Figure 1.

Quantifying the dependent relationship between two features

(A) A toy example. The states of each RF sample are sorted into two groups. The QF is then inspected while maintaining the RF sample ordering.

(B) The ESE for calculating CE. G₁ (group 1) and G₂ (group 2) are the number of minority or majority states of the RF respectively. QF_m is the total number of QF minority states. For brevity, we use x to denote QF_m,G1, the number of QF minority states that overlap with the RF minority states, which is the only independent variable. Each constant is highlighted with their corresponding colors in (A).

(C) Given any observed pair of features, we may form an ESE parabola by fixing the constants of the ESE and calculating the CE for different values of x. Points (1) and (4) correspond to the local and global minimum. (2) is the maximum CE, where the RF and QF are independent. (3) is the CE corresponding to the observed arrangement in (A). Each of (1)–(4) is illustrated by an example arrangement.