What is the AUC — ROC Curve?. AUC-ROC CURVE
By: Anuganti Suresh
Tags: Confusion Matrix, Sensitivity, Auc Roc Curve, Specificity

AUC-ROC CURVE | CONFUSION MATRIX | SENSITIVITY | SPECIFICITY|

The Receiver Operator Characteristic (ROC) curve is an evaluation metric for binary classification problems. It is a probability curve that plots the TPR against FPR at various threshold values and essentially separates the ‘signal’ from the ‘noise’. The Area Under the Curve (AUC) is the measure of the ability of a classifier to distinguish between classes and is used as a summary of the ROC curve.

AUC-ROC curve is a performance measurement for the classification problems at various threshold settings. ROC is a probability curve, and AUC represents the degree or measure of separability. It tells how much model is capable of distinguishing between classes. Higher the AUC, better the model is at predicting 0s as 0s and 1s as 1s. By analogy, Higher the AUC, better the model is at distinguishing between patients with the disease and no disease.

The ROC curve is plotted with TPR against the FPR where TPR is on the y-axis and FPR is on the x-axis.

ROC Curve

What are Sensitivity and Specificity?

Sensitivity / TPR (True Positive Rate) / Recall

Sensitivity tells us what proportion of the positive class got correctly classified. A simple example would be to determine what proportion of the actual sick people were correctly detected by the model.

Specificity / TNR (True Negative Rate)

Specificity tells us what proportion of the negative class got correctly classified. Specificity would mean determining the proportion of healthy people who were correctly identified by the model.

False Negative Rate

False Negative Rate (FNR) tells us what proportion of the positive class got incorrectly classified by the classifier. A higher TPR and a lower FNR is desirable since we want to correctly classify the positive class.

False Positive Rate

FPR tells us what proportion of the negative class got incorrectly classified by the classifier. A higher TNR and a lower FPR is desirable since we want to correctly classify the negative class.

Threshold Selection

It is immediately apparent that a ROC curve can be used to select a threshold for a classifier that maximizes the true positives while minimizing the false positives.

Probability of Predictions

When AUC = 1, then the classifier is able to perfectly distinguish between all the Positive and the Negative class points correctly. AUC =0, then the classifier would be predicting all Negatives as Positives, and all Positives as Negatives.

When 0.5<AUC<1, there is a high chance that the classifier will be able to distinguish the positive class values from the negative class values. This is so because the classifier is able to detect more numbers of True positives and True negatives than False negatives and False positives.

When AUC=0.5, then the classifier is not able to distinguish between Positive and Negative class points. Meaning either the classifier is predicting random class or constant class for all the data points.

So, the higher the AUC value for a classifier, the better its ability to distinguish between positive and negative classes.

How Does the AUC-ROC Curve Work?

In a ROC curve, a higher X-axis value indicates a higher number of False positives than True negatives. While a higher Y-axis value indicates a higher number of True positives than False negatives. So, the choice of the threshold depends on the ability to balance between False positives and False negatives.

Let’s dig a bit deeper and understand how our ROC curve would look like for different threshold values and how the specificity and sensitivity would vary.

We can try and understand this graph by generating a confusion matrix for each point corresponding to a threshold and talk about the performance of our classifier:

Point A is where the Sensitivity is the highest and Specificity the lowest. This means all the Positive class points are classified correctly and all the Negative class points are classified incorrectly.

Although Point B has the same Sensitivity as Point A, it has a higher Specificity. Meaning the number of incorrectly Negative class points is lower compared to the previous threshold. This indicates that this threshold is better than the previous one.

Between points C and D, the Sensitivity at point C is higher than point D for the same Specificity. This means, for the same number of incorrectly classified Negative class points, the classifier predicted a higher number of Positive class points. Therefore, the threshold at point C is better than point D.

Now, depending on how many incorrectly classified points we want to tolerate for our classifier, we would choose between point B or C for predicting whether you can defeat me in PUBG or not.

Point E is where the Specificity becomes highest. Meaning there are no False Positives classified by the model. The model can correctly classify all the Negative class points! We would choose this point if our problem was to give perfect song recommendations to our users.

Going by this logic, can you guess where the point corresponding to a perfect classifier would lie on the graph?

Yes! It would be on the top-left corner of the ROC graph corresponding to the coordinate (0, 1) in the cartesian plane. It is here that both, the Sensitivity and Specificity, would be the highest and the classifier would correctly classify all the Positive and Negative class points.

Relation between Sensitivity, Specificity, FPR and Threshold

Sensitivity and Specificity are inversely proportional to each other. So when we increase Sensitivity, Specificity decreases and vice versa.

When we decrease the threshold, we get more positive values thus it increases the sensitivity and decreasing the specificity.

Similarly, when we increase the threshold, we get more negative values thus we get higher specificity and lower sensitivity.

As we know FPR is 1-specificity. So when we increase TPR, FPR also increases and vice versa.

AUC-ROC CURVE: PYTHON

That’s It!

Thanks for reading!

Thanks for the read. I am going to write more beginner-friendly posts in the future. Follow me up on Medium to be informed about them. I welcome feedback and can be reached out on LinkedIn anuganti-suresh. Happy learning!

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