TENDE: Transfer Entropy Neural Diffusion Estimation

Simon Pedro Galeano Munoz, Maurizio Filippone, Giulio Franzese, Mustapha Bounoua, Pietro Michiardi
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:4843-4851, 2026.

Abstract

Transfer entropy is a fundamental measure for quantifying directed information flow in time series, with applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-munoz26a, title = { TENDE: Transfer Entropy Neural Diffusion Estimation }, author = {Munoz, Simon Pedro Galeano and Filippone, Maurizio and Franzese, Giulio and Bounoua, Mustapha and Michiardi, Pietro}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {4843--4851}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/munoz26a/munoz26a.pdf}, url = {https://proceedings.mlr.press/v300/munoz26a.html}, abstract = { Transfer entropy is a fundamental measure for quantifying directed information flow in time series, with applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data. } }
Endnote
%0 Conference Paper %T TENDE: Transfer Entropy Neural Diffusion Estimation %A Simon Pedro Galeano Munoz %A Maurizio Filippone %A Giulio Franzese %A Mustapha Bounoua %A Pietro Michiardi %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-munoz26a %I PMLR %P 4843--4851 %U https://proceedings.mlr.press/v300/munoz26a.html %V 300 %X Transfer entropy is a fundamental measure for quantifying directed information flow in time series, with applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.
APA
Munoz, S.P.G., Filippone, M., Franzese, G., Bounoua, M. & Michiardi, P.. (2026). TENDE: Transfer Entropy Neural Diffusion Estimation . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:4843-4851 Available from https://proceedings.mlr.press/v300/munoz26a.html.

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