#!/usr/bin/env python3 """Money laundering for bias: dropping the protected attribute does not remove it. DDIA 2e Ch. 14 (Doing the Right Thing), section "Bias and Discrimination": "in racially segregated neighborhoods, a person's postal code or even their IP address is a strong predictor of race ... machine learning is like money laundering for bias." The obvious fix for a discriminatory model is "fairness through unawareness": just don't feed the model the protected attribute (race), and its decisions become fair. This script shows why that fails. We build a SEEDED SYNTHETIC loan dataset: - A protected binary attribute A (A=1 is the historically disadvantaged group). - A neutral-looking PROXY feature ("neighborhood", think postal code) that is strongly correlated with A -- segregation leaks the trait into geography. - Legitimate creditworthiness features (income, credit score, employment years) drawn INDEPENDENTLY of A, so equally-qualified applicants differ only by group membership. - A historically BIASED label: approval depends on the legitimate features MINUS a penalty applied to group A=1. The bias lives entirely in A. Then we train three classifiers on the biased labels and audit each with the disparate-impact ratio = selection_rate(A=1) / selection_rate(A=0) (the four-fifths / 0.8 rule: below 0.8 is legally a red flag): M1: WITH A -- uses the protected column directly. M2: WITHOUT A -- "fairness through unawareness". M3: WITHOUT A AND the proxy -- removes the trait AND its geographic shadow. Finally we train a recovery model M4 that predicts A from the non-A features and report its AUC -- if that is well above 0.5, the proxy really does carry the trait, which is exactly why M2 stays biased. Run it: uv run --python 3.12 --with scikit-learn --with numpy python3 proxy_bias.py (Seeded: numpy rng 42, every model random_state=42 -> metrics reproduce exactly.) """ import numpy as np from sklearn.ensemble import RandomForestClassifier from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn.metrics import roc_auc_score N = 20_000 SEED = 42 def sigmoid(z): return 1.0 / (1.0 + np.exp(-z)) def build_dataset(rng): # Protected attribute: A=1 is the historically disadvantaged group (~half). A = rng.binomial(1, 0.5, N) # Proxy: a "neighborhood" score (postal code). Segregation means the two # groups live in different places -- so the proxy strongly encodes A, even # though nobody labelled it "race". Legitimate lenders DO use geography. neighborhood = rng.normal(loc=3.0 * A, scale=1.2, size=N) # Legitimate creditworthiness features -- drawn INDEPENDENTLY of A, so the # two groups are equally qualified on the merits. Any gap in approvals is # therefore pure bias, not a real difference in risk. income = rng.normal(50, 15, N) credit_score = rng.normal(680, 60, N) employment_years = rng.exponential(5, N) # True creditworthiness: a function of the legitimate features only. merit = (0.05 * (income - 50) + 0.02 * (credit_score - 680) + 0.15 * (employment_years - 5)) # Historically biased label: approve on merit, MINUS a penalty for A=1. # The bias is injected through A alone -- the proxy is only *correlated* # with A, it is not in this formula. BIAS = 2.5 logit = 1.25 + merit - BIAS * A approved = rng.binomial(1, sigmoid(logit)) X = np.column_stack([income, credit_score, employment_years, neighborhood, A]) return X, approved, A def disparate_impact(pred, A): """selection_rate(disadvantaged A=1) / selection_rate(advantaged A=0).""" rate1 = pred[A == 1].mean() rate0 = pred[A == 0].mean() return rate1, rate0, rate1 / rate0 def train_and_audit(Xtr, ytr, Xte, Ate): clf = RandomForestClassifier(n_estimators=200, random_state=SEED, n_jobs=1) clf.fit(Xtr, ytr) pred = clf.predict(Xte) return disparate_impact(pred, Ate) def main(): rng = np.random.default_rng(SEED) X, y, A = build_dataset(rng) # Column layout: 0 income, 1 credit, 2 employment, 3 neighborhood(proxy), 4 A. IDX_PROXY, IDX_A = 3, 4 Xtr, Xte, ytr, yte, Atr, Ate = train_test_split( X, y, A, test_size=0.3, random_state=SEED, stratify=A) print("=" * 68) print("SYNTHETIC LOAN DATASET (seeded, deterministic)") print("=" * 68) print(f"{N:,} applicants; A=1 is the historically disadvantaged group.") print("Legitimate features (income, credit, employment) are drawn") print("INDEPENDENTLY of A -- the two groups are equally qualified.") print("The label carries historical bias: approval = merit - penalty*(A==1).\n") r1, r0, ratio = disparate_impact(y, A) print("Disparate impact in the HISTORICAL LABELS themselves:") print(f" approval rate A=1 (disadvantaged) = {r1:6.1%}") print(f" approval rate A=0 (advantaged) = {r0:6.1%}") print(f" disparate-impact ratio = {ratio:5.2f} " f"(four-fifths rule: below 0.80 is a red flag)\n") # ---- M1: WITH the protected attribute ---- r1, r0, ratio_with = train_and_audit(Xtr, ytr, Xte, Ate) print("=" * 68) print("M1 -- train WITH the protected attribute A") print("=" * 68) print(f" selection rate A=1 = {r1:6.1%} A=0 = {r0:6.1%}") print(f" disparate-impact ratio = {ratio_with:5.2f}\n") # ---- M2: WITHOUT A (fairness through unawareness) ---- keep = [c for c in range(X.shape[1]) if c != IDX_A] r1, r0, ratio_without = train_and_audit(Xtr[:, keep], ytr, Xte[:, keep], Ate) print("=" * 68) print("M2 -- train WITHOUT A ('fairness through unawareness': drop race)") print("=" * 68) print(f" selection rate A=1 = {r1:6.1%} A=0 = {r0:6.1%}") print(f" disparate-impact ratio = {ratio_without:5.2f} " f"<-- barely moved; still unfair\n") # ---- M3: WITHOUT A AND the proxy ---- keep2 = [c for c in range(X.shape[1]) if c not in (IDX_A, IDX_PROXY)] r1, r0, ratio_no_proxy = train_and_audit(Xtr[:, keep2], ytr, Xte[:, keep2], Ate) print("=" * 68) print("M3 -- train WITHOUT A AND WITHOUT the proxy (neighborhood)") print("=" * 68) print(f" selection rate A=1 = {r1:6.1%} A=0 = {r0:6.1%}") print(f" disparate-impact ratio = {ratio_no_proxy:5.2f} " f"<-- now above 0.80\n") # ---- M4: can we reconstruct A from the non-A features? ---- rec = LogisticRegression(max_iter=1000, random_state=SEED) rec.fit(Xtr[:, keep], Atr) # predict A from everything except A auc_all = roc_auc_score(Ate, rec.predict_proba(Xte[:, keep])[:, 1]) rec_proxy = LogisticRegression(max_iter=1000, random_state=SEED) rec_proxy.fit(Xtr[:, [IDX_PROXY]], Atr) # predict A from the proxy alone auc_proxy = roc_auc_score(Ate, rec_proxy.predict_proba(Xte[:, [IDX_PROXY]])[:, 1]) print("=" * 68) print("MECHANISM CHECK -- recover A from the non-protected features") print("=" * 68) print(f" predict A from ALL non-A features : AUC = {auc_all:5.2f}") print(f" predict A from the PROXY alone : AUC = {auc_proxy:5.2f}") print(" (0.50 = coin flip. Well above 0.50 => the trait is still in there.)\n") print("=" * 68) print("SUMMARY") print("=" * 68) print(f" disparate-impact ratio WITH A = {ratio_with:5.2f}") print(f" disparate-impact ratio WITHOUT A = {ratio_without:5.2f}") print(f" disparate-impact ratio WITHOUT A AND proxy = {ratio_no_proxy:5.2f}") print(f" A recovered from remaining features AUC = {auc_all:5.2f}") if __name__ == "__main__": main()