混淆矩阵中的误报率

Question

I was trying to manually calculate TPR and FPR for the given data. But unfortunately I dont have any false positive cases in my dataset and even no true positive cases. So I am getting divided by zero error in pandas. So I have an intuition that fpr=1-tpr. Please let me know my intuition is correct if not let know how to fix this issue.

Thank you

Answer 1

Here is the full list of things you can do, once you have obtained the confusion matrix.

import numpy as np

print(cnf_matrix)

array([[13,  0,  0],
       [ 0, 10,  6],
       [ 0,  0,  9]])

FP = cnf_matrix.sum(axis=0) - np.diag(cnf_matrix)  
FN = cnf_matrix.sum(axis=1) - np.diag(cnf_matrix)
TP = np.diag(cnf_matrix)
TN = cnf_matrix.sum() - (FP + FN + TP)

FP = FP.astype(float)
FN = FN.astype(float)
TP = TP.astype(float)
TN = TN.astype(float)


# Sensitivity, hit rate, recall, or true positive rate
TPR = TP/(TP+FN)
# Specificity or true negative rate
TNR = TN/(TN+FP) 
# Precision or positive predictive value
PPV = TP/(TP+FP)
# Negative predictive value
NPV = TN/(TN+FN)
# Fall out or false positive rate
FPR = FP/(FP+TN)
# False negative rate
FNR = FN/(TP+FN)
# False discovery rate
FDR = FP/(TP+FP)

# Overall accuracy
ACC = (TP+TN)/(TP+FP+FN+TN)

Answer 2

It is possible to have FPR = 1 with TPR = 1 if your prediction is always positive no matter what your inputs are.

TPR = 1 means we predict correctly all the positives. FPR = 1 is equivalent to predicting always positively when the condition is negative.

As a reminder:

• FPR = 1 - TNR = [False Positives] / [Negatives]
• TPR = 1 - FNR = [True Positives] / [Positives]