12. Bias Detection

Bias detection identifies systematic distortions in model outputs. Effective detection requires both automated metrics and qualitative analysis, since automated scores can be gamed or miss context-dependent biases.

Demographic Parity and Equalized Odds

Statistical fairness metrics compare model behavior across demographic groups.

import numpy as np

def demographic_parity_difference(
    predictions_by_group, group_labels
):
    """Compute demographic parity: equal positive rate across groups."""
    group_rates = {}
    for group_id in np.unique(group_labels):
        mask = group_labels == group_id
        group_rates[group_id] = predictions_by_group[mask].mean()
    
    rates = list(group_rates.values())
    return max(rates) - min(rates)


def equalized_odds_difference(
    predictions_by_group, group_labels, true_labels
):
    """Equalized odds: equal true positive AND false positive rates."""
    differences = {}
    
    for metric_name, metric_func in [
        ('TPR', lambda p, t: (p[t==1].mean())),
        ('FPR', lambda p, t: (p[t==0].mean()))
    ]:
        group_rates = {}
        for group_id in np.unique(group_labels):
            mask = group_labels == group_id
            group_rates[group_id] = metric_func(
                predictions_by_group[mask], true_labels[mask]
            )
        rates = list(group_rates.values())
        differences[metric_name] = max(rates) - min(rates)
    
    return differences

Embedding Bias Measurement

Word embeddings encode societal biases present in training data. The classic WEAT test measures differential association of target word sets with attribute word sets.

def weat_effect_size(target_x, target_y, attribute_a, attribute_b, embeddings):
    """Compute WEAT effect size for embedding bias."""
    def mean_cos_sim(words, attribute_set):
        sims = []
        for w1 in words:
            for w2 in attribute_set:
                sims.append(cosine_similarity(embeddings[w1], embeddings[w2]))
        return np.mean(sims)
    
    def diff_means(words):
        return mean_cos_sim(words, attribute_a) - mean_cos_sim(words, attribute_b)
    
    total_diff = diff_means(target_x) - diff_means(target_y)
    std_diff = np.std([
        diff_means([w]) for w in list(target_x) + list(target_y)
    ])
    
    return total_diff / std_diff

Local verification checkpoint

Run the smallest example from this chapter in a local workspace and record the package version, runtime, data path, and observed output. If the result depends on model size, vector count, CPU/GPU backend, or available memory, note that constraint beside the exercise so the lesson remains reproducible.