嵌套交叉驗證（Nested CV）：徹底解決二次資料洩漏與閾值偏移

⚠️ Clinical Safety & Crisis Operations Protocol Notice
This article is a dedicated systems engineering whitepaper detailing model validation integrity and data leakage prevention algorithms for high-stakes crisis response infrastructure.

• United States / Canada: Call or text 988 (Suicide & Crisis Lifeline).
• United Kingdom: Call 111 (NHS Mental Health Services) or 116 123 (Samaritans).
• International: Visit findahelpline.com for verified confidential local crisis services worldwide.
  All logs, numerical walkthroughs, and text snippets in this article have been 100% pseudonymized and synthetically generated to strictly prevent clinical PII leakage.

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Introduction: Why Standard K-Fold Cross-Validation Betrays Clinical AI

In machine learning research and industry deployment, the most insidious mistake is over-optimistic performance estimation caused by validation data leakage.

In a consumer recommendation engine, leaking a fraction of test signals might inflate click-through predictions by 2%, causing negligible harm. In life-critical suicide crisis text detection, however, if an AI model's sensitivity degrades by even 1% upon production deployment, emergency caseworkers miss acute crisis windows, leading to catastrophic real-world consequences.

Throughout Episodes #1 to #3, we conquered the 524x Bayes prior barrier (driving FNR to 7%), defeated the 86.7% extreme value bias in 14-day rolling windows, and prevented -log(0) = inf singularities in LightGBM ordinal trees.

Our completed architecture employs a Two-Tier Stacking Pipeline:

• Level 2 Sentence NLP: A fine-tuned transformer encoder generating sentence-level posterior risk probabilities.
• Level 4 Longitudinal Fuser: An ordinal fusion tree aggregating 14-day rolling trajectories, interaction frequency, and sleep disruption metrics.

To validate this pipeline and establish an operational decision threshold ($t^*$), we implemented Nested Cross-Validation (Nested CV). Yet the moment our inner-loop tuned threshold was applied to unseen outer test folds, outer test recall plummeted from 0.90 to 0.74, or False Positive Rates surged by 2.8x.

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1. Production Incident Log: Severe Threshold Transfer Instability

During stratified evaluation across patient cohorts, our nested evaluation harness reported severe fold-to-fold performance collapse:

[ALERT] 2026-11-27 05:22:18.904 [nested_evaluator.py:182]
Fold-1 Outer Test: Recall = 0.738 (FAILED: Target 0.900, Deficit -16.2%p) | FPR = 0.038
Fold-2 Outer Test: Recall = 0.942 (PASSED) | FPR = 0.114 (FAILED: Ceiling 0.050, Surge +2.28x)
Fold-3 Outer Test: Recall = 0.741 (FAILED: Target 0.900, Deficit -15.9%p) | FPR = 0.041
Fold-4 Outer Test: Recall = 0.915 (PASSED) | FPR = 0.089 (FAILED: Ceiling 0.050, Surge +1.78x)
Fold-5 Outer Test: Recall = 0.735 (FAILED: Target 0.900, Deficit -16.5%p) | FPR = 0.035

[CRITICAL SUMMARY]
Mean Outer Recall: 0.814 +/- 0.098 (Severe Fold Variance: 0.082)
Threshold Transfer Instability Detected: Fixed threshold t* fails to generalize across unseen patient splits!

• Classification: Information Leakage & Distribution Scale Mismatch
• Impact: 3 out of 5 outer folds failed clinical certification (recall < 0.90). The other 2 folds breached the 5.0% false alarm ceiling, overwhelming caseworkers.
• Root Location: tests/synth/model/nested_cv.py and tests/synth/model/day_levels.py

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2. Mechanics of Two-Tier Stacking in Nested CV

Our system features a hierarchical decomposition:

1. Level 2 Estimator (M_L2): Maps raw sentence tokens to posterior crisis scores.
2. Level 4 Longitudinal Fuser (M_L4): Ingests 14-day Top-3 trimmed decay scores and temporal behavioral features to output final clinical risk probabilities.

Nested CV separates model optimization from generalization assessment:

• Outer Loop (5-Fold): Partitions 75 patient cohorts into 5 splits. 4 folds (60 patients) serve as training; 1 fold (15 patients) acts as an untouched holdout.
• Inner Loop (4-Fold): Recursively splits the 60 training patients into 3 folds (45 patients) for training and 1 fold (15 patients) for validation to select an optimal threshold $t_k^*$ achieving target recall $\ge 0.90$.

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3. Deep Root Cause Analysis

Thorough audit of the data flow exposed two compounding architectural flaws.

Flaw 1: Sample Size Mismatch Bias

• During Outer Test Scoring ($k$): The Level 2 feature extractor is trained on all 4 outer folds (60 patients).
• During Inner Threshold Tuning ($m$): The Level 2 model scoring validation patients is trained on only 3 inner folds (45 patients).

As sample size scales from 45 to 60, the logistic logits and probability variance of the Level 2 model undergo systematic empirical shrinkage. Consequently, the 90th percentile of predicted scores on 45 patients occurs at a completely different absolute float value than on 60 patients. Applying an absolute float threshold ($t_k^ = 0.42$) tuned on 45 patients to features extracted by a 60-patient model triggered the fatal drop to 0.74 recall.*

Flaw 2: Secondary Information Leakage

In naive nested loops, developers often extract Level 2 features once using a model trained on all 60 training patients to speed up computation. However, this means the inner validation patients ($m$) were already exposed to the feature extractor during representation learning. This secondary leakage artificially inflated inner validation metrics, blinding the tuning loop to real-world generalization drops.

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4. The Failed Solution: Naive Threshold Averaging

A common heuristic is averaging the optimal thresholds across inner folds:

# [FLAWED FIX]: Simple arithmetic average
optimal_threshold = np.mean(inner_thresholds)  # t_avg = 0.418

This failed completely:

• Folds 1, 3, and 5 remained trapped at ~0.73 recall.
• Folds 2 and 4 continued to breach the 11% false alarm ceiling.
• Outer fold variance remained unacceptably high at 0.082.

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5. Architectural Pipeline: 25-Fold Dual-Isolation Engine

flowchart TD
    subgraph Outer_Loop ["1. Outer 5-Fold Hierarchy (Unbiased Evaluation)"]
        D[75 Patient Cohorts] --> O_Train["Outer Train Fold k (60 patients)"]
        D --> O_Test["Outer Test Fold k (15 patients)"]
    end

    subgraph Inner_Loop ["2. Inner 4-Fold Isolation (Zero Leakage)"]
        O_Train --> I_Train["Inner Train Fold m (45 patients)"]
        O_Train --> I_Val["Inner Val Fold m (15 patients)"]
        I_Train --> L2_Inner["Level 2 Isolated Training<br/>(k and m simultaneously barred)"]
        L2_Inner --> I_Val_Score["0.0% Leakage Feature Scoring"]
    end

    subgraph Calibration_Engine ["3. Quantile Alignment Engine"]
        I_Val_Score --> Q_Search["Search Quantile for Target Recall 0.90<br/>q* = Percentile(Scores, 90%)"]
        Q_Search --> Quantile_Map["Consensus Relative Quantile Preservation"]
        O_Train --> L2_Outer["Level 2 Outer Model (60 patients)"]
        L2_Outer --> O_Test_Score["Outer Test Scoring (15 patients)"]
        Quantile_Map & O_Test_Score --> Decision["Apply q* Quantile to Outer Test Distribution<br/>Recall Stabilized: 0.74 -> 0.912!"]
    end

    style O_Test fill:#f87171,stroke:#dc2626,stroke-width:2px,color:#fff
    style Decision fill:#34d399,stroke:#059669,stroke-width:2px,color:#fff

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6. Production Solution Code Diff: Dual Isolation & Quantile Alignment

We replaced static thresholds with Precomputed 25-Fold Dual-Isolation and Quantile Alignment Calibration:

--- a/tests/synth/model/nested_cv.py
+++ b/tests/synth/model/nested_cv.py
@@ -82,21 +82,35 @@ class NestedTriageValidator:
     def evaluate(self, X_text, y_clinical, groups):
         outer_cv = StratifiedGroupKFold(n_splits=5)
         outer_results = []
         
         for fold_k, (train_idx, test_idx) in enumerate(outer_cv.split(X_text, y_clinical, groups)):
-            # FLAWED: Single Level-2 model leaked test folds into inner validation
-            # l2_model = train_level2(X_text[train_idx], y_clinical[train_idx])
-            # inner_t = tune_threshold_naive(l2_model, X_text[train_idx])
+            # FIX 1: Strict Dual-Isolation Split Table (25 unique models)
+            # Isolate outer test fold k AND inner validation fold m simultaneously
+            inner_cv = StratifiedGroupKFold(n_splits=4)
+            inner_quantiles = []
+            
+            for fold_m, (in_train_idx, in_val_idx) in enumerate(inner_cv.split(
+                X_text[train_idx], y_clinical[train_idx], groups[train_idx]
+            )):
+                # Train Level-2 purely on 45 patients (zero exposure to in_val or test_k)
+                l2_inner = train_isolated_level2(X_text[train_idx][in_train_idx], y_clinical[train_idx][in_train_idx])
+                val_scores = l2_inner.predict_proba(X_text[train_idx][in_val_idx])
+                
+                # FIX 2: Store Relative Quantile rank instead of absolute float score
+                q_star = find_quantile_for_recall(val_scores, y_clinical[train_idx][in_val_idx], target_recall=0.90)
+                inner_quantiles.append(q_star)
+            
+            # Compute consensus quantile across inner folds
+            consensus_q = np.median(inner_quantiles)
+            
+            # Train outer Level-2 on full 60 patients
+            l2_outer = train_isolated_level2(X_text[train_idx], y_clinical[train_idx])
+            test_scores = l2_outer.predict_proba(X_text[test_idx])
+            
+            # Apply quantile alignment thresholding to outer test distribution
+            adapted_threshold = np.quantile(test_scores, 1.0 - consensus_q)
+            preds = (test_scores >= adapted_threshold).astype(int)
+            outer_results.append(evaluate_metrics(y_clinical[test_idx], preds))

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7. Production Benchmark Results

Evaluating 5 outer test splits demonstrated complete stabilization:

xychart-beta
    title "Outer Test Fold Recall Stability Comparison"
    x-axis ["Fold 1", "Fold 2", "Fold 3", "Fold 4", "Fold 5"]
    y-axis "Outer Recall" 0.60 --> 1.00
    line [0.738, 0.942, 0.741, 0.915, 0.735]
    line [0.908, 0.918, 0.911, 0.915, 0.909]

(Blue line: Failed static threshold / Green line: Proposed Quantile Alignment)

Metric	Static Threshold	Averaged Threshold	Proposed 25-Fold + Quantile Alignment
Mean Outer Recall	0.814	0.822	0.912 (Surpasses 0.90 Target)
Outer Recall Variance	0.082 (Severe)	0.076	0.009 (-89.0% Variance Drop)
Worst-Case Fold Recall	0.735 (Fatal)	0.742	0.908 (Safety Margin Preserved)
Mean False Positive Rate	0.063	0.059	0.041 (Within 5.0% Ceiling)
Label Permutation AUROC	0.642 (Leakage)	0.638	0.501 (Perfect Null Convergence)

Under random label permutation, our architecture collapsed AUROC to exactly 0.501, mathematically proving that all secondary leakage channels were eliminated.

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8. Architectural Summary & Episode #5 Preview

1. Stacking architectures require precomputed dual-isolation tables: Never reuse intermediate representations across nested folds. Isolate outer holdout $k$ and inner validation $m$ concurrently.
2. Sample size scaling shifts probability score density: Tuning absolute score cutoffs across varying sample counts (45 vs 60) induces severe threshold transfer bias.
3. Quantile alignment guarantees operational stability: Preserving empirical percentile ranks rather than raw float scores reduced outer recall variance by 89%, sustaining a certified 0.908 worst-case recall.

flowchart LR
    EP1["Episode #1: Sentence NLP & Bayes Barrier<br/>(FNR 98% -> 7%)"] --> EP2["Episode #2: 14-Day Longitudinal Fusion<br/>(86.7% Extreme Value Bias Defeated)"]
    EP2 --> EP3["Episode #3: LightGBM Ordinal Trees<br/>(-log(0)=inf Collapse & Calibration)"]
    EP3 --> EP4["Episode #4: Nested Cross-Validation<br/>(Threshold Shift Bias & Leakage Defense)"]
    EP4 --> EP5["Episode #5: Clinical Recall Denominator Error<br/>(Construct Validity & Golden Label Formulation)"]

In Episode #5, we examine Clinical Construct Validity Breakdown (ERR-002): how an erroneous recall denominator formulation distorted clinical safety metrics and how we formulated mathematically verified golden labels.