https://www.nytimes.com/2022/01/01/upshot/pregnancy-birth-genetic-testing.html
A large number of FPs often results from applying even a good classifier on a very unbalanced data set (i.e. many more negatives than positives) – as is the case here. The situation is further exacerbated when the classifier is trained & benchmarked on a more balanced data set.
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I think the situation here is similar to that found in cancer identification or finding a terrorist at airport security.