Abstract
This dissertation presents a series of methodological advancements and novel applications of time series entropy analysis, with a particular focus on short time series signals. We developed and optimized various entropy measures to improve their performance and applicability in different contexts, providing new insights into the complexity and dynamics of time series data.
First, we developed an optimization scheme for selecting sample entropy (SampEn) hyperparameters of short time series signals, demonstrating its superiority over existing methods. This methodological advancement allows for more accurate and reliable entropy estimation across various signal modalities and application areas. Additionally, we introduced the open-source Python package, "EristroPy," which implements the proposed algorithms, enabling end-to-end entropy analysis for researchers and practitioners.
Next, we applied SampEn and our SampEn hyperparameter optimization scheme to analyze pediatric cardiopulmonary exercise testing (CPET) data, yielding new insights into how the body responds to exercise. Our analysis of a healthy pediatric cohort revealed significant patterns in gas-exchange and heart rate entropy measures, indicating how physiological responses to exercise vary among early- and late-pubertal children and between male and female participants. These studies demonstrated that SampEn could provide a novel way of capturing the complexity and variability of physiological responses to exercise in pediatric populations.
Finally, in response to the challenge of estimating the entropy of signals containing fewer than 50 observations, we developed a novel Bayesian permutation entropy estimator. This estimator not only outperformed existing implementations but also allowed us to uncover novel connections between entropy, obesity, and exercise capacity. Our work demonstrated that we could provide accurate entropy estimates even for very short signals, thereby expanding the applicability of entropy measures in various clinical and research settings, and potentially laying the groundwork for entropy as a biomarker of health.
