Aims: Granger causality (GC) and transfer entropy (TE) are two of the most used methods for causality analysis between time series. Recently, machine learning (ML) approaches for TE estimation and (nonlinear) GC detection were introduced. This study aimed to compare a traditional approach to estimate TE using adaptive partitioning (DVP) with two ML approaches: neural network GC (nnGC), based on a multilayer perceptron; and neural network TE (nnTE), based on a fully connected network, in terms of their ability to identify interactions and their computation time.
Methods: The comparison was performed on three simulation models (linear, nonlinear, and linear + nonlinear). For each model, 50 pairs of signals were generated with 200, 500, 1000 and 2000 samples to study the effect of the length of the signal on the interaction identification. Afterward, the methods were applied to 1891 pairs of one-minute segments of heart rate variability and respiratory signals from a polysomnography study of 26 subjects (median (25th;75th) age: 37 (34; 47) years).
Results: For the simulations, DVP outperformed the other two methods (mean AUC 0.99, computation time 0.07 s). nnGC performed well in general (mean AUC 0.98, 167.07 s), while nnTE struggled with the linear (mean AUC 0.75), and linear + nonlinear models (mean AUC 0.49), also it was slowest (943.83 s). In the clinical data, nnGC and nnTE identified interactions for segments from 9 and 10 subjects, respectively. These results are in line with the ones obtained by DVP and previously published in the literature (median of 12 subjects).
Conclusion: The results suggests that these ML-based methods provide a suitable alternative for studying cardio-respiratory interactions during sleep and observing their changes related to different physiological-control mechanisms, since they do not make assumptions about the dynamics or distributions of the data.