Roc auc curve

ROC- AUC Curve
21-11-2021 1
Department of Computer Science and Engineering
National Institute of Technology Silchar, Assam, INDIA
By-
Nurul Amin Choudhury
NIT Silchar - PhD Scholar

21-11-2021 2
ROC – AUC Curve
• Main idea: Receiver Operating Curve (ROC) shows the performance of the classification model at different
threshold settings.
• ROC is a probability curve and AUC represents the degree or measure of separability.
• It tells how much the model is capable of distinguishing between classes.
• Higher the AUC, the better the model is at predicting 0 classes as 0 and 1 classes as 1.
• It is consider that Higher the AUC, the better the model is at distinguishing between patients with the
disease and no disease.
• The ROC curve is plotted with True Positive Rate (TPR) against the False Positive Rate (FPR) where
TPR is on the y-axis and FPR is on the x-axis.

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Cntd…
Fig. 1. ROC-AUC Curve.
Image courtesy: My Photoshopped Collection
TPR =
𝑻𝒑
𝑻𝑷
+𝑭𝒏
• The TPR and FPR is given by-
FPR =
𝑭𝒑
𝑻𝒏
+𝑭𝒑
• It is considered that more the AUC, better the model in classifying positive class as positive and negative as
negative.
AUC

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Example Problem-
• Suppose, a classification model yields the classification probability as shown in Table 1.
Step 1 - Let us set the different Threshold as 𝜶 = [0 , 0.2, 0.4, 0.8, 1]
Step 2 - Taking first threshold as 𝜶 = [0], we will get-
Step 3 - TPR =
4
4+0
= 1
& FPR =
2
2+0
= 1
Therefore TPR, FPR at 𝜶 = [0] is (1,1)
Output Class. Prob. (Y)
1 0.8
0 0.96
1 0.4
1 0.3
0 0.2
1 0.7
Table 1. Actual Output vs Classification
yielded Prob.
Output Class.
Prob. (Y)
At 𝜶 = [0]
Y1
1 0.8 1
0 0.96 1
1 0.4 1
1 0.3 1
0 0.2 1
1 0.7 1
Table 2. Predicted Output at 𝜶 = [0]

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Cntd… Output Class. Prob.
(Y)
At 𝜶 = [0.2]
Y1
1 0.8 1
0 0.96 1
1 0.4 1
1 0.3 1
0 0.2 0
1 0.7 1
Step 4 - Repeating all the steps from Step 1 to Step 3 at 𝜶 = [0.2], we will get-
TPR =
4
4+0
= 1
& FPR =
1
1+1
= 0.5
Therefore TPR, FPR at 𝜶 = [0.2] is (1 , 0.5)
Output Class. Prob.
(Y)
At 𝜶 = [0.4]
Y1
1 0.8 1
0 0.96 1
1 0.4 0
1 0.3 0
0 0.2 0
1 0.7 1
Step 5 - Again repeating all the steps from Step 1 to Step 3 at 𝜶 = [0.4], we will get-
TPR =
2
2+2
= 0.5
& FPR =
1
1+1
= 0.5
Therefore TPR, FPR at 𝜶 = [0.4] is (0.5 , 0.5)
Table 3. Predicted Output at 𝜶 = [0.2]

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Cntd… Output Class. Prob.
(Y)
At 𝜶 = [0.8]
Y1
1 0.8 0
0 0.96 1
1 0.4 0
1 0.3 0
0 0.2 0
1 0.7 0
Step 6 - Repeating all the steps from Step 1 to Step 3 at 𝜶 = [0.8], we will get-
TPR =
0
0+4
=0
& FPR =
1
1+1
= 0.5
Therefore TPR, FPR at 𝜶 = [0.8] is (0 , 0.5)
Output Class. Prob.
(Y)
At 𝜶 = [1]
Y1
1 0.8 0
0 0.96 0
1 0.4 0
1 0.3 0
0 0.2 0
1 0.7 0
Step 7 - Again repeating all the steps from Step 1 to Step 3 at 𝜶 = [1], we will get-
TPR =
0
0+4
= 0
& FPR =
0
0+2
= 0
Therefore TPR, FPR at 𝜶 = [1] is (0 , 0)
Table 6. Predicted Output at 𝜶 = [1]

Cntd…
Threshold TPR FPR
0 1 1
0.2 1 0.5
0.4 0.5 0.5
0.8 0 0.5
1 0 0
ROC Curve
Step 8 – Finally, plotting the ROC curve at different threshold setting we will get-
Table 7. TPR, FPR values at different
threshold settings.
Fig. 2. ROC-AUC Curve.
AUC

Roc auc curve

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