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Table. 1 Comparison between uGCA methods and conventional GCA under different noise level

From: Robust unified Granger causality analysis: a normalized maximum likelihood form

 

uGCA-TP (%)

uGCA-MIX (%)

uGCA-NML (%)

GCA (\(\alpha =0.05\)) (%)

GCA (\(\alpha =0.01\)) (%)

Low

     

 TPR

100

98.678

100

100

100

 TNR

99.062

99.662

99.662

94.162

98.010

 Ground-truth rate

81.9

86.3

93.1

25.6

64.0

Moderate

     

 TPR

100

98.478

100

100

100

 TNR

98.714

99.662

99.624

93.576

97.729

 Ground-truth rate

74.5

84.6

91.2

18.9

58.4

High

      

 TPR

100

98.678

100

100

100

 TNR

98.410

99.433

99.371

93.048

97.148

 Ground-truth rate

69.7

81.7

87.5

16.0

52.1

  1. The variance of the low noise level data ranges from 1.5 to 2, and the moderate (high) level data ranges from 3.5 to 3 (5.5–6). The ground-truth rate denoted the total numbers of the obtained individual connection network which was same as the ground-truth network, divided by the sample number (1000)
  2. Bold values indicate more indicative of the method's performance