pith. sign in

arxiv: 2605.29478 · v1 · pith:BBX3ZWEQnew · submitted 2026-05-28 · 💻 cs.NE · cs.AI

Evolutionary Rule Extraction from Corporate Default Prediction Models

Desir\`e Fabbretti , Matteo Pasquino , Elia Pacioni , Caterina Lucarelli , Davide Calvaresi This is my paper

Pith reviewed 2026-06-29 00:03 UTC · model grok-4.3

classification 💻 cs.NE cs.AI
keywords SME default predictionmachine learningexplainable AIevolutionary rule extractioncredit risk modelingfinancial distresslogistic regressionItalian SMEs
0
0 comments X

The pith

ML models outperform logistic regression for SME default prediction and evolutionary rules reveal key financial distress patterns.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that machine learning classifiers significantly improve upon traditional logistic regression in predicting defaults among small and medium enterprises using a large Italian dataset. It introduces DEXiRE-EVO, an evolutionary method to extract human-readable rules from these models while preserving performance. A reader would care because SMEs drive most economies yet face high distress risk, and regulators demand interpretable credit models. The rules point to liquidity, capital, leverage, and efficiency as central factors, plus macro effects. This combination aims to deliver both accuracy and transparency in financial risk assessment.

Core claim

Using data from over 50,000 Italian SMEs from 2015 to 2024, ML models achieve better balanced accuracy and PR-AUC than logistic regression. The DEXiRE-EVO framework applies multi-objective optimization guided by Contextual Importance and Utility to derive rules that identify economically meaningful predictors of distress, including weak liquidity generation, internal capital erosion, high leverage, operational inefficiency, macroeconomic conditions, and persistence of instability.

What carries the argument

DEXiRE-EVO, an evolutionary rule extraction framework that integrates multi-objective optimization with the Contextual Importance and Utility (CIU) method to generate interpretable rules from ML models.

If this is right

  • ML classifiers deliver higher predictive performance than the logistic regression benchmark.
  • Extracted rules associate SME distress with weak liquidity, capital erosion, leverage, and inefficiency.
  • Contextual macroeconomic conditions and financial instability persistence help flag high-risk firms.
  • The approach supports more transparent decision-making in credit risk.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such rules could be directly used by lenders to explain decisions to borrowers or regulators.
  • The method might generalize to default prediction in other sectors or countries if the evolutionary search remains stable.
  • Testing the rules on out-of-sample data from post-2024 periods would confirm their robustness beyond the training panel.

Load-bearing premise

The extracted rules reflect genuine economic drivers of default rather than spurious correlations specific to the Italian SME panel or the CIU-guided search process.

What would settle it

If the rules fail to identify high-risk firms in a held-out test set from a later period or different jurisdiction at rates better than chance or simple benchmarks.

Figures

Figures reproduced from arXiv: 2605.29478 by Caterina Lucarelli, Davide Calvaresi, Desir\`e Fabbretti, Elia Pacioni, Matteo Pasquino.

Figure 1
Figure 1. Figure 1: Organization of the methodological framework. S1a,b: Data collection & inspection: The empirical analysis relies on firm￾level data drawn from AIDA (Bureau van Dijk —link), which provides account￾ing and legal information based on Italian firms’ statutory financial statements. The unit of observation is the firm-year, and the dataset is organized as an unbalanced panel covering the period 2015-2024, subjec… view at source ↗
Figure 2
Figure 2. Figure 2: Feature importance ranking for dataset configuration D1. 0.0 0.2 0.4 0.6 0.8 1.0 Importance Age Log Total Assets Interest Exp./Tot.Debt Current Ratio Retained/Tot.Assets Turnover Ratio Leverage NWC/Tot.Assets Cash Flow/Tot.Assets Debt/Equity Ratio Features [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Feature importance ranking for dataset configuration D2. 0.0 0.2 0.4 0.6 0.8 1.0 Importance Age Log Tot.Assets Annual Inflation Rate Turnover Ratio Region GDP Growth Rate Sector Default Rate Cash Flow/Tot.Assets EBIT/Interest Exp. (EWM std) ROA (EWM std) Log Sales Features [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Feature importance ranking for dataset configuration D3 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
read the original abstract

Small and medium-sized enterprises (SMEs) represent the majority of firms in most economies and often face financial constraints and higher vulnerability to financial distress. Predicting SME default is therefore crucial for financial institutions, policymakers, and researchers. Recent advances in machine learning (ML) have improved predictive performance in credit risk modeling. Yet, the limited interpretability of complex models raises concerns regarding transparency and regulatory compliance. This study investigates SME's default predictors and applies explainable artificial intelligence (XAI) techniques to them. Using a panel of 50,718 Italian SME over the period 2015-2024, we compare traditional econometric approaches with several ML classifiers. The empirical results show that ML models significantly outperform the traditional logistic regression benchmark in terms of Balanced Accuracy and PR-AUC. To address the interpretability challenge, we introduce DEXiRE-EVO, a novel evolutionary rule extraction framework that combines multi-objective optimization with the Contextual Importance and Utility (CIU) explainability method. The extracted rules reveal economically meaningful patterns associated with SME financial distress, highlighting the roles of weak internal liquidity generation, internal capital erosion, high leverage, and operational inefficiency. Additionally, contextual macroeconomic conditions and the persistence of financial instability contribute to identifying high-risk firms. In general, the results show that combining ML with evolutionary rule extraction can improve both predictive performance and interpretability in credit risk modeling, thus supporting more transparent, data-driven decision-making in financial environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper compares ML classifiers to logistic regression for SME default prediction on a 50,718-firm Italian panel (2015-2024), reporting superior Balanced Accuracy and PR-AUC for ML models. It introduces DEXiRE-EVO, a multi-objective evolutionary rule-extraction framework that integrates CIU to produce rules claimed to be economically meaningful (weak liquidity, capital erosion, high leverage, operational inefficiency, plus macro and persistence effects).

Significance. If the extracted rules can be shown to be faithful approximations of the black-box models with stability across time folds and not post-hoc artifacts, the work would strengthen the case for interpretable ML in credit-risk applications where regulatory transparency is required.

major comments (2)
  1. [Abstract, §4] Abstract and §4 (results): the central claim that DEXiRE-EVO rules are 'economically meaningful' rests on qualitative interpretation alone; no fidelity metric (e.g., agreement with black-box predictions on held-out data), no stability across temporal folds or subsamples, and no comparison to simpler rule baselines are reported, leaving open the possibility that the liquidity/leverage patterns are search artifacts or panel-specific correlations.
  2. [§3.2] §3.2 (DEXiRE-EVO description): the multi-objective evolutionary search is presented without quantitative details on how CIU is embedded in the fitness function or how rule complexity is penalized; without these, it is impossible to assess whether the reported rules are the result of genuine optimization or post-selection interpretation.
minor comments (1)
  1. [Table 1] Table 1 (dataset description): the panel construction (firm-year observations, handling of missing values, default definition) is only sketched; explicit counts of defaults per year and any macroeconomic covariate sources would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which identify key areas where additional quantitative validation can strengthen the interpretability claims. We address each major comment below and will incorporate the suggested analyses in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract, §4] Abstract and §4 (results): the central claim that DEXiRE-EVO rules are 'economically meaningful' rests on qualitative interpretation alone; no fidelity metric (e.g., agreement with black-box predictions on held-out data), no stability across temporal folds or subsamples, and no comparison to simpler rule baselines are reported, leaving open the possibility that the liquidity/leverage patterns are search artifacts or panel-specific correlations.

    Authors: We agree that the current manuscript relies primarily on qualitative economic interpretation of the extracted rules. To address this, the revised version will report fidelity metrics (e.g., rule-model agreement on held-out data), stability of rules across temporal cross-validation folds, and comparisons against simpler baselines such as standard decision-tree rule extraction and single-objective genetic algorithms. These additions will provide quantitative support that the reported patterns reflect genuine model behavior rather than artifacts. revision: yes

  2. Referee: [§3.2] §3.2 (DEXiRE-EVO description): the multi-objective evolutionary search is presented without quantitative details on how CIU is embedded in the fitness function or how rule complexity is penalized; without these, it is impossible to assess whether the reported rules are the result of genuine optimization or post-selection interpretation.

    Authors: We acknowledge that the current description of DEXiRE-EVO lacks explicit quantitative specifications. The revised manuscript will include the precise formulation of the multi-objective fitness function, detailing how CIU importance and utility scores are incorporated (including any weighting scheme), the exact penalty term applied to rule complexity (e.g., number of antecedents or total length), and the Pareto-front selection criteria. This will allow readers to evaluate the optimization process directly. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation chain is self-contained against external benchmarks

full rationale

The abstract and summary present a comparison of ML classifiers against a logistic regression benchmark on an external 50k-firm panel, followed by introduction of DEXiRE-EVO (multi-objective evolutionary search + CIU) whose outputs are interpreted post-hoc. No equations, parameter-fitting steps, or self-citation chains are shown that would reduce any claimed prediction or rule to its own inputs by construction. The outperformance metrics and rule patterns are reported as empirical results rather than tautologies, satisfying the default expectation of no significant circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5796 in / 1087 out tokens · 26710 ms · 2026-06-29T00:03:03.165304+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

34 extracted references · 2 canonical work pages · 1 internal anchor

  1. [1]

    The Journal of Finance23(4), 589–609 (1968)

    Altman,E.I.:Financialratios,discriminantanalysisandthepredictionofcorporate bankruptcy. The Journal of Finance23(4), 589–609 (1968)

    1968

  2. [2]

    In: Proceed- ings (2020)

    Anjomshoae, S., Kampik, T., Främling, K.: Py-ciu: A python library for explaining machine learning predictions using contextual importance and utility. In: Proceed- ings (2020)

    2020

  3. [3]

    In: The 40th Conference on Uncertainty in Artificial Intelligence (2024)

    Balcan, M.F., Sharma, D.: Learning accurate and interpretable decision trees. In: The 40th Conference on Uncertainty in Artificial Intelligence (2024)

    2024

  4. [4]

    Risk Management26(2024)

    Bazzana, F., Bee, M., Khatir, A.A.H.A.: Machine learning techniques for default prediction: An application to small italian companies. Risk Management26(2024)

    2024

  5. [5]

    Journal of Machine Learning Research13, 281–305 (2012)

    Bergstra, J., Bengio, Y.: Random search for hyper-parameter optimization. Journal of Machine Learning Research13, 281–305 (2012)

    2012

  6. [6]

    Socio- Economic Planning Sciences90, 101746 (2023)

    Bitetto, A., Cerchiello, P., Filomeni, S., Tanda, A., Tarantino, B.: Machine learning and credit risk: Empirical evidence from small- and mid-sized businesses. Socio- Economic Planning Sciences90, 101746 (2023)

    2023

  7. [7]

    Bitetto, A., Cerchiello, P., Filomeni, S., Tanda, A., Tarantino, B.: Can we trust ma- chine learning to predict the credit risk of small businesses? Review of Quantitative Finance and Accounting63(3), 925–954 (2024)

    2024

  8. [8]

    Machine Learning45(1), 5–32 (2001)

    Breiman, L.: Random forests. Machine Learning45(1), 5–32 (2001)

    2001

  9. [9]

    Journal of Small Business Management (2018)

    Brighi, P., Lucarelli, C., Venturelli, V.: Predictive strength of lending technologies in funding smes. Journal of Small Business Management (2018)

    2018

  10. [10]

    Annals of Operations Research354, 247–271 (2025) 18 D

    Chang, V., Xu, Q.A., Akinloye, S.H., Benson, V., Hall, K.: Prediction of bank credit worthiness through credit risk analysis: An explainable machine learning study. Annals of Operations Research354, 247–271 (2025) 18 D. Fabbretti et al

    2025

  11. [11]

    In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

    Chen, T., Guestrin, C.: Xgboost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 785–794 (2016)

    2016

  12. [12]

    Journal of Small Business Management62(6), 2847–2905 (2024)

    Cheraghali, H., Molnár, P.: Sme default prediction: A systematic methodology- focused review. Journal of Small Business Management62(6), 2847–2905 (2024)

    2024

  13. [13]

    Scientometrics126, 2141–2188 (2021)

    Ciampi, F., Giannozzi, A., Marzi, G., Altman, E.I.: Rethinking sme default predic- tion: A systematic literature review and future perspectives. Scientometrics126, 2141–2188 (2021)

    2021

  14. [14]

    Electronics11(24) (2022).https://doi.org/10 .3390/electronics11244171,https://www.mdpi.com/2079-9292/11/24/4171

    Contreras, V., Marini, N., Fanda, L., Manzo, G., Mualla, Y., Calbimonte, J.P., Schumacher, M., Calvaresi, D.: A dexire for extracting propositional rules from neural networks via binarization. Electronics11(24) (2022).https://doi.org/10 .3390/electronics11244171,https://www.mdpi.com/2079-9292/11/24/4171

    2022

  15. [15]

    Applied Stochastic Models in Business and Industry39(6), 829–846 (2023)

    Crosato, L., Liberati, C., Repetto, M.: Lost in a black-box? interpretable machine learning for assessing italian smes default. Applied Stochastic Models in Business and Industry39(6), 829–846 (2023)

    2023

  16. [16]

    Towards A Rigorous Science of Interpretable Machine Learning

    Doshi-Velez,F.,Kim,B.:Towardsarigorousscienceofinterpretablemachinelearn- ing. arXiv preprint arXiv:1702.08608 (2017)

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Official Journal of the European Union, L 124, 20 May 2003, pp

    European Commission: Commission recommendation 2003/361/ec of 6 may 2003 concerning the definition of micro, small and medium-sized enterprises. Official Journal of the European Union, L 124, 20 May 2003, pp. 36–41 (2003)

    2003

  18. [18]

    European Commission: Ethics guidelines for trustworthy ai (April 2019)

    2019

  19. [19]

    Journal of Computer and System Sciences55(1), 119–139 (1997)

    Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences55(1), 119–139 (1997)

    1997

  20. [20]

    Annals of Statistics29(5), 1189–1232 (2001)

    Friedman, J.H.: Greedy function approximation: A gradient boosting machine. Annals of Statistics29(5), 1189–1232 (2001)

    2001

  21. [21]

    Heliyon10, e27096 (2024)

    Gu, Z., Lv, J., Wu, B., Hu, Z., Yu, X.: Credit risk assessment of small and micro enterprise based on machine learning. Heliyon10, e27096 (2024)

    2024

  22. [22]

    ACM Queue16(3), 30–57 (2018)

    Lipton, Z.C.: The mythos of model interpretability. ACM Queue16(3), 30–57 (2018)

    2018

  23. [23]

    Advances in neural information processing systems30(2017)

    Lundberg, S.M., Lee, S.I.: A unified approach to interpreting model predictions. Advances in neural information processing systems30(2017)

    2017

  24. [24]

    European jour- nal of operational research183(3), 1466–1476 (2007)

    Martens, D., Baesens, B., Van Gestel, T., Vanthienen, J.: Comprehensible credit scoring models using rule extraction from support vector machines. European jour- nal of operational research183(3), 1466–1476 (2007)

    2007

  25. [25]

    Digital Signal Processing73, 1–15 (2018)

    Montavon, G., Samek, W., Müller, K.R.: Methods for interpreting and understand- ing deep neural networks. Digital Signal Processing73, 1–15 (2018)

    2018

  26. [26]

    Expert Systems with Applications161, 113567 (2020)

    Moscatelli, M., Parlapiano, F., Narizzano, S., Viggiano, G.: Corporate default fore- casting with machine learning. Expert Systems with Applications161, 113567 (2020)

    2020

  27. [27]

    nguyen et al

    Nguyen, H.H., Viviani, J.L., Ben Jabeur, S.: Bankruptcy prediction using machine learning and shapley additive explanations: H.-h. nguyen et al. Review of Quanti- tative Finance and Accounting65(1), 107–148 (2025)

    2025

  28. [28]

    Jour- nal of Accounting Research18(1), 109–131 (1980)

    Ohlson, J.A.: Financial ratios and the probabilistic prediction of bankruptcy. Jour- nal of Accounting Research18(1), 109–131 (1980)

    1980

  29. [29]

    why should i trust you?

    Ribeiro, M.T., Singh, S., Guestrin, C.: " why should i trust you?" explaining the predictions of any classifier. In: Proceedings of the 22nd ACM SIGKDD interna- tional conference on knowledge discovery and data mining. pp. 1135–1144 (2016)

    2016

  30. [30]

    Psychological Review65(6), 386–408 (1958) Evolutionary Rule Extraction from Corporate Default Prediction Models 19

    Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review65(6), 386–408 (1958) Evolutionary Rule Extraction from Corporate Default Prediction Models 19

    1958

  31. [31]

    Nature323, 533–536 (1986)

    Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning representations by back- propagating errors. Nature323, 533–536 (1986)

    1986

  32. [32]

    Zarlenga, M.E., Shams, Z., Jamnik, M.: Efficient decompositional rule extraction for deep neural networks (2021),https://arxiv.org/abs/2111.12628

    work page arXiv 2021

  33. [33]

    Research in International Business and Finance70, 102397 (2024)

    Zedda, S.: Credit scoring: Does xgboost outperform logistic regression? a test on italian smes. Research in International Business and Finance70, 102397 (2024)

    2024

  34. [34]

    International Review of Financial Analysis89, 102755 (2023)

    Zhou, Y., Shen, L., Ballester, L.: A two-stage credit scoring model based on ran- dom forest: Evidence from chinese small firms. International Review of Financial Analysis89, 102755 (2023)

    2023