Table 1.

Comparing PMI, CMI, and PC

Relation types	PMI(X;Y|Z)	CMI(X;Y|Z)	PC(X;Y|Z)	PS(X;Y|Z)
X⊥Z
Linear	1.03*	0.95*	1*	0.98*
Quadratic	0.57*	0.52*	0.03	0.04
Cubic	1.27*	1.23*	1*	1*
Sinusoidal	0.88*	0.83*	0.78*	0.78*
Exponential	0.89*	0.80*	0.98*	0.96*
Checkerboard	0.43*	0.42*	0.37*	0.37*
Circular	0.35*	0.30*	0.02	0.02
Cross-shaped	0.62*	0.61*	0.03	0.03
Sigmoid	0.73*	0.69*	0.99*	0.96*
Random	0.08	0.08	0.03	0.03
X ≈ Z
Linear	2.20*	0.03*	1.0*	0.88*
Quadratic	1.28*	0.01	0.03	0.04
Cubic	1.60*	0.02	0.11*	0.87*
Sinusoidal	1.33*	0.01	0.03	0.02
Exponential	1.30*	0.01	0.06*	0.12*
Checkerboard	0.37*	0.02	0.03	0.02
Circular	0.89*	0.01	0.03	0.03
Cross-shaped	1.16*	0.02*	0.02	0.02
Sigmoid	1.38*	0.01	0.06	0.57*
Random	0.26	0.01	0.02	0.03

PS(X;Y|Z) is the partial spearman correlation of X and Y given Z. Asterisks indicate statistically significant P values (see SI Appendix, Tables S2 and S3).