Time-Shift Permutation Cross-Mapping: A Robust Data-Driven Causality Detection Framework for Complex Physiology System

In data-driven causality estimation, traditional Granger causality (GC), transfer entropy (TE), and their variants ignore time non-separability in dynamics systems, leading to failed quantification. Recently proposed convergent cross-mapping (CCM) and CCM-inspired measures still face the limits of cumbersome parameter setting, poor convergence and accuracy. To solve these deficiencies, we develop a robust data-driven, almost-parameter-free framework: “time-shift permutation cross-mapping, TPCM.” The TPCM integrates steps of(1)delayed improved phase-space reconstruction (DIPSR),(2)rank transformation of embedding vectors’ distances,(3)cross-mapping with a fitting estimation of manifolds, and(4)causality quantification with multi-delay parameters. Numerical validations are conducted using three datasets: a multivariate logistic coupling model, a multivariate nonlinear strongly-coupled model, and realworld physiological coupling signals. The results demonstrate that our TPCM significantly improves the convergence for data length with or without noise interference, and maintains the best robustness even for very short series. The TPCM also accurately detects causality connections’ time delays. When measuring a strongly coupled system, the TPCM achieves the best quantization accuracy with the highest determination coefficient(R2) of fitting verse coupling parameters. The results of physiological dataset accurately reveal the bidirectional interactions between respiration(R)and heart rate(H), along with a dominant effect of R regulating H, i.e., causality R → H > H → R .