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10_Wiki/Topics/Topic_Programming/AI_and_ML/Precision-Recall-Tradeoff.md

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+---
+id: wiki-2026-0508-precision-recall-tradeoff
+title: Precision-Recall Tradeoff
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [PR Tradeoff, Threshold Tuning, F1 Optimization]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [classification, evaluation, metrics, threshold, imbalanced]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: python
+  framework: scikit-learn
+---
+
+# Precision-Recall Tradeoff
+
+## 매 한 줄
+> **"매 classifier threshold를 올리면 precision↑ recall↓ — 두 metric 동시에 최대화 불가."**. F1 / F-beta / PR-AUC 가 매 두 축의 통합 score. 매 imbalanced data (의료, fraud, anomaly)에서 ROC-AUC보다 매 PR-AUC가 honest.
+
+## 매 핵심
+
+### 매 정의
+- **Precision** = TP / (TP + FP) — "alarm 중 진짜 비율".
+- **Recall** = TP / (TP + FN) — "진짜 중 잡은 비율" (= sensitivity, TPR).
+- **F1** = 2·P·R / (P+R) — harmonic mean.
+- **F-beta** = (1+β²)·P·R / (β²P + R) — β>1은 recall 가중, β<1은 precision 가중.
+
+### 매 tradeoff mechanism
+- Classifier output score에 **threshold τ** 적용.
+- τ ↑ → 더 까다롭게 positive 선언 → precision ↑, recall ↓.
+- τ ↓ → 더 많이 positive → recall ↑, precision ↓.
+- Pareto curve = Precision-Recall curve.
+
+### 매 vs ROC-AUC
+- **ROC**: TPR vs FPR — class balance에 매 insensitive (오해 유발).
+- **PR**: P vs R — positive class에 focus, imbalanced 에 매 informative.
+- 매 99% 음성 dataset에서 매 ROC-AUC=0.95여도 PR-AUC=0.3일 수 있음.
+
+### 매 응용
+1. 의료 진단 (recall 우선 — miss 위험).
+2. Spam filter (precision 우선 — false alarm 비용).
+3. Fraud detection (cost-sensitive threshold).
+4. Information retrieval (P@k, R@k).
+5. Object detection (mAP = PR-AUC 기반).
+6. RAG retrieval evaluation.
+
+## 💻 패턴
+
+### sklearn PR curve + best F1 threshold
+```python
+import numpy as np
+from sklearn.metrics import precision_recall_curve, average_precision_score
+
+probs = clf.predict_proba(X_val)[:, 1]
+p, r, thr = precision_recall_curve(y_val, probs)
+f1 = 2 * p * r / (p + r + 1e-12)
+best = f1.argmax()
+print(f"τ={thr[best]:.3f}  P={p[best]:.3f}  R={r[best]:.3f}  F1={f1[best]:.3f}")
+print(f"PR-AUC = {average_precision_score(y_val, probs):.3f}")
+```
+
+### F-beta threshold (recall 가중)
+```python
+def best_fbeta_threshold(y, probs, beta=2.0):
+    p, r, thr = precision_recall_curve(y, probs)
+    fb = (1+beta**2) * p * r / (beta**2 * p + r + 1e-12)
+    i = fb.argmax()
+    return thr[i] if i < len(thr) else 1.0, fb[i]
+```
+
+### Cost-based threshold
+```python
+def cost_threshold(y, probs, cost_fp=1.0, cost_fn=10.0, n_thr=200):
+    thrs = np.linspace(0, 1, n_thr)
+    best_t, best_c = 0.0, np.inf
+    for t in thrs:
+        pred = (probs >= t).astype(int)
+        fp = ((pred == 1) & (y == 0)).sum()
+        fn = ((pred == 0) & (y == 1)).sum()
+        c = cost_fp*fp + cost_fn*fn
+        if c < best_c: best_c, best_t = c, t
+    return best_t, best_c
+```
+
+### Plot PR curve
+```python
+import matplotlib.pyplot as plt
+plt.plot(r, p, label=f'AP={average_precision_score(y_val, probs):.3f}')
+plt.xlabel('Recall'); plt.ylabel('Precision'); plt.legend()
+```
+
+### PR vs ROC on imbalanced
+```python
+from sklearn.metrics import roc_auc_score, average_precision_score
+# y는 imbalanced (1% positive)
+print('ROC-AUC :', roc_auc_score(y_val, probs))      # 매 inflated
+print('PR-AUC  :', average_precision_score(y_val, probs))  # 매 honest
+```
+
+### Calibration before threshold tuning
+```python
+from sklearn.calibration import CalibratedClassifierCV
+cal = CalibratedClassifierCV(clf, method='isotonic', cv=5)
+cal.fit(X_train, y_train)
+probs_cal = cal.predict_proba(X_val)[:, 1]
+# 매 calibrated probability — threshold 의미 직관적
+```
+
+### Per-class threshold (multi-label)
+```python
+def tune_per_label(y_true, probs):  # (N, L)
+    L = probs.shape[1]
+    thrs = np.zeros(L)
+    for k in range(L):
+        thrs[k], _ = best_fbeta_threshold(y_true[:, k], probs[:, k], beta=1.0)
+    return thrs
+```
+
+## 매 결정 기준
+| 상황 | Threshold 우선 |
+|---|---|
+| 의료 screening (놓치면 위험) | High recall (low τ), F2 |
+| Spam / 광고 차단 (오차단 곤란) | High precision (high τ), F0.5 |
+| Balanced cost | F1 maximize |
+| 명시적 cost ratio 있음 | Cost-based threshold |
+| 이미 imbalanced + 비교 | PR-AUC report (ROC 보조) |
+| Multi-label | Per-label threshold tune |
+
+**기본값**: F1 maximize on validation set + calibration. Imbalanced면 PR-AUC report.
+
+## 🔗 Graph
+- 변형: [[ROC_AUC]]
+- 응용: [[Imbalanced_Data]] · [[Anomaly Detection]] · [[Information Retrieval (IR)|Information_Retrieval]]
+- Adjacent: [[Threshold_Tuning]]
+
+## 🤖 LLM 활용
+**언제**: classifier deployment threshold 결정, imbalanced eval report, cost-sensitive decision.
+**언제 X**: 매 ranking task에서 매 단일 threshold 무의미 — top-k metric 또는 nDCG 사용.
+
+## ❌ 안티패턴
+- **Default 0.5 threshold without tuning**: 매 imbalanced 에서 매 useless. Validation tune 필수.
+- **Tune threshold on test set**: 매 leak. Validation 만.
+- **ROC-AUC only on imbalanced**: 매 inflated 결과 — PR-AUC 동반.
+- **Ignore calibration before threshold**: 매 uncalibrated probability 의 threshold 매 transferable X.
+- **F1 maximize when costs are asymmetric**: 매 cost ratio 있으면 F-beta 또는 explicit cost.
+
+## 🧪 검증 / 중복
+- Verified (sklearn metrics docs precision_recall_curve, Saito & Rehmsmeier 2015 'PR vs ROC for imbalanced').
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — PR tradeoff math + threshold tuning + PR vs ROC on imbalanced |