Evolutionary Rule Extraction from Corporate Default Prediction Models

Technical Summary: Evolutionary Rule Extraction from Corporate Default Prediction Models

Problem Statement
Small and medium-sized enterprises (SMEs) constitute the majority of firms in most economies but face significant financial constraints and vulnerability to distress. Predicting SME default is critical for financial institutions and policymakers. While machine learning (ML) has improved predictive performance in credit risk modeling compared to traditional econometric methods, the "black box" nature of complex models raises concerns regarding transparency and regulatory compliance. Existing explainable AI (XAI) approaches often focus on feature attribution rather than reconstructing the underlying decision logic, and many rule-extraction methods are not fully model-agnostic or have only been tested in synthetic, low-dimensional settings. There is a need for frameworks that balance high predictive accuracy with interpretable, economically meaningful decision rules in high-dimensional, imbalanced financial data.

Methodology
The study utilizes a panel of 50,718 Italian SMEs from 2015 to 2024, comprising 6,695 defaulted firms and 44,023 active firms. The dataset includes firm-level accounting variables (balance sheet and income statement), structural characteristics, and macroeconomic/contextual indicators (sectoral default rates, regional GDP, inflation). The data is structured as an unbalanced panel with a one-year-ahead prediction target to prevent look-ahead bias.

The methodology proceeds through four stages:

1. Data Preprocessing: The raw data is transformed into a firm-year panel. Financial ratios are capped and log-transformed to handle skewness. The dataset is split into training (70%), validation (20%), and test (10%) sets using stratified sampling at the firm level to preserve class proportions (approx. 1.4% default rate).
2. Model Estimation: Four classifiers are trained: Logistic Regression (benchmark), Random Forest, XGBoost, and Multi-Layer Perceptron (MLP). Performance is evaluated using Balanced Accuracy and Precision-Recall Area Under the Curve (PR-AUC) to address class imbalance. Hyperparameters are optimized on the validation set.
3. Rule Extraction (DEXiRE-EVO): The study introduces DEXiRE-EVO, a novel evolutionary rule extraction framework. It extends the DEXiRE pipeline to be model-agnostic, allowing application to tree-based models like XGBoost. The framework employs a multi-objective evolutionary optimization (NSGA-II algorithm) guided by the Contextual Importance and Utility (CIU) method.
   • Objective 1 (Fidelity): Maximize the rule set's ability to replicate the black-box model's predictions (measured by Balanced Accuracy).
   • Objective 2 (CIU Alignment): Maximize the semantic consistency between variables in the extracted rules and their contextual importance as estimated by CIU.
   • The process evolves a population of decision rules (conjunctions of predicates) to approximate the model's behavior, selecting Pareto-optimal solutions that balance fidelity and interpretability.
4. Analysis: The extracted rules are analyzed for economic plausibility, linking logical structures to financial vulnerability patterns.

Key Contributions

• Large-Scale Empirical Evaluation: The paper provides a comprehensive comparison of traditional and ML models on a large, realistic, and highly imbalanced dataset of Italian SMEs, addressing the scarcity of such systematic comparisons in high-dimensional settings.
• Novel Framework (DEXiRE-EVO): It proposes a model-agnostic, evolutionary approach to rule extraction that integrates CIU into the fitness function. This ensures that the extracted rules are not only faithful to the original model but also aligned with the contextual relevance of features.
• Integration of Macro-Context: The study evaluates the impact of including macroeconomic and sectoral variables, as well as historical dynamics (via exponentially weighted moving averages), on both predictive performance and feature importance.

Results

• Predictive Performance: XGBoost significantly outperformed the Logistic Regression benchmark, achieving a Balanced Accuracy of 0.901 and a PR-AUC of 0.429, compared to 0.551 and 0.016 for Logistic Regression, respectively. Random Forest and MLP also showed strong performance.
• Impact of Data Structure:
  • Including macroeconomic and sectoral variables (Dataset D1) improved performance over models using only firm-level ratios (Dataset D2), increasing Balanced Accuracy from 0.879 to 0.901 and PR-AUC from 0.366 to 0.429.
  • Adding historical dynamics (Dataset D3) further improved ranking performance (PR-AUC 0.449) with minimal change in Balanced Accuracy.
• Explainability Performance: DEXiRE-EVO demonstrated superior performance over the original DEXiRE framework, achieving higher fidelity (mean 0.856 vs. 0.832) and significantly better CIU alignment (mean 0.684 vs. 0.444).
• Extracted Rules: The evolutionary process identified consistent, economically meaningful patterns associated with default risk, including:
  • Weak internal liquidity generation (low cash flow to assets).
  • Erosion of internal capital (negative retained earnings).
  • High leverage (high debt-to-equity).
  • Operational inefficiency (low turnover ratios).
  • The rules highlighted that these signals are particularly informative for firms beyond their early life cycle and that sectoral distress and historical volatility are critical contextual factors.

Significance and Claims
The paper claims that combining ML with evolutionary rule extraction via DEXiRE-EVO offers a viable path to resolving the trade-off between predictive accuracy and interpretability in credit risk modeling. By generating transparent, human-readable decision rules that maintain high fidelity to complex models and align with contextual feature importance, the approach supports more transparent, data-driven decision-making. The study emphasizes that the extracted rules reflect coherent economic mechanisms (e.g., liquidity constraints, capital erosion) rather than arbitrary statistical correlations, thereby enhancing trust and regulatory compliance in financial environments. The authors note that while the framework is promising, future work should explore explicit time-series modeling for richer financial trajectories and apply the method to private credit markets where soft information is scarce.