Benchmarking Transfer Entropy Methods for the Study of Linear and Nonlinear Cardio-Respiratory Interactions

Figures

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  Figure 1. Results of changing the lag for the embedding vectors generation for (a) linear model (interaction at τ=1); (b) nonlinear model (interaction at τ=2); and (c) linear + nonlinear model (interaction at τ=2 and τ=4). Each plot shows the median TE vs. lag (τ) in samples. The error bars indicate the interquartile range. The columns show the methods, from left to right, LIN, KNN, FBR, KDE and DVP. It can be seen that all methods identify correctly the lag of the interaction. However, DVP presents the lowest over-estimation (bias) of TE for other lags in all the simulations.

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  Figure 2. Results of DVP for changing the interaction strength for (a) linear model; (b) nonlinear model and (c) linear + nonlinear model. Each plot shows the median TE vs. the interaction parameter. The error bars indicate the interquartile range.

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  Figure 3. Median TERESP→HRV of significant segments for each kind of interaction at 4 Hz vs. lag (τ) in seconds. (a) RESP=NAS; (b) RESP=THO. Gray lines represent higher interactions in NREM1, while black lines correspond to higher interactions in NREM3. Linear interactions are on the left, for which significant differences using NAS are found at τ=2 and τ=4 s. Nonlinear interactions are on the right, for which significant differences using NAS are found at τ=1 and τ=3 s. No significant differences are found using THO.