Why is AUC scale invariant?

Why is AUC scale invariant?

Why is AUC a desirable metric? AUC is scale-invariant. It measures how well predictions are ranked, rather than their absolute values. AUC is based on the relative predictions, so any transformation of the predictions that preserves the relative ranking has no effect on AUC.

Does AUC depend on threshold?

Depending upon the threshold, we can minimize or maximize them. When AUC is 0.7, it means there is a 70% chance that the model will be able to distinguish between positive class and negative class. When AUC is approximately 0, the model is actually reciprocating the classes.

What is threshold in AUC ROC?

The area under the ROC Curve, so-called ROC AUC, provides a single number to summarize the performance of a model in terms of its ROC Curve with a value between 0.5 (no-skill) and 1.0 (perfect skill). This would be a threshold on the curve that is closest to the top-left of the plot.

How do you interpret area under a curve?

AREA UNDER THE ROC CURVE In general, an AUC of 0.5 suggests no discrimination (i.e., ability to diagnose patients with and without the disease or condition based on the test), 0.7 to 0.8 is considered acceptable, 0.8 to 0.9 is considered excellent, and more than 0.9 is considered outstanding.

What is the purpose of the AUC ROC curve?

AUC – ROC curve is a performance measurement for classification problem at various thresholds settings.

When to use ROC curves for threshold value?

We can generally use ROC curves to decide on a threshold value. The choice of threshold value will also depend on how the classifier is intended to be used.

Is the AUC metric threshold invariant or scale invariant?

It is threshold invariant i.e. the value of the metric doesn’t depend on a chosen threshold. It is scale-invariant i.e. It measures how well predictions are ranked, rather than their absolute values. The excellent news is that AUC fulfils both the above conditions.

What does an AUC of 0.5 mean?

It can also be mathematically proven that AUC is equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one. Thus, an AUC of 0.5 means that the probability of a positive instance ranking higher than a negative instance is 0.5 and hence random.