Classification: ROC and AUC  |  Machine Learning  |  Google for Developers (2024)

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The previous section presented a set of model metrics, all calculated at asingle classification threshold value. But if you want to evaluate amodel's quality across all possible thresholds, you need different tools.

Receiver-operating characteristic curve (ROC)

The ROC curveis a visual representation of model performance across all thresholds.The long version of the name, receiver operating characteristic, is a holdoverfrom WWII radar detection.

The ROC curve is drawn by calculating the true positive rate (TPR)and false positive rate (FPR) at every possible threshold (in practice, atselected intervals), then graphing TPR over FPR. A perfect model,which at some threshold has a TPR of 1.0 and a FPR of 0.0, canbe represented by either a point at(0, 1) if all other thresholds are ignored, or by the following:

Area under the curve (AUC)

The area under the ROC curve (AUC)represents the probability that the model,if given a randomly chosen positive and negative example, will rank thepositive higher than the negative.

The perfect model above, containing a square with sides of length 1, has anarea under the curve (AUC) of 1.0. This means there is a 100% probability thatthe model will correctly rank a randomly chosen positive example higher than arandomly chosen negative example. In other words, looking at the spread ofdata points below, AUC gives the probability that the model will place arandomly chosen square to the right of a randomly chosen circle, independent ofwhere the threshold is set.

In more concrete terms, a spam classifier with AUCof 1.0 always assigns a random spam email a higher probability of beingspam than a random legitimate email. The actual classification of eachemail depends on the threshold that you choose.

For a binary classifier, a model that does exactly as well as random guesses orcoin flips has a ROC that is a diagonal line from (0,0) to (1,1). The AUC is0.5, representing a 50% probability of correctly ranking a random positive andnegative example.

In the spam classifier example, a spam classifier with AUC of 0.5 assignsa random spam email a higher probability of being spam than a randomlegitimate email only half the time.

(Optional, advanced) Precision-recall curve

AUC and ROC work well for comparing models when the dataset is roughly balanced between classes. When the dataset is imbalanced, precision-recall curves (PRCs) and the area under those curves may offer a better comparative visualization of model performance. Precision-recall curves are created by plotting precision on the y-axis and recall on the x-axis across all thresholds.

AUC and ROC for choosing model and threshold

AUC is a useful measure for comparing the performance of two different models,as long as the dataset is roughly balanced. (See Precision-recall curve,above, for imbalanced datasets.) The model with greater area underthe curve is generally the better one.

The points on a ROC curve closest to (0,1) represent a range of thebest-performing thresholds for the given model. As discussed in theThresholds,Confusion matrixandChoice of metric and tradeoffssections, the threshold you choose depends on which metric is most important tothe specific use case. Consider the points A, B, and C in the followingdiagram, each representing a threshold:

If false positives (false alarms) are highly costly, it may make sense tochoose a threshold that gives a lower FPR, like the one at point A, even if TPRis reduced. Conversely, if false positives are cheap and false negatives(missed true positives) highly costly, the threshold for point C, whichmaximizes TPR, may be preferable. If the costs are roughly equivalent, point Bmay offer the best balance between TPR and FPR.

Here is the ROC curve for the data we have seen before:

Exercise: Check your understanding