A false positive (FP) is a test example whose true class is negative but which the classifier predicted as positive. It’s a false alarm — the model said the wine was high-quality when it was actually low-quality, said the email was spam when it was actually legitimate, said the patient had cancer when they were healthy. In statistical hypothesis testing this kind of error is called a Type I error.
False positives are one of the two off-diagonal entries of the Confusion matrix, alongside False negative (FN). They represent the mistakes the classifier makes by being too eager to call something positive.
Several metrics depend on FP:
- Precision = — of predicted positives, what fraction were actually positive. A high FP count drags precision down.
- Specificity = — of actual negatives, what fraction the classifier correctly identified as negative. A high FP count drags specificity down.
- False positive rate (FPR) = — the fraction of actual negatives wrongly flagged as positive. This is plotted on the x-axis of an ROC curve.
When false positives matter most
The cost of a false positive depends on the application:
- In spam filtering, a false positive is a legitimate email sent to the spam folder — annoying or harmful (an important message lost). Spam-filter designers care deeply about minimizing false positives, even at the cost of letting some spam through.
- In cancer screening, a false positive is a healthy patient flagged as having cancer — leading to anxiety, follow-up tests, possibly invasive procedures. Costly but usually correctable.
- In fraud detection, a false positive is a legitimate transaction blocked — annoying for the customer but recoverable.
- In fingerprint matching for criminal investigation, a false positive is identifying an innocent person as the perpetrator — potentially catastrophic.
The threshold of a classifier (typically 0.5 by default in Logistic regression) can be tuned to trade false positives against false negatives. Lowering the threshold catches more positives but produces more false positives. Raising it does the reverse.
For the complementary kind of mistake — actual positives missed — see False negative. The two are in inherent tension: reducing one usually means increasing the other, and the right balance depends on the costs in the application.