machine-learning-based technique for the inference of short term causal dependence between state variables of an unknown dynamical system from time series measurements of its state variables. Our technique leverages the results of a machine learning process for short time prediction to achieve our goal. The basic idea is to use the machine learning to estimate the elements of the Jacobian matrix of the dynamical flow along an orbit. The type of machine learning that we employ is reservoir computing. We present numerical tests on link inference of a network of interacting dynamical nodes. It is seen that dynamical noise can greatly enhance the effectiveness of our technique, while observational noise degrades the effectiveness. We believe that the competition between these two opposing types of noise will be the key factor determining the success of causal inference in many of the most important application situations.