Optimizing a model to maximize precision is best for minimizing false negatives, and optimizing a model to maximize recall is best for minimizing false positives.

Question

BlackTom AI · Accepted Answer

Precision = TP / (TP + FP) and recall = TP / (TP + FN).

1) Relevant knowledge points and concepts
- Confusion-matrix terms: True Positives (TP), False Positives (FP), False Negatives (FN), True Negatives (TN).
- Precision measures the fraction of predicted positives that are actually positive: precision = TP / (TP + FP). Thus precision is directly affected by FP.
- Recall (sensitivity) measures the fraction of actual positives that are correctly identified: recall = TP / (TP + FN). Thus recall is directly affected by FN.

2) Step-by-step reasoning
- If you want fewer false positives (FP), you must increase precision because precision’s denominator includes FP; lowering FP while holding TP constant increases TP/(TP+FP).
- If you want fewer false negatives (FN), you must increase recall because recall’s denominator includes FN; lowering FN while holding TP constant increases TP/(TP+FN).
- The statement given swaps these relationships: it claims maximizing precision minimizes false negatives and maximizing recall minimizes false positives. That is the opposite of the true relationships.

3) Intermediate calculation examples
- Example A: TP = 80, FP = 20, FN = 20.
  - precision = 80 / (80 + 20) = 80 / 100 = 0.80
  - recall = 80 / (80 + 20) = 80 / 100 = 0.80
- If we reduce FP to 10 (fewer false positives) and keep TP = 80:
  - precision = 80 / (80 + 10) = 80 / 90 ≈ 0.889 (precision increased)
  - recall unchanged = 80 / (80 + 20) = 0.80
- If instead we reduce FN to 10 (fewer false negatives) and TP increases to 90 (actual positives fixed at TP+FN = 100):
  - recall = 90 / (90 + 10) = 90 / 100 = 0.90 (recall increased)
  - precision depends on FP; if FP remains 20, precision = 90 / (90 + 20) = 90 / 110 ≈ 0.818 (may change differently)

4) Why the correct answer is correct
- Maximizing precision targets FP reduction, not FN. Maximizing recall targets FN reduction, not FP. The original statement swapped these causal links, so it is incorrect.

5) Why the other option is incorrect
- Choosing "True" would accept the swapped relationships; that conflicts with the definitions and the algebraic formulas for precision and recall shown above, so "True" is incorrect.

6) Conclusion
- The correct evaluation of the statement is False. This matches the provided answer: False.

Optimizing a model to maximize precision is best for minimizing false negatives, and optimizing a model to maximize recall is best for minimizing false positives.判断题

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