Roc auc curve

Roc auc curve

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  ROC- AUC Curve 21-11-20211 Department of Computer Science and Engineering National Institute of Technology Silchar, Assam, INDIA By- Nurul Amin Choudhury NIT Silchar - PhD Scholar
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  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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  21-11-2021 3 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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  21-11-2021 4 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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  21-11-2021 5 Cntd… OutputClass. 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] Table 4. Predicted Output at 𝜶 = [0.4]
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  21-11-2021 6 Cntd… OutputClass. 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 5. Predicted Output at 𝜶 = [0.8] Table 6. Predicted Output at 𝜶 = [1]
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  Cntd… Threshold TPR FPR 01 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
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  Thank You