An Improved Bayesian Permutation Entropy Estimator with Wasserstein-Optimized Hierarchical Priors

Zachary Blanks, Donald E Brown, Marc A Adams, Siddhartha S Angadi
Proceedings of the fifth Conference on Health, Inference, and Learning, PMLR 248:120-136, 2024.

Abstract

We introduce a novel hierarchical Bayesian permutation entropy (PermEn) estimator designed to improve biomedical time series entropy assessments, especially for short signals. Unlike existing methods requiring a substantial number of observations or which impose restrictive priors, our non-centered, Wasserstein optimized hierarchical approach enables efficient MCMC inference and a broader range of PermEn priors. Evaluations on synthetic and secondary benchmark data demonstrate superior performance over the current state-of-the-art, including 13.33-63.67% lower estimation error, 8.16-47.77% lower posterior variance, and 47-60.83% lower prior construction error ($p \leq 2.42 \times 10^{-10}$). Applied to cardiopulmonary exercise test oxygen uptake signals, we reveal a previously unreported 1.55% (95% credible interval: [0.62%, 2.52%]) entropy difference between obese and lean subjects that diminishes as exercise capacity increases. For individuals capable of completing at least 7.5 minutes of testing, the 95% credible interval contained zero, suggesting potential insights into physiological complexity, exercise tolerance, and obesity. Our estimator refines biomedical signal PermEn estimation and underscores entropy’s potential value as a health biomarker, opening avenues for further physiological and biomedical exploration.

Cite this Paper

BibTeX
@InProceedings{pmlr-v248-blanks24a, title = {An Improved Bayesian Permutation Entropy Estimator with Wasserstein-Optimized Hierarchical Priors}, author = {Blanks, Zachary and Brown, Donald E and Adams, Marc A and Angadi, Siddhartha S}, booktitle = {Proceedings of the fifth Conference on Health, Inference, and Learning}, pages = {120--136}, year = {2024}, editor = {Pollard, Tom and Choi, Edward and Singhal, Pankhuri and Hughes, Michael and Sizikova, Elena and Mortazavi, Bobak and Chen, Irene and Wang, Fei and Sarker, Tasmie and McDermott, Matthew and Ghassemi, Marzyeh}, volume = {248}, series = {Proceedings of Machine Learning Research}, month = {27--28 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v248/main/assets/blanks24a/blanks24a.pdf}, url = {https://proceedings.mlr.press/v248/blanks24a.html}, abstract = {We introduce a novel hierarchical Bayesian permutation entropy (PermEn) estimator designed to improve biomedical time series entropy assessments, especially for short signals. Unlike existing methods requiring a substantial number of observations or which impose restrictive priors, our non-centered, Wasserstein optimized hierarchical approach enables efficient MCMC inference and a broader range of PermEn priors. Evaluations on synthetic and secondary benchmark data demonstrate superior performance over the current state-of-the-art, including 13.33-63.67% lower estimation error, 8.16-47.77% lower posterior variance, and 47-60.83% lower prior construction error ($p \leq 2.42 \times 10^{-10}$). Applied to cardiopulmonary exercise test oxygen uptake signals, we reveal a previously unreported 1.55% (95% credible interval: [0.62%, 2.52%]) entropy difference between obese and lean subjects that diminishes as exercise capacity increases. For individuals capable of completing at least 7.5 minutes of testing, the 95% credible interval contained zero, suggesting potential insights into physiological complexity, exercise tolerance, and obesity. Our estimator refines biomedical signal PermEn estimation and underscores entropy’s potential value as a health biomarker, opening avenues for further physiological and biomedical exploration.} }
Endnote
%0 Conference Paper %T An Improved Bayesian Permutation Entropy Estimator with Wasserstein-Optimized Hierarchical Priors %A Zachary Blanks %A Donald E Brown %A Marc A Adams %A Siddhartha S Angadi %B Proceedings of the fifth Conference on Health, Inference, and Learning %C Proceedings of Machine Learning Research %D 2024 %E Tom Pollard %E Edward Choi %E Pankhuri Singhal %E Michael Hughes %E Elena Sizikova %E Bobak Mortazavi %E Irene Chen %E Fei Wang %E Tasmie Sarker %E Matthew McDermott %E Marzyeh Ghassemi %F pmlr-v248-blanks24a %I PMLR %P 120--136 %U https://proceedings.mlr.press/v248/blanks24a.html %V 248 %X We introduce a novel hierarchical Bayesian permutation entropy (PermEn) estimator designed to improve biomedical time series entropy assessments, especially for short signals. Unlike existing methods requiring a substantial number of observations or which impose restrictive priors, our non-centered, Wasserstein optimized hierarchical approach enables efficient MCMC inference and a broader range of PermEn priors. Evaluations on synthetic and secondary benchmark data demonstrate superior performance over the current state-of-the-art, including 13.33-63.67% lower estimation error, 8.16-47.77% lower posterior variance, and 47-60.83% lower prior construction error ($p \leq 2.42 \times 10^{-10}$). Applied to cardiopulmonary exercise test oxygen uptake signals, we reveal a previously unreported 1.55% (95% credible interval: [0.62%, 2.52%]) entropy difference between obese and lean subjects that diminishes as exercise capacity increases. For individuals capable of completing at least 7.5 minutes of testing, the 95% credible interval contained zero, suggesting potential insights into physiological complexity, exercise tolerance, and obesity. Our estimator refines biomedical signal PermEn estimation and underscores entropy’s potential value as a health biomarker, opening avenues for further physiological and biomedical exploration.
APA
Blanks, Z., Brown, D.E., Adams, M.A. & Angadi, S.S.. (2024). An Improved Bayesian Permutation Entropy Estimator with Wasserstein-Optimized Hierarchical Priors. Proceedings of the fifth Conference on Health, Inference, and Learning, in Proceedings of Machine Learning Research 248:120-136 Available from https://proceedings.mlr.press/v248/blanks24a.html.

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