{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T04:24:14Z","timestamp":1761193454172,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Open Research Grant of Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining","award":["EC2024016"],"award-info":[{"award-number":["EC2024016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Financial risk early warning systems provide critical corporate financial status information to stakeholders, including corporate managers, investors, regulatory agencies, and other interested parties, enabling informed decision-making. This study proposes a corporate financial risk early warning model based on a bagging\u2013cascading\u2013boosting architecture, which can be used to predict the financial risk of a firm. The model performance is improved by integrating the residual fitting characteristics of LightGBM, the variance suppression mechanism of bagging, and the adaptive expansion ability of the cascade framework. Evaluated on 46 financial indicators from 2826 A-share-listed companies, the model demonstrates superior performance in AUC and F1-score metrics, outperforming traditional statistical methods and standalone machine-learning models. The methodological innovation lies in its tripartite mechanism: LightGBM ensures low-bias prediction, bagging controls variance, and the cascading structure dynamically adapts to data complexity, maintaining 94.09% AUC robustness, even when training data is reduced to 50%. Empirical results confirm this \u201censemble-of-ensembles\u201d framework effectively identifies Special Treatment (ST) firms, delivering early risk alerts for management while supporting investment decisions and regulatory risk mitigation.<\/jats:p>","DOI":"10.3390\/sym17101779","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:17:35Z","timestamp":1761056255000},"page":"1779","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetric Equilibrium Bagging\u2013Cascading Boosting Ensemble for Financial Risk Early Warning"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4296-8138","authenticated-orcid":false,"given":"Yao","family":"Zou","sequence":"first","affiliation":[{"name":"School of Economics and Management, Huainan Normal University, Huainan 232038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Huainan Normal University, Huainan 232038, China"},{"name":"Joint National-Local Engineering Research Centre for Safe and Precise Coal Mining, Huainan 232001, China"},{"name":"School of Engineering Sciences, University of Science and Technology of China, Hefei 230022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Huainan Normal University, Huainan 232038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenhui","family":"Yu","sequence":"additional","affiliation":[{"name":"Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.ejor.2014.06.044","article-title":"Financial Distress Drivers in Brazilian Banks: A Dynamic Slacks Approach","volume":"240","author":"Wanke","year":"2015","journal-title":"Eur. J. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/j.1540-6261.1968.tb00843.x","article-title":"Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy","volume":"23","author":"Altman","year":"1968","journal-title":"J. Financ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2307\/2490395","article-title":"Financial Ratios and the Probabilistic Prediction of Bankruptcy","volume":"18","author":"Ohlson","year":"1980","journal-title":"J. Account. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0378-4266(85)90021-4","article-title":"A Factor-Analytic Approach to Bank Condition","volume":"9","author":"West","year":"1985","journal-title":"J. Bank. Financ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10462-015-9434-x","article-title":"Financial Credit Risk Assessment: A Recent Review","volume":"45","author":"Chen","year":"2016","journal-title":"Artif. Intell. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2045","DOI":"10.1007\/s00521-022-07377-0","article-title":"Risk Prediction in Financial Management of Listed Companies Based on Optimized BP Neural Network under Digital Economy","volume":"35","author":"Li","year":"2023","journal-title":"Neural Comput. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.eswa.2004.08.009","article-title":"An Application of Support Vector Machines in Bankruptcy Prediction Model","volume":"28","author":"Shin","year":"2005","journal-title":"Expert Syst. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.dss.2011.10.007","article-title":"Comparative Analysis of Data Mining Methods for Bankruptcy Prediction","volume":"52","author":"Olson","year":"2012","journal-title":"Decis. Support Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1162\/neco.1996.8.7.1341","article-title":"The Lack of a Priori Distinctions between Learning Algorithms","volume":"8","author":"Wolpert","year":"1996","journal-title":"Neural Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"71","DOI":"10.2307\/2490171","article-title":"Financial Ratios as Predictors of Failure","volume":"4","author":"Beaver","year":"1966","journal-title":"J. Account. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0378-4266(77)90022-X","article-title":"Early Warning of Bank Failure: A Logit Regression Approach","volume":"1","author":"Martin","year":"1977","journal-title":"J. Bank. Financ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1011","DOI":"10.2308\/accr.2004.79.4.1011","article-title":"Predicting Firm Financial Distress: A Mixed Logit Model","volume":"79","author":"Jones","year":"2004","journal-title":"Account. Rev."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Odom, M.D., and Sharda, R. (1990, January 17\u201321). A Neural Network Model for Bankruptcy Prediction. Proceedings of the 1990 IJCNN International Joint Conference on Neural Networks, San Diego, CA, USA.","DOI":"10.1109\/IJCNN.1990.137710"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"113814","DOI":"10.1016\/j.dss.2022.113814","article-title":"Financial Distress Prediction Using Integrated Z-Score and Multilayer Perceptron Neural Networks","volume":"159","author":"Wu","year":"2022","journal-title":"Decis. Support Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2089","DOI":"10.1007\/s13042-022-01566-y","article-title":"A Novel Method for Financial Distress Prediction Based on Sparse Neural Networks with L 1\/2 Regularization","volume":"13","author":"Chen","year":"2022","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"11261","DOI":"10.1016\/j.eswa.2011.02.173","article-title":"Predicting Corporate Financial Distress Based on Integration of Decision Tree Classification and Logistic Regression","volume":"38","author":"Chen","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s11135-010-9376-y","article-title":"Financial Distress Prediction Based on SVM and MDA Methods: The Case of Chinese Listed Companies","volume":"45","author":"Xie","year":"2011","journal-title":"Qual. Quant."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1520\/JTE20130297","article-title":"A Novel Nonlinear Integrated Forecasting Model of Logistic Regression and Support Vector Machine for Business Failure Prediction with All Sample Sizes","volume":"43","author":"Xu","year":"2015","journal-title":"J. Test. Eval."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1080\/08839514.2021.1877481","article-title":"Classifier Selection and Ensemble Model for Multi-Class Imbalance Learning in Education Grants Prediction","volume":"35","author":"Sun","year":"2021","journal-title":"Appl. Artif. Intell."},{"key":"ref_20","first-page":"1612","article-title":"A Short Introduction to Boosting","volume":"14","author":"Freund","year":"1999","journal-title":"J. Soc. Artif. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). Xgboost: A Scalable Tree Boosting System. Proceedings of the 22nd ACM Sigkdd International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_22","first-page":"3149","article-title":"Lightgbm: A Highly Efficient Gradient Boosting Decision Tree","volume":"30","author":"Ke","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/j.asoc.2014.08.009","article-title":"AdaBoost Based Bankruptcy Forecasting of Korean Construction Companies","volume":"24","author":"Heo","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5529847","DOI":"10.1155\/2024\/5529847","article-title":"AdaFNDFS: An AdaBoost Ensemble Model with Fast Nondominated Feature Selection for Predicting Enterprise Credit Risk in the Supply Chain","volume":"2024","author":"Yao","year":"2024","journal-title":"Int. J. Intell. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"258","DOI":"10.4236\/tel.2021.112019","article-title":"A Study on Forecasting the Default Risk of Bond Based on Xgboost Algorithm and Over-Sampling Method","volume":"11","author":"Zhang","year":"2021","journal-title":"Theor. Econ. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wang, W., and Liang, Z. (2024). Financial Distress Early Warning for Chinese Enterprises from a Systemic Risk Perspective: Based on the Adaptive Weighted XGBoost-Bagging Model. Systems, 12.","DOI":"10.3390\/systems12020065"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"120375","DOI":"10.1016\/j.eswa.2023.120375","article-title":"The Measurement and Early Warning of Daily Financial Stability Index Based on XGBoost and SHAP: Evidence from China","volume":"227","author":"Tan","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"121824","DOI":"10.1016\/j.ins.2024.121824","article-title":"Stock Complex Networks Based on the GA-LightGBM Model: The Prediction of Firm Performance","volume":"700","author":"Huang","year":"2025","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"102140","DOI":"10.1016\/j.irfa.2022.102140","article-title":"Research on Optimization of an Enterprise Financial Risk Early Warning Method Based on the DS-RF Model","volume":"81","author":"Zhu","year":"2022","journal-title":"Int. Rev. Financ. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jbusres.2020.07.052","article-title":"Combining Corporate Governance Indicators with Stacking Ensembles for Financial Distress Prediction","volume":"120","author":"Liang","year":"2020","journal-title":"J. Bus. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1002\/ijfe.3020","article-title":"Multi-Class Financial Distress Prediction Based on Stacking Ensemble Method","volume":"30","author":"Chen","year":"2025","journal-title":"Int. J. Financ. Econ."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"124525","DOI":"10.1016\/j.eswa.2024.124525","article-title":"Cost-Sensitive Stacking Ensemble Learning for Company Financial Distress Prediction","volume":"255","author":"Wang","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3128","DOI":"10.1002\/for.3177","article-title":"Corporate Financial Distress Prediction in a Transition Economy","volume":"43","author":"Nguyen","year":"2024","journal-title":"J. Forecast."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3161","DOI":"10.1007\/s10614-023-10537-6","article-title":"Forecasting Bank Failure in the US: A Cost-Sensitive Approach","volume":"64","author":"Ekinci","year":"2024","journal-title":"Comput. Econ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"107758","DOI":"10.1016\/j.frl.2025.107758","article-title":"The Impact of Financial Statement Indicators on Bank Credit Ratings: Insights from Machine Learning and SHAP Techniques","volume":"85","author":"Lee","year":"2025","journal-title":"Financ. Res. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"128809","DOI":"10.1016\/j.eswa.2025.128809","article-title":"Corporate ESG Rating Prediction Based on XGBoost-SHAP Interpretable Machine Learning Model","volume":"295","author":"Zhang","year":"2026","journal-title":"Expert Syst. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"He, K., Yang, Q., Ji, L., Pan, J., and Zou, Y. (2023). Financial Time Series Forecasting with the Deep Learning Ensemble Model. Mathematics, 11.","DOI":"10.3390\/math11041054"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"240699","DOI":"10.1098\/rsos.240699","article-title":"An Ensemble Approach Integrating LSTM and ARIMA Models for Enhanced Financial Market Predictions","volume":"11","author":"Mochurad","year":"2024","journal-title":"R. Soc. Open Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3081","DOI":"10.1016\/j.eswa.2007.06.037","article-title":"Forecasting Financial Condition of Chinese Listed Companies Based on Support Vector Machine","volume":"34","author":"Ding","year":"2008","journal-title":"Expert Syst. Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1779\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T04:21:02Z","timestamp":1761193262000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1779"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"references-count":39,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["sym17101779"],"URL":"https:\/\/doi.org\/10.3390\/sym17101779","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,10,21]]}}}