Technical Summary: Auditing Discriminatory Patterns in Mortgage Lending Through Association Rules and Fair Binning

Problem Statement

Mortgage lending in the United States exhibits persistent racial and gender disparities. While prior research has focused on auditing model-level bias or constructing fair classifiers, this paper investigates whether upstream data management operations, specifically attribute binning, amplify these disparities. Standard equal-frequency binning of numeric attributes (e.g., income) can create bins with skewed demographic compositions, potentially distorting downstream pattern mining. The authors ask: Does fairness-aware binning change the discriminatory patterns mined from lending data?

The study utilizes the HMDA 2023 dataset (Home Mortgage Disclosure Act), a rich public source containing over 10 million records annually, focusing on the Chicago metropolitan area.

Methodology

The authors propose a three-stage pipeline to audit discriminatory patterns:

1. Data Cleaning and Binning

• Data Source: 103,481 cleaned mortgage applications from the Chicago-Naperville-Elgin Metropolitan Division (filtered from the national HMDA 2023 snapshot).
• Preprocessing: The pipeline filters for originated and denied loans, removes records with missing demographic data, casts financial fields, and clips income outliers (0.5th–99.5th percentile).
• Binning Strategies:
  • Standard Equal-Frequency Binning: Divides numeric attributes (income, loan amount) into $k=5$ buckets with approximately equal counts.
  • $\epsilon$-Biased Fair Binning: Implements the Divide-and-Conquer (D&C) algorithm proposed by Asudeh et al. [1]. This algorithm seeks to bound the demographic deviation within each bin to at most $\epsilon$. It minimizes the "Price of Fairness" (PoF), defined as the deviation of bin sizes from equal frequency.

2. Association Rule Mining (FP-Growth)

• Technique: FP-Growth is used to mine frequent itemsets and association rules predicting loan denial.
• Input: Applications are converted into transactions of 11 categorical items (e.g., race, sex, income bin, DTI category, outcome).
• Goal: Compare the rule sets generated under standard vs. fair binning to identify if fairness constraints alter the explicit discriminatory patterns (e.g., rules where race is an antecedent).
• Parameters: Minimum support of 0.10, minimum confidence of 0.50, minimum lift of 1.0.

3. Clustering and Disparate Impact Audit

• Clustering: K-Means clustering is applied to four financial features (income, loan amount, DTI, combined loan-to-value ratio) to group applicants by financial profile. Interest rates are excluded to avoid filtering out denied loans.
• Audit: Within each cluster, the Disparate Impact Ratio (DIR) is calculated for demographic groups (race, ethnicity, sex) against a reference group.
• Metric: A DIR below 0.80 (the "four-fifths rule") indicates disparate impact. This approach isolates discrimination that cannot be explained by legitimate financial risk factors captured in the clusters.

Key Results

1. Binning Bias and Feasibility

• Standard Binning: Produces a 9.63% racial bias in income discretization, consistent with prior findings (8–10%).
• Fair Binning Feasibility: With seven race groups, the $\epsilon$-biased algorithm is infeasible at tight thresholds ($\epsilon=0.03$). It only succeeds at $\epsilon=0.08$ for income and $\epsilon=0.06$ for loan amount.
• Price of Fairness (PoF): Achieving fairness at these thresholds incurs a high cost, with bin sizes deviating significantly from equal frequency (PoF of 29.4% for income and 23.5% for loan amount).

2. Association Rule Mining (FP-Growth)

• Dominant Predictor: High debt-to-income ratio (DTI) is the primary predictor of denial (67.2% confidence, 2.81 lift).
• Rule Consistency: The top denial rules are identical under both standard and fair binning regimes.
• Absence of Explicit Bias: No rules with race, sex, or ethnicity as antecedents met the 10% support threshold. The authors note this does not imply an absence of bias; rather, racial bias operates indirectly through correlated financial features (e.g., Black applicants have lower average incomes, placing them in higher-risk bins).

3. Clustering and Disparate Impact

• Cluster Profiles: Five clusters were identified, ranging from debt-overloaded applicants (79% denial) to affluent applicants (11% denial).
• Disparate Impact Findings: While FP-Growth found no explicit racial rules, the K-Means + DIR audit flagged 10 out of 45 cluster-group pairs as showing disparate impact (DIR < 0.80).
• Specific Findings:
  • All flagged pairs involved race.
  • In Cluster 3 (financially similar group: avg income $104K, DTI 34.5), Black applicants faced a 44.8% denial rate compared to 20.3% for White applicants (DIR = 0.693).
  • The mean DIR for race-based audits was 0.814, whereas ethnicity and sex audits showed no systematic disparate impact (Mean DIRs of 0.932 and 1.094, respectively).

Contributions and Significance

The paper makes the following contributions:

1. Validation of Upstream Bias: It confirms that standard data preprocessing (binning) introduces measurable racial bias (9.63%) in HMDA data, validating the relevance of unbiased binning problems in lending contexts.
2. Feasibility Constraints of Multi-Group Fairness: It demonstrates that while $\epsilon$-biased binning works for binary groups, applying it to seven race groups drastically reduces the set of feasible solutions and incurs a high Price of Fairness, suggesting practical limitations for multi-group fairness in data discretization.
3. Complementary Auditing Approaches: The study highlights that FP-Growth and Clustering offer complementary insights:
   • FP-Growth identifies dominant denial factors (DTI) across the population but may miss indirect bias due to support thresholds.
   • Clustering combined with DIR audits reveals systemic disparate impact that persists even among financially similar applicants, uncovering discrimination that standard rule mining might overlook.
4. Empirical Evidence of Indirect Bias: The results suggest that racial bias in mortgage lending often manifests indirectly through correlated financial distributions (income/DTI) rather than as explicit, high-support rules involving protected attributes.

Limitations

The authors acknowledge several limitations:

• Missing Credit Scores: HMDA data lacks credit scores, a primary lending factor, meaning the clustering cannot fully separate discrimination from legitimate risk.
• Support Thresholds: The 10% support threshold for FP-Growth may be too high to capture minority-group patterns; lowering it risks spurious results.
• Geographic Scope: The analysis is limited to the Chicago metropolitan area.
• Algorithmic Assumptions: K-Means assumes spherical clusters of similar size, which may not perfectly fit the data's asymmetry (cluster sizes ranging from 3,500 to 48,000).