Granger Causality Analysis Based on Quantized Minimum Error Entropy Criterion

Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals are seriously contaminated by non-Gaussian noises, the LRM coefficients will be inaccurately identified. This may cause the GCA to detect a wrong causal relationship. Minimum error entropy (MEE) criterion can be used to replace the MSE criterion to deal with the non-Gaussian noises. But its calculation requires a double summation operation, which brings computational bottlenecks to GCA especially when sizes of the signals are large. To address the aforementioned problems, in this study we propose a new method called GCA based on the quantized MEE (QMEE) criterion (GCA-QMEE), in which the QMEE criterion is applied to identify the LRM coefficients and the quantized error entropy is used to calculate the causality indexes. Compared with the traditional GCA, the proposed GCA-QMEE not only makes the results more discriminative, but also more robust. Its computational complexity is also not high because of the quantization operation. Illustrative examples on synthetic and EEG datasets are provided to verify the desirable performance and the availability of the GCA-QMEE.