Specificity if TN + FN = 0

[Lukas Ewecker]

The specificity is defined as $\text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}}$. As far as I see, in case $\text{FP} = 0$, the specificity should be 1.

The docs say that in case $\text{FP} + \text{TP} = 0$, the metric is not defined (see reference below). To put this into words, this means that if the dataset does not contain any positive samples, the metric is not defined and it will return 0.

Is this really intended? It might be a weird edge case. But from the metric definition, I see no argument why the metric should not be defined in case there are no positive samples in the data. In case $\text{FP} + \text{TP} = 0$, I think the metric should return 1, not 0.

torchmetrics version: 1.3.2

torchmetrics/src/torchmetrics/classification/specificity.py

Lines 450 to 459 in c1f8334

 class Specificity(_ClassificationTaskWrapper): 
     r"""Compute `Specificity`_. 
  
     .. math:: \text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}} 
  
     Where :math:`\text{TN}` and :math:`\text{FP}` represent the number of true negatives and false positives 
     respectively. The metric is only proper defined when :math:`\text{TP} + \text{FP} \neq 0`. If this case is 
     encountered for any class/label, the metric for that class/label will be set to 0 and the overall metric may 
     therefore be affected in turn. 
  

[Lukas Ewecker]

I just saw that this might be just a documentation issue. The classes BinarySpecificity, MulticlassSpecificity, and Multilabelspecificity all have the correct description:

torchmetrics/src/torchmetrics/classification/specificity.py

Lines 31 to 39 in c1f8334

 class BinarySpecificity(BinaryStatScores): 
     r"""Compute `Specificity`_ for binary tasks. 
  
     .. math:: \text{Specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}} 
  
     Where :math:`\text{TN}` and :math:`\text{FP}` represent the number of true negatives and false positives 
     respectively. The metric is only proper defined when :math:`\text{TN} + \text{FP} \neq 0`. If this case is 
     encountered a score of 0 is returned. 
  

Also, the implementation seems to follow this definition.