关于ROC与AUC的测量：是否仅适用于概率分类器而非离散分类器？

Great question—this is a common point of confusion, so let’s break it down clearly.

First, remember that ROC curves are built by plotting True Positive Rate (TPR) against False Positive Rate (FPR) across a range of classification thresholds. The key here isn’t whether the classifier outputs probabilities specifically—it’s whether you can get a continuous or ordered score that represents how "confident" the model is that a sample belongs to the positive class.

Tree-based models and discrete classifiers can absolutely work with ROC/AUC #

• Many tree models (like Random Forest, XGBoost, or gradient-boosted trees) natively output class probabilities via methods like predict_proba() (in scikit-learn, for example). You can use these probabilities directly to test different thresholds and compute the TPR/FPR pairs needed for the ROC curve.
• Even simple decision trees that only output hard 0/1 classifications can be adapted. Instead of using the final class label, you can use the proportion of positive class samples in a leaf node as a confidence score. For example, if a leaf has 70% positive samples, treat that 0.7 as a score and adjust thresholds (e.g., classify as positive if the score is ≥0.6, ≥0.5, etc.) to generate the full ROC curve.
• For ensemble tree models that use voting, you can also use the number of trees that vote for the positive class as a continuous score. More votes = higher confidence, and you can set thresholds based on this count to map out the ROC curve.

What if a classifier only outputs hard labels with no confidence scores? #

In the rare case where you have a classifier that gives you nothing but 0/1 with no underlying score, you can still compute a single ROC point (at the fixed threshold the model uses). But to get a full ROC curve and AUC score, you’d need to modify the model to output some kind of ordered confidence metric—or use less common techniques like bootstrapping to generate variability in predictions.

The bottom line: ROC and AUC aren’t limited to probabilistic classifiers. Any model that can produce a ranked measure of how likely a sample is to be positive can be evaluated with these metrics.

内容的提问来源于stack exchange，提问作者amiref