Grouped Stratification — Stratified and Group… | OneNoughtOne

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Machine LearningStratified and Group Cross-Validation

Stratified and Group Cross-Validation

LevelIntermediate

Duration90 mins

TopicStratified and Group Cross-Validation

4 / 5

Grouped Stratification

The Dual Challenge

You're building a disease classifier from medical images. Your dataset has: Group structure : Multiple images per patient (must stay together) Class imbalance : 5% disease, 95% healthy Using Group K-Fold prevents patient leakage, but random group assignment might put all high-disease-rate patients in one fold. Using Stratified K-Fold balances classes, but might split patient images across folds. You need both : group integrity AND class balance. This is the problem of grouped stratification (also called "stratified group k-fold")—partitioning groups into folds such that each fold has similar class proportions while never splitting groups. This is fundamentally harder than either problem alone. With standard stratification, you can freely assign samples to balance classes. With groups, your assignment unit is the entire group, and groups have varying internal class distributions. Perfect stratification is often impossible; we seek the best approximation.

What You Will Learn

By the end of this page, you will understand why grouped stratification is NP-hard, master approximate algorithms that work well in practice, implement production-ready solutions, and develop intuition for when perfect stratification is achievable versus when approximation must suffice.

The Theoretical Challenge

Why Grouped Stratification Is Hard In standard stratification, we distribute individual samples. Each sample has a single class label, and we can place it in any fold. The problem reduces to counting. In grouped stratification, each group is a fixed "bundle" of samples with a specific class distribution. We must assign entire bundles to folds without breaking them apart. Formal Problem Statement Given: Groups $\mathcal{G} = {g_1, g_2, ..., g_G}$ Each group $g_j$ has class counts $n_{j,c}$ for classes $c \in {1, ..., C}$ Total class counts $N_c = \sum_{j=1}^{G} n_{j,c}$ Target: $k$ folds with approximately $N_c / k$ samples of class $c$ each Objective: Assign groups to folds such that each fold's class distribution is as close to proportional as possible. This is a variant of the multi-way number partitioning problem, which is NP-hard. With $G$ groups and $k$ folds, there are $k^G$ possible assignments—exponential in the number of groups. When Perfect Stratification Is Possible Perfect stratification (exact proportions in every fold) is possible only when: Every group has the same class distribution as the overall dataset, OR Groups can be combined to achieve exact proportions In practice, neither condition holds. Groups have varying sizes and class mixes, making perfect stratification impossible.

Impossibility of Perfect Stratification

Consider why perfect stratification may be impossible even in simple cases.

Scenario: 10 patients, 2-fold CV Overall class distribution: 20% positive (10 positive samples total) Patient class distributions: 3 patients: 100% positive (all samples positive) 7 patients: 0% positive (all samples negative) Problem: Each fold needs ~10% positive to match overall distribution But patients with positive samples are "all or nothing" If we put 2 positive patients in fold 1 and 1 in fold 2: Fold 1: ~67% of positives \to too many Fold 2: ~33% of positives \to too few Best possible: We can balance to some extent, but perfect 50-50 split of positives is only achievable if patient counts align perfectly. Lesson: Grouped stratification seeks the best approximation, not perfection.

The Approximation Mindset

Unlike standard stratification which guarantees near-exact proportions, grouped stratification is an optimization problem. We minimize deviation from ideal proportions, accepting that some deviation is inevitable. Success is measured by the magnitude of deviation, not its absence.

Algorithmic Approaches

Several algorithms approximate optimal grouped stratification. We'll examine three main approaches: Approach 1: Greedy Class-Priority Assignment Assign groups to folds greedily, prioritizing balance of the minority class: Compute target class counts per fold Sort groups by minority class count (descending) For each group, assign to the fold that most needs its class contribution This prioritizes the most constrained class (minority) while letting majority class balance follow. Approach 2: Multi-Objective Optimization Define a loss function that penalizes deviation from target proportions: $$L(\text{assignment}) = \sum_{\text{fold } f} \sum_{\text{class } c} w_c \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ where $w_c$ is a weight (higher for rare classes), $n_{f,c}$ is class $c$ count in fold $f$, $n_f$ is total size of fold $f$, and $p_c$ is the target proportion. Use greedy, simulated annealing, or genetic algorithms to minimize this loss. Approach 3: Iterative Stratification (Multi-Label Style) Adapt the iterative stratification algorithm from multi-label to grouped data: Order classes by total count (rarest first) For each class, distribute groups with that class to balance needs Update fold targets after each assignment

grouped_stratification_algorithms.py
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import numpy as np
from collections import defaultdict
from typing import List, Dict, Tuple, Any
 
class StratifiedGroupKFold:
    """
    Stratified Group K-Fold cross-validator.
    
    Balances class distributions across folds while keeping
    all samples from the same group together.
    """
    
    def __init__(
        self,
        n_splits: int = 5,
        shuffle: bool = True,
        random_state: int = None
    ):
        self.n_splits = n_splits
        self.shuffle = shuffle
        self.random_state = random_state
    
    def split(
        self,
        X: np.ndarray,
        y: np.ndarray,
        groups: np.ndarray
    ) -> List[Tuple[np.ndarray, np.ndarray]]:
        """
        Generate stratified group k-fold splits.
        """
        if self.random_state is not None:
            np.random.seed(self.random_state)
        
        n_samples = len(y)
        unique_groups = np.unique(groups)
        n_groups = len(unique_groups)
        classes = np.unique(y)
        n_classes = len(classes)
        k = self.n_splits
        
        if n_groups < k:
            raise ValueError(
                f"Cannot have more splits ({k}) than groups ({n_groups})"
            )
        
        # Compute per-group class counts
        group_class_counts = {}  # group -> {class: count}
        group_indices = {}  # group -> list of indices
        
        for group in unique_groups:
            mask = groups == group
            group_indices[group] = np.where(mask)[0]
            y_group = y[mask]
            group_class_counts[group] = {
                c: int((y_group == c).sum()) for c in classes
            }
        
        # Target class counts per fold
        total_class_counts = {
            c: int((y == c).sum()) for c in classes
        }
        target_per_fold = {
            c: total_class_counts[c] / k for c in classes
        }
        
        # Initialize fold assignments and current counts
        fold_class_counts = [{c: 0 for c in classes} for _ in range(k)]
        fold_groups = [[] for _ in range(k)]
        
        # Sort groups by minority class count (descending)
        # This ensures we handle constrained groups first
        minority_class = min(classes, key=lambda c: total_class_counts[c])
        
        sorted_groups = sorted(
            unique_groups,
            key=lambda g: group_class_counts[g].get(minority_class, 0),
            reverse=True
        )
        
        if self.shuffle:
            # Partial shuffle: shuffle within size tiers
            tier_size = max(1, len(sorted_groups) // 4)
            for i in range(0, len(sorted_groups), tier_size):
                tier = sorted_groups[i:i + tier_size]
                np.random.shuffle(tier)
                sorted_groups[i:i + tier_size] = tier
        
        # Greedy assignment
        for group in sorted_groups:
            group_counts = group_class_counts[group]
            
            # Find fold with greatest need for this group's class distribution
            # Score = sum of (target - current) * group_contribution for each class
            best_fold = None
            best_score = float('-inf')
            
            for fold_idx in range(k):
                score = 0
                for c in classes:
                    need = target_per_fold[c] - fold_class_counts[fold_idx][c]
                    contribution = group_counts.get(c, 0)
                    # Weight by class rarity
                    weight = 1.0 / (total_class_counts[c] + 1)
                    score += weight * min(need, contribution)
                
                # Small tiebreaker: prefer smaller folds
                score -= 0.001 * sum(fold_class_counts[fold_idx].values())
                
                if score > best_score:
                    best_score = score
                    best_fold = fold_idx
            
            # Assign group to best fold
            fold_groups[best_fold].append(group)
            for c in classes:
                fold_class_counts[best_fold][c] += group_counts.get(c, 0)
        
        # Store diagnostics
        self.fold_class_counts_ = fold_class_counts
        self.target_per_fold_ = target_per_fold
        
        # Convert to train/test indices
        splits = []
        for fold_idx in range(k):
            test_groups = set(fold_groups[fold_idx])
            test_indices = []
            train_indices = []
            
            for group in unique_groups:
                indices = group_indices[group].tolist()
                if group in test_groups:
                    test_indices.extend(indices)
                else:
                    train_indices.extend(indices)
            
            splits.append((
                np.array(train_indices),
                np.array(test_indices)
            ))
        
        return splits
    
    def get_diagnostics(self) -> Dict[str, Any]:
        """Return stratification quality diagnostics."""
        if not hasattr(self, 'fold_class_counts_'):
            return {}
        
        diagnostics = {
            'target_per_fold': self.target_per_fold_,
            'actual_per_fold': self.fold_class_counts_,
            'deviations': []
        }
        
        for fold_idx, actual in enumerate(self.fold_class_counts_):
            fold_total = sum(actual.values())
            fold_devs = {}
            for c in actual:
                target_prop = self.target_per_fold_[c] / sum(self.target_per_fold_.values())
                actual_prop = actual[c] / fold_total if fold_total > 0 else 0
                fold_devs[c] = actual_prop - target_prop
            diagnostics['deviations'].append(fold_devs)
        
        return diagnostics
 
 
def evaluate_stratification_quality(
    y: np.ndarray,
    groups: np.ndarray,
    splits: List[Tuple[np.ndarray, np.ndarray]]
) -> Dict[str, Any]:
    """
    Evaluate how well stratification was achieved.
    """
    classes = np.unique(y)
    overall_dist = {c: (y == c).mean() for c in classes}
    
    fold_metrics = []
    max_deviations = {c: 0.0 for c in classes}
    
    for fold_idx, (train_idx, test_idx) in enumerate(splits):
        y_test = y[test_idx]
        fold_dist = {c: (y_test == c).mean() if len(y_test) > 0 else 0 for c in classes}
        
        deviations = {c: abs(fold_dist[c] - overall_dist[c]) for c in classes}
        
        for c in classes:
            max_deviations[c] = max(max_deviations[c], deviations[c])
        
        # Test group integrity
        test_groups = set(groups[test_idx])
        train_groups = set(groups[train_idx])
        overlap = test_groups.intersection(train_groups)
        
        fold_metrics.append({
            'fold': fold_idx + 1,
            'test_size': len(test_idx),
            'test_groups': len(test_groups),
            'distribution': fold_dist,
            'deviations': deviations,
            'group_leak': len(overlap) > 0
        })
    
    return {
        'overall_distribution': overall_dist,
        'fold_metrics': fold_metrics,
        'max_class_deviations': max_deviations,
        'any_group_leaks': any(fm['group_leak'] for fm in fold_metrics)
    }
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    
    # Create grouped imbalanced dataset
    n_groups = 30
    
    X_list, y_list, groups_list = [], [], []
    
    for group_id in range(n_groups):
        group_size = np.random.randint(20, 100)
        # Vary class balance per group
        group_pos_rate = np.random.beta(1, 9)  # Most groups have low positive rate
        
        X_g = np.random.randn(group_size, 10)
        y_g = (np.random.random(group_size) < group_pos_rate).astype(int)
        
        X_list.append(X_g)
        y_list.append(y_g)
        groups_list.extend([f"G{group_id:02d}"] * group_size)
    
    X = np.vstack(X_list)
    y = np.concatenate(y_list)
    groups = np.array(groups_list)
    
    print(f"Dataset: {len(y)} samples, {n_groups} groups")
    print(f"Overall class distribution: {dict(zip(*np.unique(y, return_counts=True)))}")
    print(f"Overall positive rate: {y.mean():.1%}")
    print()
    
    # Compare with non-stratified GroupKFold
    from sklearn.model_selection import GroupKFold
    
    print("=" * 60)
    print("STANDARD GROUP K-FOLD (NO STRATIFICATION)")
    print("=" * 60)
    gkf = GroupKFold(n_splits=5)
    gkf_splits = list(gkf.split(X, y, groups))
    gkf_quality = evaluate_stratification_quality(y, groups, gkf_splits)
    
    for fm in gkf_quality['fold_metrics']:
        print(f"Fold {fm['fold']}: n={fm['test_size']}, pos_rate={fm['distribution'][1]:.1%}, "
              f"deviation={fm['deviations'][1]:.1%}")
    print(f"Max deviation (positive class): {gkf_quality['max_class_deviations'][1]:.1%}")
    print()
    
    print("=" * 60)
    print("STRATIFIED GROUP K-FOLD")
    print("=" * 60)
    sgkf = StratifiedGroupKFold(n_splits=5, shuffle=True, random_state=42)
    sgkf_splits = sgkf.split(X, y, groups)
    sgkf_quality = evaluate_stratification_quality(y, groups, sgkf_splits)
    
    for fm in sgkf_quality['fold_metrics']:
        print(f"Fold {fm['fold']}: n={fm['test_size']}, pos_rate={fm['distribution'][1]:.1%}, "
              f"deviation={fm['deviations'][1]:.1%}")
    print(f"Max deviation (positive class): {sgkf_quality['max_class_deviations'][1]:.1%}")
    print(f"Any group leaks: {sgkf_quality['any_group_leaks']}")

Measuring Stratification Quality

Since perfect stratification is often impossible, we need metrics to quantify how close we got. Metric 1: Maximum Absolute Deviation (MAD) For each class $c$, the maximum deviation from target proportion across all folds: $$\text{MAD}c = \max{f \in \text{folds}} \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ Lower is better. MAD = 0 means perfect stratification for that class. Metric 2: Root Mean Square Deviation (RMSD) Average deviation across all classes and folds: $$\text{RMSD} = \sqrt{\frac{1}{k \cdot C} \sum_{f} \sum_{c} \left( \frac{n_{f,c}}{n_f} - p_c \right)^2}$$ Penalizes large deviations more heavily than MAD. Metric 3: Class-Weighted Deviation Weight deviations by class rarity (rare class deviations matter more): $$\text{WD} = \sum_{f} \sum_{c} \frac{1}{p_c} \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ Metric 4: Group Integrity Check Binary check: Does any group appear in both train and test for any fold? $$\text{Integrity} = \begin{cases} 1 & \text{if no leakage} \ 0 & \text{if any leakage} \end{cases}$$ This should always be 1; any failure is critical.

Stratification Quality Metrics Summary
Metric	Formula	Interpretation	Target
MAD (per class)	\|actual_prop - target_prop\|_max	Worst-case deviation	< 0.05 (5%)
RMSD	sqrt(mean(deviations²))	Average deviation	< 0.02 (2%)
Weighted deviation	sum(deviation / class_prop)	Rare-class-focused	Minimize
Group integrity	1 if no leakage	Validity check	= 1 (mandatory)

stratification_quality_metrics.py
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import numpy as np
from typing import Dict, List, Tuple
 
def compute_stratification_metrics(
    y: np.ndarray,
    groups: np.ndarray,
    splits: List[Tuple[np.ndarray, np.ndarray]]
) -> Dict[str, float]:
    """
    Compute comprehensive stratification quality metrics.
    """
    classes = np.unique(y)
    k = len(splits)
    n_total = len(y)
    
    # Target proportions
    target_props = {c: (y == c).sum() / n_total for c in classes}
    
    # Collect deviations
    all_deviations = {c: [] for c in classes}
    group_integrity_violations = 0
    
    for train_idx, test_idx in splits:
        y_test = y[test_idx]
        n_test = len(y_test)
        
        # Check group integrity
        train_groups = set(groups[train_idx])
        test_groups = set(groups[test_idx])
        if train_groups.intersection(test_groups):
            group_integrity_violations += 1
        
        # Compute deviations
        for c in classes:
            actual_prop = (y_test == c).sum() / n_test if n_test > 0 else 0
            deviation = actual_prop - target_props[c]
            all_deviations[c].append(deviation)
    
    # Compute metrics
    metrics = {}
    
    # MAD per class
    for c in classes:
        metrics[f'mad_class_{c}'] = max(abs(d) for d in all_deviations[c])
    metrics['mad_max'] = max(metrics[f'mad_class_{c}'] for c in classes)
    
    # RMSD
    all_sq_devs = []
    for c in classes:
        all_sq_devs.extend([d**2 for d in all_deviations[c]])
    metrics['rmsd'] = np.sqrt(np.mean(all_sq_devs))
    
    # Weighted deviation (by rarity)
    weighted_sum = 0
    for c in classes:
        weight = 1 / target_props[c] if target_props[c] > 0 else 0
        weighted_sum += sum(abs(d) * weight for d in all_deviations[c])
    metrics['weighted_deviation'] = weighted_sum / (k * len(classes))
    
    # Group integrity
    metrics['group_integrity'] = 1.0 if group_integrity_violations == 0 else 0.0
    metrics['n_integrity_violations'] = group_integrity_violations
    
    return metrics
 
 
def print_quality_report(metrics: Dict[str, float]) -> None:
    """Print formatted quality report."""
    print("Stratification Quality Report")
    print("-" * 40)
    
    print(f"Group Integrity: {'✓ PASSED' if metrics['group_integrity'] == 1 else '✗ FAILED'}")
    if metrics['n_integrity_violations'] > 0:
        print(f"  ⚠️ {metrics['n_integrity_violations']} folds have group leakage!")
    
    print(f"
Class Deviation Metrics:")
    print(f"  Max Absolute Deviation: {metrics['mad_max']:.2%}")
    print(f"  RMSD: {metrics['rmsd']:.4f}")
    print(f"  Weighted Deviation: {metrics['weighted_deviation']:.4f}")
    
    # Quality rating
    if metrics['mad_max'] < 0.03:
        quality = "Excellent"
    elif metrics['mad_max'] < 0.05:
        quality = "Good"
    elif metrics['mad_max'] < 0.10:
        quality = "Acceptable"
    else:
        quality = "Poor"
    
    print(f"
Overall Quality: {quality}")

Acceptable Thresholds

For most applications, MAD < 5% is acceptable, MAD < 3% is good, and MAD < 1% is excellent. If you're seeing MAD > 10%, either your groups are too heterogeneous or you have too few groups. Consider increasing k (fewer groups per fold) or collecting more data.

Using StratifiedGroupKFold in Scikit-Learn

As of scikit-learn 1.0+, StratifiedGroupKFold is available natively. Let's explore its usage and compare with our custom implementation.

sklearn_stratified_group_kfold.py
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from sklearn.model_selection import StratifiedGroupKFold, cross_validate
from sklearn.ensemble import RandomForestClassifier
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
import numpy as np
 
def production_stratified_group_cv(
    model,
    X: np.ndarray,
    y: np.ndarray,
    groups: np.ndarray,
    n_splits: int = 5,
    random_state: int = 42,
    verbose: bool = True
):
    """
    Production-ready stratified group cross-validation.
    """
    # Create stratified group k-fold splitter
    sgkf = StratifiedGroupKFold(
        n_splits=n_splits,
        shuffle=True,
        random_state=random_state
    )
    
    # Create preprocessing pipeline
    pipeline = Pipeline([
        ('scaler', StandardScaler()),
        ('model', model)
    ])
    
    # Define scoring
    scoring = {
        'accuracy': 'accuracy',
        'f1': 'f1',
        'roc_auc': 'roc_auc',
        'precision': 'precision',
        'recall': 'recall'
    }
    
    # Perform cross-validation
    cv_results = cross_validate(
        pipeline, X, y,
        cv=sgkf,
        groups=groups,  # Required for group-aware CV
        scoring=scoring,
        return_train_score=True,
        n_jobs=-1
    )
    
    if verbose:
        # Print fold details
        print("=" * 60)
        print("STRATIFIED GROUP K-FOLD CROSS-VALIDATION")
        print("=" * 60)
        
        # Analyze each fold
        overall_pos_rate = y.mean()
        print(f"
Overall positive rate: {overall_pos_rate:.2%}")
        print(f"
Fold Analysis:")
        
        for fold_idx, (train_idx, test_idx) in enumerate(sgkf.split(X, y, groups)):
            test_pos_rate = y[test_idx].mean()
            n_test_groups = len(np.unique(groups[test_idx]))
            deviation = abs(test_pos_rate - overall_pos_rate)
            
            print(f"  Fold {fold_idx + 1}: n={len(test_idx):4d}, "
                  f"groups={n_test_groups:2d}, "
                  f"pos_rate={test_pos_rate:.2%} "
                  f"(deviation: {deviation:.2%})")
        
        print(f"
Metrics Summary:")
        for metric in scoring:
            test_scores = cv_results[f'test_{metric}']
            train_scores = cv_results[f'train_{metric}']
            print(f"  {metric:12s}: {test_scores.mean():.4f} ± {test_scores.std():.4f} "
                  f"(train: {train_scores.mean():.4f})")
    
    return cv_results
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    
    # Create realistic medical imaging dataset
    n_patients = 60
    
    X_list, y_list, groups_list = [], [], []
    
    for patient_id in range(n_patients):
        # Number of scans per patient
        n_scans = np.random.randint(5, 30)
        
        # Patient-level disease probability
        # Some patients are definitely diseased, some healthy
        if patient_id % 10 == 0:  # 10% of patients have disease
            patient_disease_prob = 0.8
        else:
            patient_disease_prob = 0.05
        
        # Generate scans
        X_p = np.random.randn(n_scans, 20)
        y_p = (np.random.random(n_scans) < patient_disease_prob).astype(int)
        
        X_list.append(X_p)
        y_list.append(y_p)
        groups_list.extend([f"patient_{patient_id:03d}"] * n_scans)
    
    X = np.vstack(X_list)
    y = np.concatenate(y_list)
    groups = np.array(groups_list)
    
    print(f"Dataset: {len(y)} scans from {n_patients} patients")
    print(f"Class distribution: {np.bincount(y)} (positive rate: {y.mean():.2%})")
    print()
    
    model = RandomForestClassifier(n_estimators=100, random_state=42)
    results = production_stratified_group_cv(model, X, y, groups)

Common Mistake: Forgetting groups=

StratifiedGroupKFold requires both y (for stratification) AND groups (for group separation). Omitting the groups= parameter in cross_validate() silently falls back to regular StratifiedKFold, losing group separation. Always verify with a diagnostic check.

Edge Cases and Special Challenges

Grouped stratification encounters several challenging edge cases:

Edge Cases and Solutions

•Homogeneous groups: Some groups have only one class (all positive or all negative). These are "all-or-nothing" for their class, making perfect balance impossible. Solution: Accept imperfect stratification; prioritize group integrity.
•Extreme imbalance: With 99:1 class ratio, minority class may exist in very few groups. Solution: Increase number of folds (smaller test sets can handle having 0 minority samples) or use stratified bootstrap instead.
•Variable group sizes: One group has 1000 samples, another has 10. Solution: Weight groups by size in the optimization objective, or use size-balanced group assignment as a secondary objective.
•Multi-label groups: Each sample has multiple labels, and groups have complex label combinations. Solution: Use iterative stratification adapted for groups.
•Continuous targets (regression): No natural classes for stratification. Solution: Bin the target into quantiles and stratify on binned labels.

Handling Homogeneous Groups Groups that are internally homogeneous (all samples have the same class) are the primary cause of imperfect stratification. Here's how to diagnose and handle them:

homogeneous_groups.py
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import numpy as np
from collections import Counter
 
def analyze_group_homogeneity(
    y: np.ndarray,
    groups: np.ndarray
) -> dict:
    """
    Analyze group-level class distributions to identify
    stratification constraints.
    """
    unique_groups = np.unique(groups)
    classes = np.unique(y)
    
    homogeneous_groups = {c: [] for c in classes}
    mixed_groups = []
    
    for group in unique_groups:
        mask = groups == group
        y_group = y[mask]
        unique_classes = np.unique(y_group)
        
        if len(unique_classes) == 1:
            # Homogeneous group
            homogeneous_groups[unique_classes[0]].append(group)
        else:
            # Mixed group
            mixed_groups.append({
                'group': group,
                'distribution': dict(Counter(y_group)),
                'n_samples': len(y_group)
            })
    
    # Compute stratifiability score
    # Lower = more constrained
    n_total = len(unique_groups)
    n_mixed = len(mixed_groups)
    stratifiability = n_mixed / n_total if n_total > 0 else 0
    
    return {
        'n_groups': len(unique_groups),
        'n_classes': len(classes),
        'homogeneous_groups': homogeneous_groups,
        'n_homogeneous': {c: len(gs) for c, gs in homogeneous_groups.items()},
        'mixed_groups': mixed_groups,
        'n_mixed': len(mixed_groups),
        'stratifiability_score': stratifiability,
        'recommendation': get_recommendation(stratifiability)
    }
 
 
def get_recommendation(stratifiability: float) -> str:
    """Get recommendation based on stratifiability score."""
    if stratifiability > 0.7:
        return "High stratifiability: Standard algorithms should work well."
    elif stratifiability > 0.4:
        return "Moderate stratifiability: Expect some deviation, but manageable."
    elif stratifiability > 0.2:
        return "Low stratifiability: Consider using more folds or fewer groups."
    else:
        return "Very low stratifiability: Consider binned target or relaxed constraints."
 
 
# Example usage
if __name__ == "__main__":
    np.random.seed(42)
    
    # Simulate varying homogeneity
    n_groups = 50
    groups_list = []
    y_list = []
    
    for g in range(n_groups):
        size = np.random.randint(10, 50)
        
        if g < 15:  # 30% pure positive
            y_g = np.ones(size)
        elif g < 35:  # 40% pure negative
            y_g = np.zeros(size)
        else:  # 30% mixed
            y_g = (np.random.random(size) < 0.3).astype(int)
        
        groups_list.extend([f"G{g:02d}"] * size)
        y_list.extend(y_g)
    
    groups = np.array(groups_list)
    y = np.array(y_list)
    
    analysis = analyze_group_homogeneity(y, groups)
    
    print("Group Homogeneity Analysis")
    print("-" * 40)
    print(f"Total groups: {analysis['n_groups']}")
    print(f"Homogeneous groups: {sum(analysis['n_homogeneous'].values())}")
    for c, count in analysis['n_homogeneous'].items():
        print(f"  Class {c}: {count} pure groups")
    print(f"Mixed groups: {analysis['n_mixed']}")
    print(f"Stratifiability score: {analysis['stratifiability_score']:.2f}")
    print(f"
Recommendation: {analysis['recommendation']}")

Best Practices for Grouped Stratification

Based on the theoretical and practical considerations discussed, here are best practices for production use:

Production Best Practices

•Always verify group integrity first — Before analyzing stratification quality, confirm no group leakage. Any leakage invalidates results entirely.
•Analyze group homogeneity before choosing k — If 80% of groups are homogeneous, you need more groups in each test fold for any minority representation.
•Use fewer folds for high homogeneity — With many pure groups, k=3 might achieve better stratification than k=5 because you have more flexibility in assignment.
•Report stratification metrics — Don't just run CV; report MAD and RMSD so readers understand the validity of your evaluation.
•Use multiple random seeds — Greedy algorithms are sensitive to initial ordering. Run with 5-10 seeds and average results.
•Consider weighted evaluation — If class proportions vary across folds, compute weighted averages using fold sizes as weights.
•Document inevitable deviations — If perfect stratification is impossible, document why and quantify the impact on interpretation.

Avoid

•Ignoring stratification quality
•Using high k with few groups
•Splitting groups for "better" stratification
•Treating imperfect stratification as failure

•Report MAD and RMSD metrics
•Choose k based on group count and homogeneity
•Preserve group integrity at all costs
•Accept and document deviation bounds

The Priority Order

When conflicts arise: 1) Group integrity (non-negotiable), 2) Minority class stratification (most impactful), 3) Majority class stratification (least constrained). Never sacrifice group integrity for better class balance—you'll get optimistic biased results.

Summary: Grouped Stratification

We've comprehensively covered the challenging problem of combining class stratification with group-based cross-validation. Here are the essential takeaways:

Key Takeaways

•Grouped stratification is NP-hard — Perfect class balance while preserving groups is often impossible; we seek good approximations.
•Groups are the assignment unit — We assign entire groups to folds, not individual samples, limiting flexibility.
•Homogeneous groups limit stratifiability — Groups with only one class are "all-or-nothing," making perfect balance impossible.
•Greedy algorithms work well in practice — Prioritize minority class balance and let majority class follow.
•Use quality metrics — MAD (max absolute deviation) and RMSD quantify stratification quality; always report them.
•sklearn has native support — StratifiedGroupKFold (scikit-learn 1.0+) handles this automatically.
•Group integrity is paramount — Never sacrifice group separation for better stratification; biased evaluation is worse than imperfect balance.

What's Next

You now understand how to handle both class imbalance and group structure. But there's a deeper issue lurking: data leakage. Even with perfect group separation, information can leak through preprocessing, feature engineering, or target encoding. The next page covers Data Leakage Prevention—a critical topic for trustworthy ML evaluation.

Machine LearningStratified and Group Cross-Validation

Stratified and Group Cross-Validation

LevelIntermediate

Duration90 mins

TopicStratified and Group Cross-Validation

4 / 5

Grouped Stratification

The Dual Challenge

You're building a disease classifier from medical images. Your dataset has: Group structure : Multiple images per patient (must stay together) Class imbalance : 5% disease, 95% healthy Using Group K-Fold prevents patient leakage, but random group assignment might put all high-disease-rate patients in one fold. Using Stratified K-Fold balances classes, but might split patient images across folds. You need both : group integrity AND class balance. This is the problem of grouped stratification (also called "stratified group k-fold")—partitioning groups into folds such that each fold has similar class proportions while never splitting groups. This is fundamentally harder than either problem alone. With standard stratification, you can freely assign samples to balance classes. With groups, your assignment unit is the entire group, and groups have varying internal class distributions. Perfect stratification is often impossible; we seek the best approximation.

What You Will Learn

By the end of this page, you will understand why grouped stratification is NP-hard, master approximate algorithms that work well in practice, implement production-ready solutions, and develop intuition for when perfect stratification is achievable versus when approximation must suffice.

The Theoretical Challenge

Why Grouped Stratification Is Hard In standard stratification, we distribute individual samples. Each sample has a single class label, and we can place it in any fold. The problem reduces to counting. In grouped stratification, each group is a fixed "bundle" of samples with a specific class distribution. We must assign entire bundles to folds without breaking them apart. Formal Problem Statement Given: Groups $\mathcal{G} = {g_1, g_2, ..., g_G}$ Each group $g_j$ has class counts $n_{j,c}$ for classes $c \in {1, ..., C}$ Total class counts $N_c = \sum_{j=1}^{G} n_{j,c}$ Target: $k$ folds with approximately $N_c / k$ samples of class $c$ each Objective: Assign groups to folds such that each fold's class distribution is as close to proportional as possible. This is a variant of the multi-way number partitioning problem, which is NP-hard. With $G$ groups and $k$ folds, there are $k^G$ possible assignments—exponential in the number of groups. When Perfect Stratification Is Possible Perfect stratification (exact proportions in every fold) is possible only when: Every group has the same class distribution as the overall dataset, OR Groups can be combined to achieve exact proportions In practice, neither condition holds. Groups have varying sizes and class mixes, making perfect stratification impossible.

Impossibility of Perfect Stratification

Consider why perfect stratification may be impossible even in simple cases.

Scenario: 10 patients, 2-fold CV Overall class distribution: 20% positive (10 positive samples total) Patient class distributions: 3 patients: 100% positive (all samples positive) 7 patients: 0% positive (all samples negative) Problem: Each fold needs ~10% positive to match overall distribution But patients with positive samples are "all or nothing" If we put 2 positive patients in fold 1 and 1 in fold 2: Fold 1: ~67% of positives \to too many Fold 2: ~33% of positives \to too few Best possible: We can balance to some extent, but perfect 50-50 split of positives is only achievable if patient counts align perfectly. Lesson: Grouped stratification seeks the best approximation, not perfection.

The Approximation Mindset

Unlike standard stratification which guarantees near-exact proportions, grouped stratification is an optimization problem. We minimize deviation from ideal proportions, accepting that some deviation is inevitable. Success is measured by the magnitude of deviation, not its absence.

Algorithmic Approaches

Several algorithms approximate optimal grouped stratification. We'll examine three main approaches: Approach 1: Greedy Class-Priority Assignment Assign groups to folds greedily, prioritizing balance of the minority class: Compute target class counts per fold Sort groups by minority class count (descending) For each group, assign to the fold that most needs its class contribution This prioritizes the most constrained class (minority) while letting majority class balance follow. Approach 2: Multi-Objective Optimization Define a loss function that penalizes deviation from target proportions: $$L(\text{assignment}) = \sum_{\text{fold } f} \sum_{\text{class } c} w_c \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ where $w_c$ is a weight (higher for rare classes), $n_{f,c}$ is class $c$ count in fold $f$, $n_f$ is total size of fold $f$, and $p_c$ is the target proportion. Use greedy, simulated annealing, or genetic algorithms to minimize this loss. Approach 3: Iterative Stratification (Multi-Label Style) Adapt the iterative stratification algorithm from multi-label to grouped data: Order classes by total count (rarest first) For each class, distribute groups with that class to balance needs Update fold targets after each assignment

grouped_stratification_algorithms.py
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import numpy as np
from collections import defaultdict
from typing import List, Dict, Tuple, Any
 
class StratifiedGroupKFold:
    """
    Stratified Group K-Fold cross-validator.
    
    Balances class distributions across folds while keeping
    all samples from the same group together.
    """
    
    def __init__(
        self,
        n_splits: int = 5,
        shuffle: bool = True,
        random_state: int = None
    ):
        self.n_splits = n_splits
        self.shuffle = shuffle
        self.random_state = random_state
    
    def split(
        self,
        X: np.ndarray,
        y: np.ndarray,
        groups: np.ndarray
    ) -> List[Tuple[np.ndarray, np.ndarray]]:
        """
        Generate stratified group k-fold splits.
        """
        if self.random_state is not None:
            np.random.seed(self.random_state)
        
        n_samples = len(y)
        unique_groups = np.unique(groups)
        n_groups = len(unique_groups)
        classes = np.unique(y)
        n_classes = len(classes)
        k = self.n_splits
        
        if n_groups < k:
            raise ValueError(
                f"Cannot have more splits ({k}) than groups ({n_groups})"
            )
        
        # Compute per-group class counts
        group_class_counts = {}  # group -> {class: count}
        group_indices = {}  # group -> list of indices
        
        for group in unique_groups:
            mask = groups == group
            group_indices[group] = np.where(mask)[0]
            y_group = y[mask]
            group_class_counts[group] = {
                c: int((y_group == c).sum()) for c in classes
            }
        
        # Target class counts per fold
        total_class_counts = {
            c: int((y == c).sum()) for c in classes
        }
        target_per_fold = {
            c: total_class_counts[c] / k for c in classes
        }
        
        # Initialize fold assignments and current counts
        fold_class_counts = [{c: 0 for c in classes} for _ in range(k)]
        fold_groups = [[] for _ in range(k)]
        
        # Sort groups by minority class count (descending)
        # This ensures we handle constrained groups first
        minority_class = min(classes, key=lambda c: total_class_counts[c])
        
        sorted_groups = sorted(
            unique_groups,
            key=lambda g: group_class_counts[g].get(minority_class, 0),
            reverse=True
        )
        
        if self.shuffle:
            # Partial shuffle: shuffle within size tiers
            tier_size = max(1, len(sorted_groups) // 4)
            for i in range(0, len(sorted_groups), tier_size):
                tier = sorted_groups[i:i + tier_size]
                np.random.shuffle(tier)
                sorted_groups[i:i + tier_size] = tier
        
        # Greedy assignment
        for group in sorted_groups:
            group_counts = group_class_counts[group]
            
            # Find fold with greatest need for this group's class distribution
            # Score = sum of (target - current) * group_contribution for each class
            best_fold = None
            best_score = float('-inf')
            
            for fold_idx in range(k):
                score = 0
                for c in classes:
                    need = target_per_fold[c] - fold_class_counts[fold_idx][c]
                    contribution = group_counts.get(c, 0)
                    # Weight by class rarity
                    weight = 1.0 / (total_class_counts[c] + 1)
                    score += weight * min(need, contribution)
                
                # Small tiebreaker: prefer smaller folds
                score -= 0.001 * sum(fold_class_counts[fold_idx].values())
                
                if score > best_score:
                    best_score = score
                    best_fold = fold_idx
            
            # Assign group to best fold
            fold_groups[best_fold].append(group)
            for c in classes:
                fold_class_counts[best_fold][c] += group_counts.get(c, 0)
        
        # Store diagnostics
        self.fold_class_counts_ = fold_class_counts
        self.target_per_fold_ = target_per_fold
        
        # Convert to train/test indices
        splits = []
        for fold_idx in range(k):
            test_groups = set(fold_groups[fold_idx])
            test_indices = []
            train_indices = []
            
            for group in unique_groups:
                indices = group_indices[group].tolist()
                if group in test_groups:
                    test_indices.extend(indices)
                else:
                    train_indices.extend(indices)
            
            splits.append((
                np.array(train_indices),
                np.array(test_indices)
            ))
        
        return splits
    
    def get_diagnostics(self) -> Dict[str, Any]:
        """Return stratification quality diagnostics."""
        if not hasattr(self, 'fold_class_counts_'):
            return {}
        
        diagnostics = {
            'target_per_fold': self.target_per_fold_,
            'actual_per_fold': self.fold_class_counts_,
            'deviations': []
        }
        
        for fold_idx, actual in enumerate(self.fold_class_counts_):
            fold_total = sum(actual.values())
            fold_devs = {}
            for c in actual:
                target_prop = self.target_per_fold_[c] / sum(self.target_per_fold_.values())
                actual_prop = actual[c] / fold_total if fold_total > 0 else 0
                fold_devs[c] = actual_prop - target_prop
            diagnostics['deviations'].append(fold_devs)
        
        return diagnostics
 
 
def evaluate_stratification_quality(
    y: np.ndarray,
    groups: np.ndarray,
    splits: List[Tuple[np.ndarray, np.ndarray]]
) -> Dict[str, Any]:
    """
    Evaluate how well stratification was achieved.
    """
    classes = np.unique(y)
    overall_dist = {c: (y == c).mean() for c in classes}
    
    fold_metrics = []
    max_deviations = {c: 0.0 for c in classes}
    
    for fold_idx, (train_idx, test_idx) in enumerate(splits):
        y_test = y[test_idx]
        fold_dist = {c: (y_test == c).mean() if len(y_test) > 0 else 0 for c in classes}
        
        deviations = {c: abs(fold_dist[c] - overall_dist[c]) for c in classes}
        
        for c in classes:
            max_deviations[c] = max(max_deviations[c], deviations[c])
        
        # Test group integrity
        test_groups = set(groups[test_idx])
        train_groups = set(groups[train_idx])
        overlap = test_groups.intersection(train_groups)
        
        fold_metrics.append({
            'fold': fold_idx + 1,
            'test_size': len(test_idx),
            'test_groups': len(test_groups),
            'distribution': fold_dist,
            'deviations': deviations,
            'group_leak': len(overlap) > 0
        })
    
    return {
        'overall_distribution': overall_dist,
        'fold_metrics': fold_metrics,
        'max_class_deviations': max_deviations,
        'any_group_leaks': any(fm['group_leak'] for fm in fold_metrics)
    }
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    
    # Create grouped imbalanced dataset
    n_groups = 30
    
    X_list, y_list, groups_list = [], [], []
    
    for group_id in range(n_groups):
        group_size = np.random.randint(20, 100)
        # Vary class balance per group
        group_pos_rate = np.random.beta(1, 9)  # Most groups have low positive rate
        
        X_g = np.random.randn(group_size, 10)
        y_g = (np.random.random(group_size) < group_pos_rate).astype(int)
        
        X_list.append(X_g)
        y_list.append(y_g)
        groups_list.extend([f"G{group_id:02d}"] * group_size)
    
    X = np.vstack(X_list)
    y = np.concatenate(y_list)
    groups = np.array(groups_list)
    
    print(f"Dataset: {len(y)} samples, {n_groups} groups")
    print(f"Overall class distribution: {dict(zip(*np.unique(y, return_counts=True)))}")
    print(f"Overall positive rate: {y.mean():.1%}")
    print()
    
    # Compare with non-stratified GroupKFold
    from sklearn.model_selection import GroupKFold
    
    print("=" * 60)
    print("STANDARD GROUP K-FOLD (NO STRATIFICATION)")
    print("=" * 60)
    gkf = GroupKFold(n_splits=5)
    gkf_splits = list(gkf.split(X, y, groups))
    gkf_quality = evaluate_stratification_quality(y, groups, gkf_splits)
    
    for fm in gkf_quality['fold_metrics']:
        print(f"Fold {fm['fold']}: n={fm['test_size']}, pos_rate={fm['distribution'][1]:.1%}, "
              f"deviation={fm['deviations'][1]:.1%}")
    print(f"Max deviation (positive class): {gkf_quality['max_class_deviations'][1]:.1%}")
    print()
    
    print("=" * 60)
    print("STRATIFIED GROUP K-FOLD")
    print("=" * 60)
    sgkf = StratifiedGroupKFold(n_splits=5, shuffle=True, random_state=42)
    sgkf_splits = sgkf.split(X, y, groups)
    sgkf_quality = evaluate_stratification_quality(y, groups, sgkf_splits)
    
    for fm in sgkf_quality['fold_metrics']:
        print(f"Fold {fm['fold']}: n={fm['test_size']}, pos_rate={fm['distribution'][1]:.1%}, "
              f"deviation={fm['deviations'][1]:.1%}")
    print(f"Max deviation (positive class): {sgkf_quality['max_class_deviations'][1]:.1%}")
    print(f"Any group leaks: {sgkf_quality['any_group_leaks']}")

Measuring Stratification Quality

Since perfect stratification is often impossible, we need metrics to quantify how close we got. Metric 1: Maximum Absolute Deviation (MAD) For each class $c$, the maximum deviation from target proportion across all folds: $$\text{MAD}c = \max{f \in \text{folds}} \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ Lower is better. MAD = 0 means perfect stratification for that class. Metric 2: Root Mean Square Deviation (RMSD) Average deviation across all classes and folds: $$\text{RMSD} = \sqrt{\frac{1}{k \cdot C} \sum_{f} \sum_{c} \left( \frac{n_{f,c}}{n_f} - p_c \right)^2}$$ Penalizes large deviations more heavily than MAD. Metric 3: Class-Weighted Deviation Weight deviations by class rarity (rare class deviations matter more): $$\text{WD} = \sum_{f} \sum_{c} \frac{1}{p_c} \left| \frac{n_{f,c}}{n_f} - p_c \right|$$ Metric 4: Group Integrity Check Binary check: Does any group appear in both train and test for any fold? $$\text{Integrity} = \begin{cases} 1 & \text{if no leakage} \ 0 & \text{if any leakage} \end{cases}$$ This should always be 1; any failure is critical.

Stratification Quality Metrics Summary
Metric	Formula	Interpretation	Target
MAD (per class)	\|actual_prop - target_prop\|_max	Worst-case deviation	< 0.05 (5%)
RMSD	sqrt(mean(deviations²))	Average deviation	< 0.02 (2%)
Weighted deviation	sum(deviation / class_prop)	Rare-class-focused	Minimize
Group integrity	1 if no leakage	Validity check	= 1 (mandatory)

stratification_quality_metrics.py
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import numpy as np
from typing import Dict, List, Tuple
 
def compute_stratification_metrics(
    y: np.ndarray,
    groups: np.ndarray,
    splits: List[Tuple[np.ndarray, np.ndarray]]
) -> Dict[str, float]:
    """
    Compute comprehensive stratification quality metrics.
    """
    classes = np.unique(y)
    k = len(splits)
    n_total = len(y)
    
    # Target proportions
    target_props = {c: (y == c).sum() / n_total for c in classes}
    
    # Collect deviations
    all_deviations = {c: [] for c in classes}
    group_integrity_violations = 0
    
    for train_idx, test_idx in splits:
        y_test = y[test_idx]
        n_test = len(y_test)
        
        # Check group integrity
        train_groups = set(groups[train_idx])
        test_groups = set(groups[test_idx])
        if train_groups.intersection(test_groups):
            group_integrity_violations += 1
        
        # Compute deviations
        for c in classes:
            actual_prop = (y_test == c).sum() / n_test if n_test > 0 else 0
            deviation = actual_prop - target_props[c]
            all_deviations[c].append(deviation)
    
    # Compute metrics
    metrics = {}
    
    # MAD per class
    for c in classes:
        metrics[f'mad_class_{c}'] = max(abs(d) for d in all_deviations[c])
    metrics['mad_max'] = max(metrics[f'mad_class_{c}'] for c in classes)
    
    # RMSD
    all_sq_devs = []
    for c in classes:
        all_sq_devs.extend([d**2 for d in all_deviations[c]])
    metrics['rmsd'] = np.sqrt(np.mean(all_sq_devs))
    
    # Weighted deviation (by rarity)
    weighted_sum = 0
    for c in classes:
        weight = 1 / target_props[c] if target_props[c] > 0 else 0
        weighted_sum += sum(abs(d) * weight for d in all_deviations[c])
    metrics['weighted_deviation'] = weighted_sum / (k * len(classes))
    
    # Group integrity
    metrics['group_integrity'] = 1.0 if group_integrity_violations == 0 else 0.0
    metrics['n_integrity_violations'] = group_integrity_violations
    
    return metrics
 
 
def print_quality_report(metrics: Dict[str, float]) -> None:
    """Print formatted quality report."""
    print("Stratification Quality Report")
    print("-" * 40)
    
    print(f"Group Integrity: {'✓ PASSED' if metrics['group_integrity'] == 1 else '✗ FAILED'}")
    if metrics['n_integrity_violations'] > 0:
        print(f"  ⚠️ {metrics['n_integrity_violations']} folds have group leakage!")
    
    print(f"
Class Deviation Metrics:")
    print(f"  Max Absolute Deviation: {metrics['mad_max']:.2%}")
    print(f"  RMSD: {metrics['rmsd']:.4f}")
    print(f"  Weighted Deviation: {metrics['weighted_deviation']:.4f}")
    
    # Quality rating
    if metrics['mad_max'] < 0.03:
        quality = "Excellent"
    elif metrics['mad_max'] < 0.05:
        quality = "Good"
    elif metrics['mad_max'] < 0.10:
        quality = "Acceptable"
    else:
        quality = "Poor"
    
    print(f"
Overall Quality: {quality}")

Acceptable Thresholds

For most applications, MAD < 5% is acceptable, MAD < 3% is good, and MAD < 1% is excellent. If you're seeing MAD > 10%, either your groups are too heterogeneous or you have too few groups. Consider increasing k (fewer groups per fold) or collecting more data.

Using StratifiedGroupKFold in Scikit-Learn

As of scikit-learn 1.0+, StratifiedGroupKFold is available natively. Let's explore its usage and compare with our custom implementation.

sklearn_stratified_group_kfold.py
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from sklearn.model_selection import StratifiedGroupKFold, cross_validate
from sklearn.ensemble import RandomForestClassifier
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
import numpy as np
 
def production_stratified_group_cv(
    model,
    X: np.ndarray,
    y: np.ndarray,
    groups: np.ndarray,
    n_splits: int = 5,
    random_state: int = 42,
    verbose: bool = True
):
    """
    Production-ready stratified group cross-validation.
    """
    # Create stratified group k-fold splitter
    sgkf = StratifiedGroupKFold(
        n_splits=n_splits,
        shuffle=True,
        random_state=random_state
    )
    
    # Create preprocessing pipeline
    pipeline = Pipeline([
        ('scaler', StandardScaler()),
        ('model', model)
    ])
    
    # Define scoring
    scoring = {
        'accuracy': 'accuracy',
        'f1': 'f1',
        'roc_auc': 'roc_auc',
        'precision': 'precision',
        'recall': 'recall'
    }
    
    # Perform cross-validation
    cv_results = cross_validate(
        pipeline, X, y,
        cv=sgkf,
        groups=groups,  # Required for group-aware CV
        scoring=scoring,
        return_train_score=True,
        n_jobs=-1
    )
    
    if verbose:
        # Print fold details
        print("=" * 60)
        print("STRATIFIED GROUP K-FOLD CROSS-VALIDATION")
        print("=" * 60)
        
        # Analyze each fold
        overall_pos_rate = y.mean()
        print(f"
Overall positive rate: {overall_pos_rate:.2%}")
        print(f"
Fold Analysis:")
        
        for fold_idx, (train_idx, test_idx) in enumerate(sgkf.split(X, y, groups)):
            test_pos_rate = y[test_idx].mean()
            n_test_groups = len(np.unique(groups[test_idx]))
            deviation = abs(test_pos_rate - overall_pos_rate)
            
            print(f"  Fold {fold_idx + 1}: n={len(test_idx):4d}, "
                  f"groups={n_test_groups:2d}, "
                  f"pos_rate={test_pos_rate:.2%} "
                  f"(deviation: {deviation:.2%})")
        
        print(f"
Metrics Summary:")
        for metric in scoring:
            test_scores = cv_results[f'test_{metric}']
            train_scores = cv_results[f'train_{metric}']
            print(f"  {metric:12s}: {test_scores.mean():.4f} ± {test_scores.std():.4f} "
                  f"(train: {train_scores.mean():.4f})")
    
    return cv_results
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    
    # Create realistic medical imaging dataset
    n_patients = 60
    
    X_list, y_list, groups_list = [], [], []
    
    for patient_id in range(n_patients):
        # Number of scans per patient
        n_scans = np.random.randint(5, 30)
        
        # Patient-level disease probability
        # Some patients are definitely diseased, some healthy
        if patient_id % 10 == 0:  # 10% of patients have disease
            patient_disease_prob = 0.8
        else:
            patient_disease_prob = 0.05
        
        # Generate scans
        X_p = np.random.randn(n_scans, 20)
        y_p = (np.random.random(n_scans) < patient_disease_prob).astype(int)
        
        X_list.append(X_p)
        y_list.append(y_p)
        groups_list.extend([f"patient_{patient_id:03d}"] * n_scans)
    
    X = np.vstack(X_list)
    y = np.concatenate(y_list)
    groups = np.array(groups_list)
    
    print(f"Dataset: {len(y)} scans from {n_patients} patients")
    print(f"Class distribution: {np.bincount(y)} (positive rate: {y.mean():.2%})")
    print()
    
    model = RandomForestClassifier(n_estimators=100, random_state=42)
    results = production_stratified_group_cv(model, X, y, groups)

Common Mistake: Forgetting groups=

StratifiedGroupKFold requires both y (for stratification) AND groups (for group separation). Omitting the groups= parameter in cross_validate() silently falls back to regular StratifiedKFold, losing group separation. Always verify with a diagnostic check.

Edge Cases and Special Challenges

Grouped stratification encounters several challenging edge cases:

Edge Cases and Solutions

•Homogeneous groups: Some groups have only one class (all positive or all negative). These are "all-or-nothing" for their class, making perfect balance impossible. Solution: Accept imperfect stratification; prioritize group integrity.
•Extreme imbalance: With 99:1 class ratio, minority class may exist in very few groups. Solution: Increase number of folds (smaller test sets can handle having 0 minority samples) or use stratified bootstrap instead.
•Variable group sizes: One group has 1000 samples, another has 10. Solution: Weight groups by size in the optimization objective, or use size-balanced group assignment as a secondary objective.
•Multi-label groups: Each sample has multiple labels, and groups have complex label combinations. Solution: Use iterative stratification adapted for groups.
•Continuous targets (regression): No natural classes for stratification. Solution: Bin the target into quantiles and stratify on binned labels.

Handling Homogeneous Groups Groups that are internally homogeneous (all samples have the same class) are the primary cause of imperfect stratification. Here's how to diagnose and handle them:

homogeneous_groups.py
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import numpy as np
from collections import Counter
 
def analyze_group_homogeneity(
    y: np.ndarray,
    groups: np.ndarray
) -> dict:
    """
    Analyze group-level class distributions to identify
    stratification constraints.
    """
    unique_groups = np.unique(groups)
    classes = np.unique(y)
    
    homogeneous_groups = {c: [] for c in classes}
    mixed_groups = []
    
    for group in unique_groups:
        mask = groups == group
        y_group = y[mask]
        unique_classes = np.unique(y_group)
        
        if len(unique_classes) == 1:
            # Homogeneous group
            homogeneous_groups[unique_classes[0]].append(group)
        else:
            # Mixed group
            mixed_groups.append({
                'group': group,
                'distribution': dict(Counter(y_group)),
                'n_samples': len(y_group)
            })
    
    # Compute stratifiability score
    # Lower = more constrained
    n_total = len(unique_groups)
    n_mixed = len(mixed_groups)
    stratifiability = n_mixed / n_total if n_total > 0 else 0
    
    return {
        'n_groups': len(unique_groups),
        'n_classes': len(classes),
        'homogeneous_groups': homogeneous_groups,
        'n_homogeneous': {c: len(gs) for c, gs in homogeneous_groups.items()},
        'mixed_groups': mixed_groups,
        'n_mixed': len(mixed_groups),
        'stratifiability_score': stratifiability,
        'recommendation': get_recommendation(stratifiability)
    }
 
 
def get_recommendation(stratifiability: float) -> str:
    """Get recommendation based on stratifiability score."""
    if stratifiability > 0.7:
        return "High stratifiability: Standard algorithms should work well."
    elif stratifiability > 0.4:
        return "Moderate stratifiability: Expect some deviation, but manageable."
    elif stratifiability > 0.2:
        return "Low stratifiability: Consider using more folds or fewer groups."
    else:
        return "Very low stratifiability: Consider binned target or relaxed constraints."
 
 
# Example usage
if __name__ == "__main__":
    np.random.seed(42)
    
    # Simulate varying homogeneity
    n_groups = 50
    groups_list = []
    y_list = []
    
    for g in range(n_groups):
        size = np.random.randint(10, 50)
        
        if g < 15:  # 30% pure positive
            y_g = np.ones(size)
        elif g < 35:  # 40% pure negative
            y_g = np.zeros(size)
        else:  # 30% mixed
            y_g = (np.random.random(size) < 0.3).astype(int)
        
        groups_list.extend([f"G{g:02d}"] * size)
        y_list.extend(y_g)
    
    groups = np.array(groups_list)
    y = np.array(y_list)
    
    analysis = analyze_group_homogeneity(y, groups)
    
    print("Group Homogeneity Analysis")
    print("-" * 40)
    print(f"Total groups: {analysis['n_groups']}")
    print(f"Homogeneous groups: {sum(analysis['n_homogeneous'].values())}")
    for c, count in analysis['n_homogeneous'].items():
        print(f"  Class {c}: {count} pure groups")
    print(f"Mixed groups: {analysis['n_mixed']}")
    print(f"Stratifiability score: {analysis['stratifiability_score']:.2f}")
    print(f"
Recommendation: {analysis['recommendation']}")

Best Practices for Grouped Stratification

Based on the theoretical and practical considerations discussed, here are best practices for production use:

Production Best Practices

•Always verify group integrity first — Before analyzing stratification quality, confirm no group leakage. Any leakage invalidates results entirely.
•Analyze group homogeneity before choosing k — If 80% of groups are homogeneous, you need more groups in each test fold for any minority representation.
•Use fewer folds for high homogeneity — With many pure groups, k=3 might achieve better stratification than k=5 because you have more flexibility in assignment.
•Report stratification metrics — Don't just run CV; report MAD and RMSD so readers understand the validity of your evaluation.
•Use multiple random seeds — Greedy algorithms are sensitive to initial ordering. Run with 5-10 seeds and average results.
•Consider weighted evaluation — If class proportions vary across folds, compute weighted averages using fold sizes as weights.
•Document inevitable deviations — If perfect stratification is impossible, document why and quantify the impact on interpretation.

Avoid

•Ignoring stratification quality
•Using high k with few groups
•Splitting groups for "better" stratification
•Treating imperfect stratification as failure

•Report MAD and RMSD metrics
•Choose k based on group count and homogeneity
•Preserve group integrity at all costs
•Accept and document deviation bounds

The Priority Order

When conflicts arise: 1) Group integrity (non-negotiable), 2) Minority class stratification (most impactful), 3) Majority class stratification (least constrained). Never sacrifice group integrity for better class balance—you'll get optimistic biased results.

Summary: Grouped Stratification

We've comprehensively covered the challenging problem of combining class stratification with group-based cross-validation. Here are the essential takeaways:

Key Takeaways

•Grouped stratification is NP-hard — Perfect class balance while preserving groups is often impossible; we seek good approximations.
•Groups are the assignment unit — We assign entire groups to folds, not individual samples, limiting flexibility.
•Homogeneous groups limit stratifiability — Groups with only one class are "all-or-nothing," making perfect balance impossible.
•Greedy algorithms work well in practice — Prioritize minority class balance and let majority class follow.
•Use quality metrics — MAD (max absolute deviation) and RMSD quantify stratification quality; always report them.
•sklearn has native support — StratifiedGroupKFold (scikit-learn 1.0+) handles this automatically.
•Group integrity is paramount — Never sacrifice group separation for better stratification; biased evaluation is worse than imperfect balance.

What's Next

You now understand how to handle both class imbalance and group structure. But there's a deeper issue lurking: data leakage. Even with perfect group separation, information can leak through preprocessing, feature engineering, or target encoding. The next page covers Data Leakage Prevention—a critical topic for trustworthy ML evaluation.

Grouped Stratification

The Dual Challenge

The Theoretical Challenge

Algorithmic Approaches

Measuring Stratification Quality

Using StratifiedGroupKFold in Scikit-Learn

Edge Cases and Special Challenges

Best Practices for Grouped Stratification

Summary: Grouped Stratification

There’s more to understand.

Grouped Stratification

The Dual Challenge

The Theoretical Challenge

Algorithmic Approaches

Measuring Stratification Quality

Using StratifiedGroupKFold in Scikit-Learn

Edge Cases and Special Challenges

Best Practices for Grouped Stratification

Summary: Grouped Stratification

There’s more to understand.