最大灵敏度/特异性与ROC曲线的关系及下采样模型ROC相似性疑问
Great question! Let's unpack these two key points with your Sonar dataset example as context.
First, let's clarify the core relationship:
- An ROC curve plots all possible classification thresholds by plotting Sensitivity (True Positive Rate, TPR) on the y-axis against 1 - Specificity (False Positive Rate, FPR) on the x-axis.
- Each individual pair of Sensitivity/Specificity values you're looking at is just one point on this curve—it corresponds to a single threshold the model uses to turn predicted probabilities into class labels.
- If you set an extremely low threshold, the model will label every sample as positive: Sensitivity hits 1, but Specificity drops to 0 (this is the top-right corner of the ROC curve).
- If you set an extremely high threshold, the model labels every sample as negative: Sensitivity drops to 0, but Specificity hits 1 (the bottom-left corner).
- In your experiment, the "max ROC" row from
max_accuracy()gives you the Sensitivity/Specificity pair for the threshold that optimized overall ROC performance during cross-validation. For the normal (unbalanced) dataset, this threshold was biased toward labeling more samples as the majority class (M), hence the perfect Sensitivity but very low Specificity.
This is a common source of confusion—here's why it happens:
ROC curves are invariant to class distribution
ROC curves are built from the ranking of predicted probabilities, not the absolute class counts or the threshold you pick. When you downsample the training data, you're changing the model's training context (making classes balanced), but if the model's ability to rank positive samples above negative samples doesn't change much, the ROC curve will stay similar.
You're comparing single points vs. the entire curve
The Sensitivity/Specificity values you extracted are just one point on each ROC curve:
- For the normal model, that point is
(FPR=1-0.16=0.84, TPR=1)—a point far to the right on the curve, prioritizing catching all positive samples. - For the downsampled model, that point is
(FPR=1-0.77=0.23, TPR=0.827)—a more balanced point closer to the top-left corner.
But the full ROC curve includes every possible threshold, so even though these two points are different, the overall shape of the curve (which reflects the model's general ability to distinguish classes) remains similar.
Your AUC values are close
Looking at your results, the normal model has an AUC of 0.910, and the downsampled model has 0.872—this small difference means their overall classification performance is nearly identical. AUC measures the area under the ROC curve, so similar AUCs translate to visually similar curves.
To put it simply: The downsampling changes where the model's "optimal" threshold lands on the curve, but it doesn't drastically alter the curve itself because the model's core ability to tell M and R apart hasn't changed much.
内容的提问来源于stack exchange，提问作者prmlmu
