Boosting transfer entropy estimation accuracy with machine learning for finite-length sequences

Lu Qiu, Huijie Yang,
Boosting transfer entropy estimation accuracy with machine learning for finite-length sequences,
Chaos, Solitons & Fractals,
Volume 201, Part 3,
2025,
117252,
ISSN 0960-0779,
https://doi.org/10.1016/j.chaos.2025.117252.
(https://www.sciencedirect.com/science/article/pii/S0960077925012652)
Abstract: Transfer entropy is widely adopted to reconstruct causal structures of complex systems from multi-variate sequences. A reliable detection requires the sequence be mathematically infinite and practically long enough. And its performance gets worse exponentially with the decrease of sequence length. This requirement cannot be met in many cases in reality. How to obtain a reliable estimation of transfer entropy from a finite-length sequence is accordingly an essential task and a crucial challenge. In this paper, Machine Learning based Estimation of Transfer Entropy (ML-TE) is proposed to address this issue, i.e., to improve the precision and reliability of the estimation for transfer entropy from finite-length sequences. A meticulous evaluation of various machine learning models is conducted, where the Feed-forward Neural Network(FNN) turns out to be the most suitable model. Extensive testing calculations show that ML-TE outperforms significantly the currently adopted methods such as the Normal Transfer Entropy(NTE), the Correlation-Dependent Balanced Estimation of Diffusion Transfer Entropy(CBEDTE), and the Kendall Transfer Entropy(KTE), especially when the sequences become very short ranging from 10 to 50. As typical applications, ML-TE is used to investigate the stock market risks and the climate physical risks, yielding intriguing results.
Keywords: Transfer entropy; Finite-length sequences; Machine learning; Stock market; Climate physical risks