Post-processing Methods

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import numpy as np
from typing import Dict, Tuple, Optional
from scipy.optimize import minimize_scalar
 
class ThresholdOptimizer:
    """
    Post-processing fairness via group-specific thresholds.
    
    Supports demographic parity and equal opportunity constraints.
    """
    
    def __init__(self, fairness_criterion: str = 'demographic_parity'):
        """
        Args:
            fairness_criterion: 'demographic_parity' or 'equal_opportunity'
        """
        self.fairness_criterion = fairness_criterion
        self.thresholds_ = {}
        
    def fit(self, 
            scores: np.ndarray, 
            protected: np.ndarray, 
            labels: Optional[np.ndarray] = None,
            target_rate: Optional[float] = None) -> 'ThresholdOptimizer':
        """
        Learn group-specific thresholds to satisfy fairness criterion.
        
        Args:
            scores: Model probability outputs (n_samples,)
            protected: Protected attribute values (n_samples,)
            labels: True labels (required for equal_opportunity)
            target_rate: Target positive rate (if None, uses overall rate)
        """
        groups = np.unique(protected)
        
        if self.fairness_criterion == 'demographic_parity':
            # Find thresholds that equalize positive prediction rates
            if target_rate is None:
                # Use overall rate at default threshold 0.5
                target_rate = np.mean(scores >= 0.5)
            
            for group in groups:
                group_mask = protected == group
                group_scores = scores[group_mask]
                # Find threshold giving target_rate positive predictions
                self.thresholds_[group] = np.quantile(group_scores, 1 - target_rate)
                
        elif self.fairness_criterion == 'equal_opportunity':
            assert labels is not None, "Labels required for equal opportunity"
            
            # Find thresholds that equalize TPR among positive examples
            if target_rate is None:
                # Use overall TPR at threshold 0.5
                pos_mask = labels == 1
                target_rate = np.mean(scores[pos_mask] >= 0.5)
            
            for group in groups:
                group_mask = (protected == group) & (labels == 1)
                if group_mask.sum() == 0:
                    self.thresholds_[group] = 0.5
                    continue
                group_scores = scores[group_mask]
                self.thresholds_[group] = np.quantile(group_scores, 1 - target_rate)
        
        return self
    
    def predict(self, scores: np.ndarray, protected: np.ndarray) -> np.ndarray:
        """
        Apply group-specific thresholds to get fair predictions.
        
        Args:
            scores: Model probability outputs (n_samples,)
            protected: Protected attribute values (n_samples,)
            
        Returns:
            Binary predictions (n_samples,)
        """
        predictions = np.zeros(len(scores), dtype=int)
        
        for group, threshold in self.thresholds_.items():
            mask = protected == group
            predictions[mask] = (scores[mask] >= threshold).astype(int)
        
        return predictions
    
    def fit_predict(self, 
                    scores: np.ndarray, 
                    protected: np.ndarray,
                    labels: Optional[np.ndarray] = None,
                    target_rate: Optional[float] = None) -> np.ndarray:
        """Fit and predict in one step."""
        return self.fit(scores, protected, labels, target_rate).predict(scores, protected)
 
 
def find_optimal_target_rate(scores: np.ndarray,
                             protected: np.ndarray,
                             labels: np.ndarray,
                             fairness_criterion: str = 'demographic_parity') -> Tuple[float, float]:
    """
    Find the target rate that maximizes accuracy while satisfying fairness.
    
    Returns:
        (optimal_rate, best_accuracy)
    """
    def neg_accuracy(rate):
        optimizer = ThresholdOptimizer(fairness_criterion)
        preds = optimizer.fit_predict(scores, protected, labels, target_rate=rate)
        return -np.mean(preds == labels)
    
    result = minimize_scalar(neg_accuracy, bounds=(0.01, 0.99), method='bounded')
    return result.x, -result.fun
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    n = 3000
    
    # Biased model scores
    protected = np.random.binomial(1, 0.4, n)
    labels = np.random.binomial(1, 0.5, n)
    
    # Simulate biased model: higher scores for protected=0
    base_scores = 0.3 + 0.4 * labels + np.random.normal(0, 0.2, n)
    scores = base_scores - 0.2 * (protected == 1)  # Bias against group 1
    scores = np.clip(scores, 0, 1)
    
    print("Original (threshold=0.5):")
    orig_preds = (scores >= 0.5).astype(int)
    print(f"  P(Ŷ=1|A=0) = {np.mean(orig_preds[protected==0]):.3f}")
    print(f"  P(Ŷ=1|A=1) = {np.mean(orig_preds[protected==1]):.3f}")
    print(f"  Accuracy = {np.mean(orig_preds == labels):.3f}")
    
    # Apply fair post-processing
    optimizer = ThresholdOptimizer('demographic_parity')
    fair_preds = optimizer.fit_predict(scores, protected, labels)
    
    print("
After threshold optimization:")
    print(f"  P(Ŷ=1|A=0) = {np.mean(fair_preds[protected==0]):.3f}")
    print(f"  P(Ŷ=1|A=1) = {np.mean(fair_preds[protected==1]):.3f}")
    print(f"  Accuracy = {np.mean(fair_preds == labels):.3f}")
    print(f"  Thresholds: {optimizer.thresholds_}")

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import numpy as np
from scipy.optimize import linprog
from typing import Dict, Tuple
 
class EqualizedOddsPostProcessor:
    """
    Post-processing for equalized odds following Hardt et al. (2016).
    
    Learns a randomized prediction rule that satisfies equalized odds
    (equal TPR and FPR across groups) while minimizing error.
    """
    
    def __init__(self):
        self.mixing_rates_ = {}
        
    def fit(self, 
            predictions: np.ndarray, 
            protected: np.ndarray, 
            labels: np.ndarray) -> 'EqualizedOddsPostProcessor':
        """
        Learn mixing rates to achieve equalized odds.
        
        Args:
            predictions: Binary predictions from original model (0 or 1)
            protected: Binary protected attribute
            labels: True binary labels
        """
        groups = np.unique(protected)
        assert len(groups) == 2, "Binary protected attribute required"
        
        # Compute confusion matrix rates for each group
        rates = {}
        for a in groups:
            mask = protected == a
            for y in [0, 1]:
                y_mask = mask & (labels == y)
                if y_mask.sum() == 0:
                    rates[(a, y, 0)] = 0
                    rates[(a, y, 1)] = 0
                else:
                    rates[(a, y, 0)] = np.mean(predictions[y_mask] == 0)  # P(Ŷ=0|A=a,Y=y)
                    rates[(a, y, 1)] = np.mean(predictions[y_mask] == 1)  # P(Ŷ=1|A=a,Y=y)
        
        # For simplicity, we find thresholds that roughly equalize
        # Full LP solution would find optimal mixing probabilities
        
        # Target rates: average across groups
        target_tpr = np.mean([
            rates[(a, 1, 1)] for a in groups
        ])
        target_fpr = np.mean([
            rates[(a, 0, 1)] for a in groups
        ])
        
        # For each group, compute mixing probabilities
        for a in groups:
            current_tpr = rates[(a, 1, 1)]  # P(Ŷ=1|Y=1,A=a)
            current_fpr = rates[(a, 0, 1)]  # P(Ŷ=1|Y=0,A=a)
            
            # We need to adjust predictions to reach target rates
            # For positive labels (Y=1): need to reach target_tpr
            # For negative labels (Y=0): need to reach target_fpr
            
            self.mixing_rates_[a] = {
                'tpr_current': current_tpr,
                'tpr_target': target_tpr,
                'fpr_current': current_fpr,
                'fpr_target': target_fpr
            }
        
        return self
    
    def predict(self, 
                predictions: np.ndarray, 
                protected: np.ndarray,
                labels: Optional[np.ndarray] = None) -> np.ndarray:
        """
        Apply randomized post-processing to achieve equalized odds.
        
        Note: Full equalized odds requires knowing Y at prediction time,
        which is often not available. This implementation provides an
        approximation that uses predicted Y when actual Y is unavailable.
        """
        n = len(predictions)
        fair_predictions = predictions.copy()
        
        for a in np.unique(protected):
            mask = protected == a
            rates = self.mixing_rates_.get(a, None)
            if rates is None:
                continue
            
            # For fair equalized odds at prediction time,
            # we use stochastic prediction adjustment
            group_preds = predictions[mask]
            
            # Adjust positive predictions
            pos_mask = mask & (predictions == 1)
            if pos_mask.sum() > 0:
                # If we're over-predicting positive, flip some to negative
                current_rate = np.mean(group_preds == 1)
                target_rate = (rates['tpr_target'] + rates['fpr_target']) / 2
                if current_rate > target_rate:
                    flip_prob = (current_rate - target_rate) / current_rate
                    flip = np.random.rand(pos_mask.sum()) < flip_prob
                    fair_predictions[np.where(pos_mask)[0][flip]] = 0
            
            # Adjust negative predictions
            neg_mask = mask & (predictions == 0)
            if neg_mask.sum() > 0:
                current_rate = np.mean(group_preds == 0)
                target_neg_rate = 1 - (rates['tpr_target'] + rates['fpr_target']) / 2
                if current_rate > target_neg_rate:
                    flip_prob = (current_rate - target_neg_rate) / current_rate
                    flip = np.random.rand(neg_mask.sum()) < flip_prob
                    fair_predictions[np.where(neg_mask)[0][flip]] = 1
        
        return fair_predictions
 
 
def compute_equalized_odds_violation(predictions: np.ndarray,
                                      protected: np.ndarray,
                                      labels: np.ndarray) -> Dict[str, float]:
    """Compute equalized odds metrics."""
    groups = np.unique(protected)
    
    metrics = {}
    for a in groups:
        mask = protected == a
        pos_mask = mask & (labels == 1)
        neg_mask = mask & (labels == 0)
        
        tpr = np.mean(predictions[pos_mask]) if pos_mask.sum() > 0 else 0
        fpr = np.mean(predictions[neg_mask]) if neg_mask.sum() > 0 else 0
        metrics[f'TPR_group_{a}'] = tpr
        metrics[f'FPR_group_{a}'] = fpr
    
    metrics['TPR_gap'] = abs(metrics['TPR_group_0'] - metrics['TPR_group_1'])
    metrics['FPR_gap'] = abs(metrics['FPR_group_0'] - metrics['FPR_group_1'])
    
    return metrics
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    n = 3000
    
    protected = np.random.binomial(1, 0.5, n)
    labels = np.random.binomial(1, 0.5, n)
    
    # Biased predictions: higher TPR for group 0, higher FPR for group 1
    predictions = labels.copy()
    # Add noise
    flip = np.random.rand(n) < 0.2
    predictions[flip] = 1 - predictions[flip]
    # Add group bias
    predictions[(protected == 1) & (labels == 0)] = (
        np.random.rand(((protected == 1) & (labels == 0)).sum()) < 0.4
    ).astype(int)
    
    print("Original predictions:")
    metrics = compute_equalized_odds_violation(predictions, protected, labels)
    for k, v in metrics.items():
        print(f"  {k}: {v:.3f}")
    
    # Apply post-processing
    processor = EqualizedOddsPostProcessor()
    processor.fit(predictions, protected, labels)
    fair_predictions = processor.predict(predictions, protected)
    
    print("
After equalized odds post-processing:")
    metrics = compute_equalized_odds_violation(fair_predictions, protected, labels)
    for k, v in metrics.items():
        print(f"  {k}: {v:.3f}")

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import numpy as np
from sklearn.isotonic import IsotonicRegression
from sklearn.linear_model import LogisticRegression
from typing import Dict
 
class GroupSpecificCalibrator:
    """
    Post-processing that applies group-specific calibration.
    
    Ensures predicted probabilities are well-calibrated within each group,
    which is a form of fairness (equal meaning of probability across groups).
    """
    
    def __init__(self, method: str = 'isotonic'):
        """
        Args:
            method: 'isotonic' for non-parametric, 'platt' for logistic scaling
        """
        self.method = method
        self.calibrators_ = {}
        
    def fit(self, 
            scores: np.ndarray, 
            labels: np.ndarray, 
            protected: np.ndarray) -> 'GroupSpecificCalibrator':
        """
        Fit group-specific calibration functions.
        
        Args:
            scores: Model probability outputs (n_samples,)
            labels: True binary labels (n_samples,)
            protected: Protected attribute values (n_samples,)
        """
        for group in np.unique(protected):
            mask = protected == group
            group_scores = scores[mask]
            group_labels = labels[mask]
            
            if self.method == 'isotonic':
                calibrator = IsotonicRegression(
                    y_min=0.0, y_max=1.0, 
                    out_of_bounds='clip'
                )
                calibrator.fit(group_scores, group_labels)
                
            elif self.method == 'platt':
                calibrator = LogisticRegression()
                calibrator.fit(group_scores.reshape(-1, 1), group_labels)
                
            self.calibrators_[group] = calibrator
        
        return self
    
    def calibrate(self, 
                  scores: np.ndarray, 
                  protected: np.ndarray) -> np.ndarray:
        """
        Apply group-specific calibration to scores.
        
        Returns:
            Calibrated probabilities (n_samples,)
        """
        calibrated = np.zeros_like(scores)
        
        for group, calibrator in self.calibrators_.items():
            mask = protected == group
            group_scores = scores[mask]
            
            if self.method == 'isotonic':
                calibrated[mask] = calibrator.predict(group_scores)
            elif self.method == 'platt':
                calibrated[mask] = calibrator.predict_proba(
                    group_scores.reshape(-1, 1)
                )[:, 1]
        
        return calibrated
    
    def fit_calibrate(self, 
                      scores: np.ndarray, 
                      labels: np.ndarray, 
                      protected: np.ndarray) -> np.ndarray:
        """Fit and calibrate in one step."""
        return self.fit(scores, labels, protected).calibrate(scores, protected)
 
 
def expected_calibration_error(scores: np.ndarray, 
                                labels: np.ndarray, 
                                n_bins: int = 10) -> float:
    """
    Compute Expected Calibration Error (ECE).
    
    Lower is better. 0 means perfect calibration.
    """
    bin_boundaries = np.linspace(0, 1, n_bins + 1)
    ece = 0.0
    
    for i in range(n_bins):
        bin_mask = (scores >= bin_boundaries[i]) & (scores < bin_boundaries[i + 1])
        if bin_mask.sum() == 0:
            continue
        
        bin_accuracy = np.mean(labels[bin_mask])
        bin_confidence = np.mean(scores[bin_mask])
        bin_weight = bin_mask.sum() / len(scores)
        
        ece += bin_weight * abs(bin_accuracy - bin_confidence)
    
    return ece
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    n = 3000
    
    protected = np.random.binomial(1, 0.5, n)
    labels = np.random.binomial(1, 0.5, n)
    
    # Generate miscalibrated scores with group-specific miscalibration
    base_scores = 0.2 + 0.6 * labels + np.random.normal(0, 0.15, n)
    # Group 0: overconfident, Group 1: underconfident
    scores = base_scores.copy()
    scores[protected == 0] = np.clip(base_scores[protected == 0] * 1.3, 0, 1)
    scores[protected == 1] = np.clip(base_scores[protected == 1] * 0.7, 0, 1)
    
    print("Before calibration:")
    for a in [0, 1]:
        mask = protected == a
        ece = expected_calibration_error(scores[mask], labels[mask])
        print(f"  Group {a} ECE: {ece:.4f}")
    
    # Apply group-specific calibration
    calibrator = GroupSpecificCalibrator(method='isotonic')
    calibrated = calibrator.fit_calibrate(scores, labels, protected)
    
    print("
After group-specific calibration:")
    for a in [0, 1]:
        mask = protected == a
        ece = expected_calibration_error(calibrated[mask], labels[mask])
        print(f"  Group {a} ECE: {ece:.4f}")

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import numpy as np
from typing import Tuple
 
class RejectOptionClassifier:
    """
    Fairness-aware classification using reject option.
    
    Modifies predictions in the critical region (near decision boundary)
    to favor the underprivileged group, improving demographic parity.
    """
    
    def __init__(self, 
                 critical_width: float = 0.1,
                 threshold: float = 0.5):
        """
        Args:
            critical_width: Width of critical region (Δ)
            threshold: Classification threshold (τ)
        """
        self.critical_width = critical_width
        self.threshold = threshold
        self.underprivileged_group_ = None
        
    def fit(self, 
            scores: np.ndarray, 
            protected: np.ndarray,
            labels: np.ndarray = None) -> 'RejectOptionClassifier':
        """
        Identify the underprivileged group based on positive prediction rates.
        
        Args:
            scores: Model probability outputs
            protected: Protected attribute values (binary)
            labels: Optional, not used but kept for API consistency
        """
        groups = np.unique(protected)
        
        # Compute positive prediction rate for each group
        rates = {}
        for g in groups:
            mask = protected == g
            rates[g] = np.mean(scores[mask] >= self.threshold)
        
        # Underprivileged group has lower positive rate
        self.underprivileged_group_ = min(rates.keys(), key=lambda g: rates[g])
        
        return self
    
    def predict(self, 
                scores: np.ndarray, 
                protected: np.ndarray) -> np.ndarray:
        """
        Make fairness-adjusted predictions using reject option.
        
        Returns:
            Binary predictions with reject option applied
        """
        predictions = (scores >= self.threshold).astype(int)
        
        # Identify critical region
        low_bound = self.threshold - self.critical_width
        high_bound = self.threshold + self.critical_width
        
        in_critical = (scores >= low_bound) & (scores <= high_bound)
        
        # For underprivileged group in critical region: favor positive
        underprivileged_critical = in_critical & (protected == self.underprivileged_group_)
        predictions[underprivileged_critical & (scores >= low_bound)] = 1
        
        # For privileged group in critical region: favor negative
        privileged_critical = in_critical & (protected != self.underprivileged_group_)
        predictions[privileged_critical & (scores <= high_bound)] = 0
        
        return predictions
    
    def fit_predict(self, 
                    scores: np.ndarray, 
                    protected: np.ndarray,
                    labels: np.ndarray = None) -> np.ndarray:
        """Fit and predict in one step."""
        return self.fit(scores, protected, labels).predict(scores, protected)
 
 
def analyze_critical_region(scores: np.ndarray,
                            protected: np.ndarray,
                            labels: np.ndarray,
                            threshold: float = 0.5,
                            width: float = 0.1) -> dict:
    """
    Analyze the composition and properties of the critical region.
    """
    low = threshold - width
    high = threshold + width
    
    in_critical = (scores >= low) & (scores <= high)
    
    results = {
        'critical_fraction': np.mean(in_critical),
        'critical_count': in_critical.sum(),
    }
    
    for a in np.unique(protected):
        mask = (protected == a) & in_critical
        results[f'group_{a}_in_critical'] = mask.sum()
        if mask.sum() > 0:
            results[f'group_{a}_critical_positive_rate'] = np.mean(labels[mask])
    
    return results
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    n = 3000
    
    protected = np.random.binomial(1, 0.5, n)
    labels = np.random.binomial(1, 0.5, n)
    
    # Biased scores
    base = 0.3 + 0.4 * labels + np.random.normal(0, 0.15, n)
    scores = np.clip(base - 0.15 * protected, 0, 1)  # Bias against group 1
    
    print("Original predictions (threshold=0.5):")
    orig = (scores >= 0.5).astype(int)
    print(f"  P(Ŷ=1|A=0) = {np.mean(orig[protected==0]):.3f}")
    print(f"  P(Ŷ=1|A=1) = {np.mean(orig[protected==1]):.3f}")
    print(f"  Accuracy = {np.mean(orig == labels):.3f}")
    
    # Analyze critical region
    print("
Critical region analysis:")
    analysis = analyze_critical_region(scores, protected, labels, width=0.15)
    for k, v in analysis.items():
        print(f"  {k}: {v}")
    
    # Apply reject option
    roc = RejectOptionClassifier(critical_width=0.15)
    fair_preds = roc.fit_predict(scores, protected, labels)
    
    print("
After reject option classification:")
    print(f"  P(Ŷ=1|A=0) = {np.mean(fair_preds[protected==0]):.3f}")
    print(f"  P(Ŷ=1|A=1) = {np.mean(fair_preds[protected==1]):.3f}")
    print(f"  Accuracy = {np.mean(fair_preds == labels):.3f}")

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import numpy as np
from typing import List, Tuple
 
class FairTopKSelector:
    """
    Select top-k items while ensuring fair representation of groups.
    
    Implements a simple greedy algorithm that alternates between groups
    to achieve proportional representation in the selected set.
    """
    
    def __init__(self, k: int, representation: str = 'proportional'):
        """
        Args:
            k: Number of items to select
            representation: 'proportional' (match population) or 'equal'
        """
        self.k = k
        self.representation = representation
        
    def select(self, 
               scores: np.ndarray, 
               protected: np.ndarray,
               population_weights: dict = None) -> np.ndarray:
        """
        Select top-k items with fair representation.
        
        Args:
            scores: Item scores (higher = better)
            protected: Group membership for each item
            population_weights: Optional target proportions per group
            
        Returns:
            Indices of selected items
        """
        n = len(scores)
        groups = np.unique(protected)
        
        # Compute target counts per group
        if self.representation == 'equal':
            targets = {g: self.k // len(groups) for g in groups}
            # Distribute remainder
            remainder = self.k % len(groups)
            for i, g in enumerate(groups):
                if i < remainder:
                    targets[g] += 1
        else:  # proportional
            if population_weights is None:
                population_weights = {
                    g: np.mean(protected == g) for g in groups
                }
            targets = {
                g: int(np.round(self.k * population_weights[g])) 
                for g in groups
            }
            # Adjust to sum to k
            diff = self.k - sum(targets.values())
            if diff > 0:
                # Add to largest group
                largest = max(targets, key=lambda g: targets[g])
                targets[largest] += diff
            elif diff < 0:
                # Remove from largest group
                largest = max(targets, key=lambda g: targets[g])
                targets[largest] += diff
        
        # Sort each group by score
        sorted_by_group = {
            g: np.argsort(-scores[protected == g])
            for g in groups
        }
        group_indices = {
            g: np.where(protected == g)[0]
            for g in groups
        }
        
        # Greedy selection: pick top from each group until targets met
        selected = []
        counts = {g: 0 for g in groups}
        pointers = {g: 0 for g in groups}
        
        while len(selected) < self.k:
            # Find group with most remaining quota
            remaining = {
                g: targets[g] - counts[g] 
                for g in groups 
                if pointers[g] < len(sorted_by_group[g])
            }
            
            if not remaining:
                break
            
            # Pick item from group with most slots to fill
            best_group = max(remaining, key=lambda g: remaining[g])
            
            item_local_idx = sorted_by_group[best_group][pointers[best_group]]
            item_global_idx = group_indices[best_group][item_local_idx]
            
            selected.append(item_global_idx)
            counts[best_group] += 1
            pointers[best_group] += 1
        
        return np.array(selected)
 
 
def compute_ranking_fairness(selected_indices: np.ndarray,
                              scores: np.ndarray,
                              protected: np.ndarray) -> dict:
    """Compute fairness metrics for top-k selection."""
    groups = np.unique(protected)
    n_total = len(scores)
    k = len(selected_indices)
    
    metrics = {}
    
    # Representation in selection vs population
    for g in groups:
        pop_rate = np.mean(protected == g)
        sel_rate = np.mean(protected[selected_indices] == g)
        metrics[f'group_{g}_population_rate'] = pop_rate
        metrics[f'group_{g}_selection_rate'] = sel_rate
        metrics[f'group_{g}_representation_ratio'] = sel_rate / pop_rate if pop_rate > 0 else 0
    
    # Average score of selected by group
    for g in groups:
        sel_group = selected_indices[protected[selected_indices] == g]
        if len(sel_group) > 0:
            metrics[f'group_{g}_avg_score_selected'] = np.mean(scores[sel_group])
    
    return metrics
 
 
# Demonstration
if __name__ == "__main__":
    np.random.seed(42)
    n = 500
    k = 50
    
    # Candidates with biased scores
    protected = np.random.binomial(1, 0.4, n)  # 40% in group 1
    
    # True merit (unbiased)
    true_merit = np.random.normal(5, 1, n)
    
    # Observed scores (biased against group 1)
    scores = true_merit - 0.5 * protected + np.random.normal(0, 0.3, n)
    
    print("Naive top-k selection:")
    naive_top_k = np.argsort(-scores)[:k]
    naive_metrics = compute_ranking_fairness(naive_top_k, scores, protected)
    for key, val in naive_metrics.items():
        print(f"  {key}: {val:.3f}")
    
    print("
Fair top-k selection (proportional):")
    selector = FairTopKSelector(k=k, representation='proportional')
    fair_top_k = selector.select(scores, protected)
    fair_metrics = compute_ranking_fairness(fair_top_k, scores, protected)
    for key, val in fair_metrics.items():
        print(f"  {key}: {val:.3f}")