A false positive occurs when a classifier predicts the desired class for something that is actually negative. A nodule detector creates one by flagging an uninteresting candidate for radiologist review; a guard dog creates one by barking at a cat, thunderstorm, or mail carrier. False positives waste attention and can make an apparently successful model impractical. section 14.2
False positives become especially important when evaluating classifiers:
- Precision improves when false positives decrease: it measures true positives among everything predicted positive. section 14.3.2
- A classification threshold can trade false positives against false negatives: a cautious threshold rejects more negative cases, while an inclusive threshold catches more positives but raises false alarms. section 14.3.2 section 14.3.1
- Class imbalance can make a small negative-case error produce many false positives relative to the positive cases, despite high overall accuracy. section 14.4.2
A misleadingly accurate nodule detector
Suppose validation contains 54,971 negative samples and 136 positive samples. Misclassifying only 1% of the negative samples creates about 550 false positives—roughly four times the number of actual positives. A balanced training run reports 98.4% negative accuracy but only 0.1102 precision, showing why accuracy alone can hide poor practical utility. section 14.4.2
Listing 14.1 Computing counts for true/false positives and negatives
neg_count = int(negLabel_mask.sum()) pos_count = int(posLabel_mask.sum()) trueNeg_count = neg_correct = int((negLabel_mask & negPred_mask).sum()) truePos_count = pos_correct = int((posLabel_mask & posPred_mask).sum()) falseNeg_count = pos_count - pos_correct falsePos_count = neg_count - neg_correct
The count calculation makes false positives concrete: subtract correctly classified negative samples from all negative samples. section 14.3.3
