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I'm looking at the results of an ML model I made and I've calculated the PPV, TPR, NPV and TNR. As is expected, there is a tradeoff between the PPV and TPR (from which the F1 score can be calculated) but I was wondering if a similar relationship exists between NPV and TNR, as I have observed that in my results - if so, is there a similar metric to the F1 score for these measurements?

Edit: is it even necessary to look at the NPV and TNR? Wikipedia (I know, not a great source) says that a perfect precision eliminates false positives and a perfect recall eliminates false negatives, so what does knowing the NPV and TNR bring to the table? Because surely a perfect NPV eliminates false negatives and a perfect TNR eliminates false positives, so they don't really add any insight into the model.

Thanks!

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The logic of binary classification measures is as follows:

Usually there is a natural 'positive' class for the application, and if not one is defined by convention. Evaluation measures are supposed to represent how well a model recognizes this positive class by contrast to the negative one. Naturally if the model can identify the positive class well then it means that it distinguishes the two classes well, therefore it also identifies the negative class well. This is why there is no need for a negative-focused equivalent of F1-score (especially since the positive class is chosen based on the application), but it could perfectly be defined indeed.

There's indeed no particular need for negative-focused measures like NPV and TNR, these values are sometimes useful in specific applications but they do not provide any additional information about the ability of the model. The 2 dimensions which are needed are precision (PPV) and recall (TPR).

For the record the Wikipedia page on precision/recall is a good reference :)

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  • $\begingroup$ That's brilliant, thank you so much for that :) $\endgroup$
    – RedMoose
    Aug 30, 2022 at 11:24

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