Detecting Causality using Deep Gaussian Processes.

Area of Science:

• Complex Systems Science
• Computational Neuroscience
• Biomedical Data Analysis

Background:

• Convergent Cross Mapping (CCM) is a causal discovery method for coupled time series.
• Traditional CCM has limitations including high data requirements, noise sensitivity, and parameter selection challenges.
• Existing methods often rely on delay embedding for state space reconstruction, necessitating grid search for parameter optimization.

Purpose of the Study:

• To develop a robust and data-efficient Bayesian version of CCM.
• To integrate deep Gaussian processes (DGPs) for state space reconstruction within a non-parametric Bayesian framework.
• To improve causal discovery in time series data, particularly in noisy or limited-observation scenarios.

Main Methods:

• Proposed a Bayesian CCM framework utilizing deep Gaussian processes (DGPs).
• Employed DGPs for state space reconstruction within a principled non-parametric Bayesian approach.
• Validated the method on simulated datasets and real-world obstetrics data (fetal heart rate and uterine activity).

Main Results:

• The Bayesian CCM with DGPs demonstrated improved performance on simulated data.
• Analysis of fetal heart rate (FHR) and uterine activity (UA) signals revealed a causal link from UA to FHR.
• Findings align with recent clinical observations regarding fetal well-being monitoring.

Conclusions:

• The proposed Bayesian CCM using DGPs offers a principled and robust alternative to traditional CCM.
• This novel approach effectively addresses limitations of existing CCM methods, including data requirements and noise sensitivity.
• The method provides valuable insights into physiological time series, exemplified by the discovered causal relationship between uterine activity and fetal heart rate.