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corrected the mistake and misunderstanding (of mine)
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If you have a perfect classifier, thensince it will make no mistakes, your FPR is $0$ and TPR isare $0$ and $1$ respectively, which meansso, you're right on (0,1) point in the ROC curve start from $(0,1)$plane. However, notthis isn't a $(0,0)$curve; classifiers are represented as points in ROC. This is also written

The question should be restated for a perfect predictor as @AdamO pointed out, in which we really have the wiki pagecurve because now we have a set of classifiers, which represent a set of points in ROC curveplane, therefore a curve, going from (0,0) to (1,1) as it should be. It typicallyWe still start from $(0,0)$the origin because you change some sortperfect prediction is not perfect classification. It's all about the choice of athe tuning parameter for plotting ROC, e.g. thresholdAdam's example in logistic regressionhis 3rd paragraph is the execution of this idea. When you don't pay anything, you typically don't get anything

Before editing this answer, like havingI was actually thinking of a model $\tau=0$, i.$M$ with some tuning parameter (e.g. like threshold) having no effect on the threshold zero, in logistic regression would correspondresult because it was meant to be a TPR=perfect classifier and try to visualize what happens when we change the tuning parameter. In that case, it starts from FPR(0,1)=$0$, therefore making the ROC curve start from thebut it actually stays originthere. But and doesn't move towards (1,1), simply because the situation is different in perfect classificationparameter has no effect.

If you have a perfect classifier, then your FPR is $0$ and TPR is $1$, which means the ROC curve start from $(0,1)$, not $(0,0)$. This is also written in the wiki page of ROC curve. It typically start from $(0,0)$ because you change some sort of a parameter for plotting ROC, e.g. threshold in logistic regression. When you don't pay anything, you typically don't get anything, like having $\tau=0$, i.e. having the threshold zero, in logistic regression would correspond to TPR=FPR=$0$, therefore making the ROC curve start from the origin. But, the situation is different in perfect classification.

If you have a perfect classifier, since it will make no mistakes, your FPR and TPR are $0$ and $1$ respectively, so, you're right on (0,1) point in the ROC plane. However, this isn't a curve; classifiers are represented as points in ROC.

The question should be restated for a perfect predictor as @AdamO pointed out, in which we really have the curve because now we have a set of classifiers, which represent a set of points in ROC plane, therefore a curve, going from (0,0) to (1,1) as it should be. We still start from the origin because perfect prediction is not perfect classification. It's all about the choice of the tuning parameter. Adam's example in his 3rd paragraph is the execution of this idea.

Before editing this answer, I was actually thinking of a model $M$ with some tuning parameter (e.g. like threshold) having no effect on the result because it was meant to be a perfect classifier and try to visualize what happens when we change the tuning parameter. In that case, it starts from (0,1), but it actually stays there and doesn't move towards (1,1), simply because the parameter has no effect.

added 21 characters in body
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gunes
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If you have a perfect classifier, then your FPR is $0$ and TPR is $1$, which means the ROC curve start from $(0,1)$, not $(0,0)$. This is also written in the wiki page of ROC curve. It typically start from $(0,0)$ because you change some sort of a parameter for plotting ROC, e.g. threshold in logistic regression. When you don't pay anything, you typically don't get anything, like having $\tau=0$, i.e. having the threshold zero, in logistic regression would correspond to TPR=FPR=$0$, and so startingtherefore making the ROC curve start from the origin. But, the situation is different in perfect classification.

If you have a perfect classifier, then your FPR is $0$ and TPR is $1$, which means the ROC curve start from $(0,1)$, not $(0,0)$. This is also written in the wiki page of ROC curve. It typically start from $(0,0)$ because you change some sort of a parameter for plotting ROC, e.g. threshold in logistic regression. When you don't pay anything, you typically don't get anything, like having $\tau=0$ in logistic regression would correspond to TPR=FPR=$0$, and so starting from the origin. But, the situation is different in perfect classification.

If you have a perfect classifier, then your FPR is $0$ and TPR is $1$, which means the ROC curve start from $(0,1)$, not $(0,0)$. This is also written in the wiki page of ROC curve. It typically start from $(0,0)$ because you change some sort of a parameter for plotting ROC, e.g. threshold in logistic regression. When you don't pay anything, you typically don't get anything, like having $\tau=0$, i.e. having the threshold zero, in logistic regression would correspond to TPR=FPR=$0$, therefore making the ROC curve start from the origin. But, the situation is different in perfect classification.

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gunes
gunes
  • 58.2k
  • 4
  • 50
  • 88

If you have a perfect classifier, then your FPR is $0$ and TPR is $1$, which means the ROC curve start from $(0,1)$, not $(0,0)$. This is also written in the wiki page of ROC curve. It typically start from $(0,0)$ because you change some sort of a parameter for plotting ROC, e.g. threshold in logistic regression. When you don't pay anything, you typically don't get anything, like having $\tau=0$ in logistic regression would correspond to TPR=FPR=$0$, and so starting from the origin. But, the situation is different in perfect classification.