You’ve built your machine learning model — so what’s next? You need to evaluate it and validate how good (or bad) it is, so you can then decide on whether to implement it. That’s where the AUC-ROC curve comes in.
For now, just know that the AUC-ROC curve helps us visualize how well our machine learning classifier is performing. Although it works for only binary classification problems, we will see towards the end how we can extend it to evaluate multi-class classification problems too.
We’ll cover topics like sensitivity and specificity as well since these are key topics behind the AUC-ROC curve.
Table of Contents
What are Sensitivity and Specificity?
What is the AUC-ROC Curve?
How Does the AUC-ROC Curve Work?
AUC-ROC in Python
AUC-ROC for Multi-Class Classification
Sensitivity / True Positive Rate / Recall
Sensitivity tells us what proportion of the positive class got correctly classified.
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.
Specificity / True Negative Rate
Specificity tells us what proportion of the negative class got correctly classified.
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.
What is the AUC-ROC Curve?
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.
The higher the AUC, the better the performance of the model at distinguishing between the positive and negative classes.
When AUC = 1, then the classifier is able to perfectly distinguish between all the Positive and the Negative class points correctly. If, however, the AUC had been 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.
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.
Understanding the AUC-ROC Curve in Python
Creating normal distributions that clearly separates the target variable In the following cell you can see that the AUC score is = 1 if the distributions per class are clearly separable.
Creating normal distributions that overlaps a little bit
Now you can see that the AUC score decreases if the distributions per class overlapping a little bit.
Let’s create our arbitrary data using the sklearn make_classification method:
AUC-ROC for Multi-Class Classification
Like I said before, the AUC-ROC curve is only for binary classification problems. But we can extend it to multiclass classification problems by using the One vs All technique.
So, if we have three classes 0, 1, and 2, the ROC for class 0 will be generated as classifying 0 against not 0, i.e. 1 and 2. The ROC for class 1 will be generated as classifying 1 against not 1, and so on.
The ROC curve for multi-class classification models can be determined as below:
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