Supplemental: Active Diagnosis via AUC Maximization
نویسندگان
چکیده
1 AUC Estimation The area under the ROC curve can be approximated using lower rectangles, upper rectangles or by using a linear approximation, as shown in Figure 1. The expressions related to each of these approximations are Al(zA) = M−1 ∑ t=0 (1− M̂Rt)(F̂ARt+1 − F̂ARt) Au(zA) = M−1 ∑ t=0 (1− M̂Rt+1)(F̂ARt+1 − F̂ARt) Am(zA) = M−1 ∑ t=0 (1− M̂Rt + M̂Rt+1 2 )(F̂ARt+1 − F̂ARt). Substituting the estimates for miss rate and false alarm rate, the corresponding approximations for the area above the ROC curve are given by Al(zA) = M ∑ i=1 M ∑ j=i Pr(Xr(i) = 0|zA)Pr(Xr(j) = 1|zA) M ∑ i=1 Pr(Xi = 1|zA) M ∑ i=1 Pr(Xi = 0|zA) (1a)
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