Symmetric Equilibrium Bagging–Cascading Boosting Ensemble for Financial Risk Early Warning

Abstract

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–cascading–boosting 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 “ensemble-of-ensembles” framework effectively identifies Special Treatment (ST) firms, delivering early risk alerts for management while supporting investment decisions and regulatory risk mitigation.

1. Introduction

Against the background of the current domestic and international economic fluctuations, numerous enterprises face financial distress or even imminent bankruptcy risks due to pressures from global supply chain restructuring, divergent monetary policies, and internal debt structure imbalances. Such risks not only jeopardize corporate interests but also inflict direct or indirect losses on all stakeholders [1]. Consequently, financial risk early warning has emerged as a critical focus. Corporate financial conditions are now drawing heightened attention from both management and diverse stakeholders, including employees, government agencies, creditors, and investors. These stakeholders monitor financial health to mitigate systemic repercussions.

The development of high-performance early warning models is imperative, given the critical impact of corporate financial risk alerts on financial institutions’ risk management efficacy and profitability. At present, the financial risk early warning models mainly include statistical methods and machine-learning-based artificial intelligence techniques. Statistical methods include linear discriminant analysis (LDA) [2], logistic regression (LR) [3], and factor analysis [4]. Although widely adopted, statistical methods suffer from restrictive assumptions—including multivariate normality, linearity, and independence of predictors—that limit their validity and applicability [5]. With the development of information processing technology, single machine-learning methods such as a neural network (NN) [6], a support vector machine (SVM) [7], and a decision tree (DT) [8] are gradually being applied to financial risk early warning; this has taken the research of financial risk management to a new level. However, exponential growth in dataset dimensionality and variable complexity within financial risk data renders standalone machine-learning methods inadequate under the “No Free Lunch” theorem [9]. A more effective scheme is to construct an ensemble learning framework to improve the model performance by fusing multiple base classifiers. According to the difference of ensemble strategies, the ensemble algorithms in the field of enterprise financial risk early warning are mainly divided into three categories: bagging-type methods reduce the prediction variance by training multiple base learners in parallel, thereby mitigating overfitting through bootstrap aggregation and model averaging; boosting-type methods reduce the prediction deviation by iterative optimization; the stacking method achieves variance-deviation equilibrium by hierarchical transformation of feature space. The symmetry structure of financial data introduces additional considerations for ensemble design. For instance, bagging-type methods may benefit from symmetric sampling to preserve invariant financial patterns, while boosting algorithms could leverage symmetry-aware loss functions to better capture cyclical market behaviors. Stacking’s hierarchical transformations can be further enhanced by incorporating symmetry-preserving feature mappings, ensuring that the fused representations maintain essential geometric properties of the financial state space. These symmetry-aware adaptations provide a principled way to address the No Free Lunch challenge in financial risk prediction. All three methods can effectively improve the performance of enterprise risk early warning.

Capitalizing on the complementary advantages of bagging ensembles in variance optimization and boosting ensembles in bias reduction, this study leverages the cascading framework’s intrinsic capacity for adaptive extensibility in corporate financial risk modeling. The proposed architecture combines these strengths to create a bagging–cascading-boosted tree solution specifically designed for financial risk early warning. The proposed framework employs a tripartite optimization mechanism to enhance model performance. Light Gradient Boosting Machine (LightGBM) serves as the base learner, leveraging its sequential residual fitting properties to achieve low-bias predictions. A bagging ensemble is then applied to bootstrap-aggregate multiple LightGBM outputs, which can effectively suppress the prediction variance. Ultimately, a depth-adaptive cascading structure enables architectural expansion, where model complexity dynamically adjusts to match the dimensional characteristics of financial risk datasets. This design synergistically integrates bagging’s variance control, boosting’s bias optimization, and cascading’s structural scalability, thereby establishing a dynamic learning paradigm tailored for corporate financial risk analytics. The innovations of this study are primarily manifested in the following aspects:

(1)

Existing ensemble methods typically rely on either bagging (variance reduction) or boosting (bias reduction) in isolation, limiting their ability to address the complex trade-offs in financial risk modeling. This study pioneers a bagging–cascading–boosting tripartite architecture, where LightGBM’s sequential residual fitting minimizes bias, bagging aggregates multiple outputs to suppress variance, and the cascading framework dynamically adjusts model depth. This integration outperforms traditional single-strategy ensembles by simultaneously optimizing prediction performance and stability.

(2)

Existing ensemble frameworks often suffer from rigid structures that cannot adapt to evolving data complexity. The proposed cascading strategy overcomes this limitation by dynamically adjusting model depth based on the complexity of datasets. Unlike static architectures, this design enables seamless incorporation of new risk indicators, ensuring scalability without compromising performance.

(3)

While prior studies have explored bagging or boosting in isolation, this work pioneers their synergistic integration. The LightGBM–bagging combination not only enhances prediction stability but also mitigates overfitting risks, a common issue in financial risk modeling. The cascading layer further refines this robustness by allowing iterative feature selection. This triple innovation—hybrid architecture, adaptive scaling, and robust optimization—sets this work apart from existing ensemble approaches.

2. Literature Review

Financial risk early warning research is a key focus in modern corporate risk management. These studies rely on scientifically validated predictive models. Financial risk early warning research is crucial for modern businesses. It helps companies spot potential financial problems early. By using advanced predictive models, executives can track their company’s health in real time. These models also guide investors in making smart choices and reducing risks.

2.1. Statistical Methods and Individual ML-Based Algorithms

Early warning models constitute the backbone of financial risk management by enabling early detection of potential financial distress. To date, scholars have extensively researched financial early warning models, which broadly fall into statistical and non-statistical categories. Initial models predominantly employed statistical approaches, exemplified by LDA and LR. Beaver [10] pioneered the use of univariate models in financial distress prediction; subsequently, Altman [2] developed the classic multivariate Z-score model using five financial ratios. Martin [11] first applied logistic regression to bank failure forecasting, while Ohlson [3] formalized a logit-based financial warning model. Jones and Hensher [12] proposed a mixed logit model to overcome the limitations of standard logit, demonstrating superior performance in financial distress prediction.

As corporate operating environments grow increasingly complex, information relevant to financial risk early warning expands exponentially, while data structures become increasingly intricate. Traditional statistical methods, however, require high-quality data, complex underlying assumptions, and strict adherence to data distributions—requirements that constrain their development in financial risk prediction. In contrast, machine-learning algorithms typically operate without such restrictive assumptions and enable continuous model refinement through adaptive recalibration to new data. Commonly employed machine-learning algorithms within corporate financial risk forecasting include NN, DT, KNN, and SVM. Odom and Sharda [13] first utilized artificial neural networks to construct an early warning model, demonstrating its superior performance compared to traditional models based on methods like logistic regression. Wu et al. [14] combined a multi-layer perceptron artificial neural network (MLP-ANN) with the traditional Altman Z-Score model for stock market forecasting, achieving 99.4% classification accuracy in predicting financial distress. Chen et al. [15] introduced a sparse neural-network-based model (FDP-SNN) that integrates financial and non-financial predictors, demonstrating superior accuracy and interpretability in financial distress prediction. Mu-Yen Chen [16] compares decision tree (C5.0, CART, CHAID) and logistic regression models integrated with PCA for financial distress prediction, demonstrating that decision trees achieve superior short-term accuracy. Xie et al. [17] constructed support vector machine (SVM) and multivariate discriminant analysis (MDA) models using Chinese-listed companies as research samples, with empirical results demonstrating SVM’s superiority over MDA. This performance advantage was further substantiated by Xu and Xiao et al. [18], who found SVM exhibits enhanced accuracy and generalization capabilities compared to logistic regression.

2.2. Ensemble Approaches

As research on corporate financial distress early warning continues to evolve, researchers have observed that individual warning models possess distinctive strengths and limitations. To enhance predictive accuracy, scholars have consequently turned to ensemble learning approaches, which fundamentally operate through three frameworks: boosting, bagging, and stacking. Boosting, a machine-learning meta-algorithm designed to reduce bias, systematically transforms weak learners—classifiers performing marginally better than random guessing—into strong learners capable of achieving high predictive accuracy. As established in foundational literature [19], these complementary learner types constitute the core mechanism of boosting frameworks. Prominent implementations include AdaBoost [20], XGBoost [21], and LightGBM [22], each demonstrating this transformative capability through iterative weak classifier optimization. AdaBoost, or Adaptive Boosting, is a machine-learning ensemble technique that combines multiple weak classifiers to create a strong classifier. Heo et al. [23] demonstrated that AdaBoost outperformed traditional models in predicting bankruptcy among Korean construction companies, particularly for larger firms with significant capital. The study highlighted the model’s ability to adapt to the unique financial structures of different industries, thereby enhancing predictive accuracy. Yao et al. [24] proposed an AdaBoost ensemble model with fast nondominated feature selection (AdaFNDFS). The findings demonstrate that the predictive performance of AdaFNDFS surpasses that of other comparative models. XGBoost, or Extreme Gradient Boosting, is another powerful machine-learning algorithm that has been widely adopted for financial risk prediction. Zhang et al. [25] utilized XGBoost to predict bond defaults in China’s emerging market, demonstrating its superiority over traditional algorithms in managing imbalanced data. Wang et al. [26] developed an adaptive weighted XGBoost-bagging model to predict financial distress in Chinese enterprises. Their research highlighted the model’s effectiveness in addressing data imbalance and information scarcity, significantly enhancing prediction accuracy during periods of economic turmoil. Tan et al. [27] leveraged XGBoost to analyze 20 financial indicators, achieving superior risk prediction accuracy and identifying eight key risk factors (real economy, institutions, etc.) with actionable early warning thresholds for policymakers. The application of LightGBM in enterprise financial risk warning has garnered considerable attention in recent research, demonstrating its effectiveness in handling high-dimensional financial data and improving prediction accuracy. Huang et al. [28] found that the LightGBM model outperforms other GBDT-based techniques in efficiency and prediction accuracy. The bagging algorithm constructs multiple base learners through bootstrap sampling of training subsets, then integrates their predictions via voting (for classification) or averaging (for regression) to produce final outputs. Representative implementations include Random Forests (RF) and other ensemble methods. Notably, Zhu et al. [29] developed a comprehensive corporate financial risk warning system using a DS-RF model, which demonstrates enhanced capability in revealing financial risk characteristics and underlying drivers. Stacking (stacked generalization) is a hierarchical ensemble learning method that enhances overall predictive performance by consolidating the predictions of multiple heterogeneous base models as new input features for a meta-model. Deron Liang et al. [30] developed a stacking ensemble model for bankruptcy prediction using six optimized financial ratios and six corporate governance indicators, demonstrating superior performance in high-cost misclassification scenarios. Chen et al. [31] proposed a stacking ensemble model (DNN + MNLogit + MDA) with stock data integration for multi-class financial distress prediction, achieving an 88.7% F1-score in classifying Chinese firms’ financial health states. Wang and Chi [32] proposed a cost-sensitive stacking (CSStacking) model with two-phase feature selection, significantly outperforming benchmarks in predicting Chinese-listed companies’ financial distress 5 years ahead.

2.3. Other Related Research

Unbalanced learning is a significant challenge in financial risk prediction, as the distribution of financial distress cases is often skewed. Traditional models may struggle to accurately predict minority classes, leading to high false-negative rates. To address this issue, researchers have proposed various strategies, including those at the data level and algorithm level. Minh Nguyen, Bang Nguyen, and Minh-Lý Liêu [33] applied SMOTE to address data scarcity in Vietnam’s transition economy, testing seven models where neural networks with combined Altman-Ohlson variables perform best. Aykut Ekinci and Safa Sen [34] highlighted a cost-sensitive-learning approach as the optimal imbalance treatment, effectively minimizing Type-II errors in bank failure prediction compared to conventional sampling methods.

Interpretability can be defined as the degree to which a model’s predictions can be clearly and intuitively understood and explained. Interpretability is particularly crucial in the field of enterprise financial risk management, as decision-makers need to comprehend the rationale behind a model’s outputs to trust its results. Currently, Local Interpretable Model-agnostic Explanations (LIME) and SHapley Additive exPlanations (SHAP) represent two predominant approaches for interpreting model predictions. Min-Jae Lee and Sun-Yong Choi [35] employed SHAP analysis on GBR/LightGBM models to quantify 28 financial indicators’ contributions, revealing net interest income as the dominant factor in bank credit ratings. Jianfeng Zhang and Zexin Zhao [36] adopted the XGBoost-SHAP framework to predict ESG ratings (91% accuracy) with interpretable feature analysis, revealing that financial metrics dominate over non-financial factors in Chinese A-shares (2013–2022).

Additionally, the application of time-series ensembles in corporate financial risk warning has demonstrated remarkable effectiveness by leveraging the collective strengths of multiple predictive models to enhance accuracy and robustness. Kaijian He et al. [37] (2023) proposed a CNN-LSTM-ARMA ensemble model to capture spatiotemporal and autocorrelation features in financial time series, outperforming standalone models in accuracy and robustness through hybrid linear–nonlinear feature integration. Lesia Mochurad and Andrii Dereviannyi [38] integrated LSTM and ARIMA models to enhance financial market forecasting accuracy. The hybrid approach demonstrates a 15% RMSE improvement over standalone LSTM models, validated across three real-world datasets. Parallelization potential further boosts efficiency for future research.

3. Methodology

The proposed algorithm fundamentally integrates multiple learners to identify and screen financial distress enterprises, comprising three key phases: generating robust and diverse individual learners, designing ensemble strategies to integrate these base learners, and fusing their predictions. The subsequent sections demonstrate critical technical implementations in detail.

3.1. LightGBM as Base Learner

Gradient Boosting Decision Trees (GBDT) constitute a prominent boosting ensemble methodology that significantly enhances the predictive performance of early warning models by strategically adjusting sample weighting priorities during iterative training cycles. This approach fundamentally iteratively minimizes errors by directing each subsequent base learner to focus more intensively on samples misclassified in preceding iterations. This contrasts with AdaBoost’s strategy of increasing misclassified sample weights, as GBDT instead leverages negative gradients as a proxy for prior base learner errors and corrects these deviations in subsequent iterations by fitting negative gradients, thereby implementing gradient descent in function space.

Based on the ensemble structure of gradient boosting, LightGBM is also an additive model, which can be defined as

$$F_M(x)={\displaystyle \sum _{m=1}^M}{\beta }_m{f}_m(x;{\alpha }_m)$$

(1)

where $\beta$ is the weight coefficient of the base learner, $f_m(x;\alpha )$ represents the t-th base learner. In GBDT, $f$ represents a DT, $\alpha$ is the structural parameter of the DT. Conventional full-parameter optimization of additive ensemble models typically faces computational challenges due to high complexity. To address this, Friedman proposed the Forward Stagewise Algorithm as an iterative approximation solution. The core idea of this algorithm is to incrementally optimize local parameters to approach the global optimum, with its $m$-th iteration formally expressed as

$$F_m\left(x\right)=F_{m-1}\left(x\right)+{\beta }_m{f}_m\left(x\right)$$

(2)

The objective of machine learning-based corporate financial risk early warning systems is to identify the likelihood of companies being designated as Special Treatment (ST). Consequently, the optimization goal for the $m$-th decision tree aims to further reduce the value of the loss function L from the ensemble model formed by the previous $m-1$ iterations. Based on this analysis, Equation (2) can be reformulated as

$$F_m(x)=F_{m-1}(x)+\begin{array}{c}a\mathit{rg}min\\ f_t\end{array}\sum _{i=1}^N\left[L\right(y_i,F_{m-1}(x_i)+f_m(x_i))]$$

(3)

where $N$ denotes the total number of samples in the enterprise financial risk early-waring training set, and $x_i$ represents the feature of the $i$-th sample.

LightGBM inherits the training paradigm from XGBoost, which approximates the loss function using first-order and second-order Taylor expansions while incorporating regularization terms to control the complexity of each tree

$$L(y,F_m(x))\simeq \sum _{i=1}^N\left[L\right(y_i,F_{m-1}(x_i))+g_i{f}_m(x_i)+{\displaystyle \frac{1}{2}}{h}_i{f_m}^2(x_i)]+\Omega (f_m)$$

(4)

where $g_i={\displaystyle \frac{\partial L(y_i,F_{m-1}(x_i\left)\right)}{\partial F_{m-1}\left(x_i\right)}}$ is the first derivative of the loss function, $h_i={\displaystyle \frac{{\partial }^{2}L(y_i,F_{m-1}(x_i\left)\right)}{{{\partial }^{2}F}_{m-1}\left(x_i\right)}}$ represents the second derivative of the loss function. The regularization term $\Omega$ controls the complexity of each decision tree (DT), where the tree’s complexity is determined by both the number of leaf nodes and the values assigned to these nodes. Consequently, the regularization term can be explicitly formulated as

$$\Omega (f_m)=\mathsf{\rho }{M}_L+{\displaystyle \frac{1}{2}}\lambda \sum _{j=1}^{M_L}{b}_j^2$$

(5)

where $M_L$ is the number of leaf nodes, $j$ is the number of leaf nodes and $b_j$ is the value at the $j$-th leaf node. The parameters $\rho$ and $\lambda$ respectively govern the weights assigned to the number of leaf nodes and the values within these nodes. This regularization term constrains tree complexity by effectively reducing the number of nodes while simultaneously limiting leaf scores—since higher prediction scores accelerate fitting and increase overfitting risk.

To minimize the objective function, we set the first-order derivative of the loss function to zero, thereby determining the optimal prediction scores for each leaf node as

$$b_j^{\mathrm{*}}=-{\displaystyle \frac{{\sum }_{i\in I_j}{g}_i}{{\sum }_{i\in I_j}{h}_i+\lambda }}$$

(6)

here, where $I_j=\left\{i\right|q\left(x_i\right)=j\}$, and q(xi) is a function that maps $i$-th instance into a leaf node. Because the object of the $m$-th DT is to further reduce the loss of $m-1$ iterations. Therefore, the objective function at $m$-th boosting can be simplified as

$$L(y,F_m(x))=-{\displaystyle \frac{1}{2}}\sum _{j=1}^{M_{\mathrm{L}}}{\displaystyle \frac{(\sum _{i\in I}{g}_i{)}^2}{\sum _{i\in I}{h}_i+\lambda }}+\gamma M_{\mathrm{L}}$$

(7)

Compared to gradient boosting, LightGBM, an enhanced Gradient Boosting Decision Tree (GBDT) algorithm proposed by Ke et al. [22], addresses the limitations of GBDT in scalability and effectiveness when handling high-dimensional features or large-scale datasets. Building upon GBDT’s framework, LightGBM integrates multifaceted optimizations to achieve accelerated training efficiency, reduced memory consumption, improved accuracy, parallel learning capabilities, and enhanced large-data processing capacity. Key innovations include the histogram algorithm for computational acceleration; depth-constrained leaf-wise growth strategy for higher precision under equivalent splits; Gradient-based One-Side Sampling (GOSS), balancing data reduction with decision tree accuracy; Exclusive Feature Bundling (EFB), reducing feature dimensionality; histogram differencing for operational speed gains. Consequently, LightGBM demonstrates exceptional advantages in processing voluminous financial fraud data from listed companies.

3.2. Base Learner Training Based on the Cascade Framework

Bagging is a parallelized ensemble algorithm characterized by the absence of dependency relationships between weak learners, allowing for parallel fitting. For example, in a random sampling of a training set containing $m$ samples, the probability of being collected each time is ${\displaystyle \frac{1}{m}}$, and the probability of not being collected is $1-{\displaystyle \frac{1}{m}}$. The probability that is not collected in each $m$-th resampling is ${(1-{\displaystyle \frac{1}{m}})}^m$. According to the central limit theorem, when $m\to \mathrm{\infty }$, ${(1-{\displaystyle \frac{1}{m}})}^m\to {\displaystyle \frac{1}{e}}\approx 0.368$. That is to say, in each round of random sampling in bagging, approximately 36.8% of the data in the training set is not included in the sampling set. For approximately 36.8% of the data that has not been sampled, we often refer to it as Out of Bag (OOB) data. This data did not participate in the fitting of the training set model, so it can be used to test the model’s generalization ability.

In this study, we propose a new bagging algorithm for training and integrating base learners to enhance the generalization ability of ensemble models in financial risk warning tasks. Unlike traditional bagging algorithms that perform sample-level bootstrap resampling, our approach adopts a level-set-based framework. Given the financial risk warning training set $D_{train}=\left\{\right(x_1,y_1),(x_2,y_2),\dots ,(x_m,y_m\left)\right\}$ and the test set $D_{test}=\left\{\right(x_{m+1},y_{m+1}),(x_{m+2},y_{m+2}),\dots ,(x_n,y_n\left)\right\}$, where $x_i$, $y_m\in \{-\mathrm{1,1}\}$ respectively represent the features and labels of the $i$-th sample. If we set the number of random samples to $T$, we can obtain a training subset of $T$ samples $\{D_1,D_{2,},\dots ,D_T\}$. In each bagging iteration, according to the previous description, 36.8% of the out-of-bag data will not participate in the generation of the training subset, which can be expressed as $D_{train\backslash }=\{D_{train\backslash 1},D_{train\backslash 2},\dots ,D_{train\backslash t},\dots ,D_{train\backslash T}\}$. Among them, $D_{train\backslash t}$ is a subset formed by the out-of-package data in the $t$-th bagging loop, which can be represented as $D_{train\backslash t}=\left\{\right(x_1^{\left(t\right)},y_1^{\left(t\right)}),(x_2^{\left(t\right)},y_2^{\left(t\right)}),\dots ,(x_O^{\left(t\right)},y_O^{\left(t\right)}\left)\right\}$, Among them, $O$ represents the number of samples in the data outside the package.

In each iteration of the bagging algorithm, each base learner is trained on a sampled training subset. Considering the impact of the robustness of the base learners on the performance of the ensemble algorithm, in this study, we use four LightGBM models $\{f_1,f_2,f_3,f_4\}$ as base learners. Due to LightGBM being a highly integrated algorithm that relies on fine-tuning, we use the fine-tuned LightGBM model as the base learner for our proposed model in a mechanism where LightGBM serves as the base model. Under this mechanism, LightGBM, as a mechanism that minimizes losses through iteration, ensures low bias. Secondly, the bagging style training mechanism makes LightGBM’s inputs more diverse, further reducing the model’s prediction variance and effectively balancing the trade-off between variance and bias in machine-learning prediction models. After T rounds of repeated training based on different sample sets, each base learner can generate confidence information for a financial risk warning sample based on the determined structure and parameters of the training stage. This confidence information details the probability of which category the enterprise’s financial status belongs to, and this probability can be further transformed into the discrimination of the enterprise’s financial status based on the selection of a threshold. We will specifically represent the probability information of samples outside the package and samples in the test set as follows:

$$p_i^{\left(f\right)}\left(D_{train}\right)=\left[p_i^{\left(f_1\right)}\right(D_{train}),p_i^{\left(f_2\right)}(D_{train}),p_i^{\left(f_3\right)}(D_{train}),p_i^{\left(f_4\right)}(D_{train}\left)\right]$$

(8)

$$p_i^{\left(f\right)}\left(D_{train\backslash }\right)=\left[p_i^{\left(f_1\right)}\right(D_{train\backslash }),p_i^{\left(f_2\right)}(D_{train\backslash }),p_i^{\left(f_3\right)}(D_{train\backslash }),p_i^{\left(f_4\right)}(D_{train\backslash }\left)\right]$$

(9)

$$p_i^{\left(f\right)}\left(D_{test}\right)=\left[p_i^{\left(f_1\right)}\right(D_{test}),p_i^{\left(f_2\right)}(D_{test}),p_i^{\left(f_3\right)}(D_{test}),p_i^{\left(f_4\right)}(D_{test}\left)\right]$$

(10)

here, $p_i^{(f_j)}(D_{train\backslash })\in R^{L\times 1}$ is the prediction confidence information of the ensemble model on the OOB, $p_i^{\left(f\right)}\left(D_{train\backslash }\right)\in R^{L\times 4}$, $p_i^{\left(f\right)}\left(D_{test}\right)\in R^{(n-m)\times 4}$, $D_{train\backslash }$ represents the OOB data, and $D_{test}$ represents test data.

3.3. Aggregate Multiple Base Learners for Financial Risk Early Warning

Cascaded ensemble methodology constitutes a specialized stacking mechanism that progressively strengthens weak risk early warning models through sequential training of base learners across tiers, fundamentally comprising three integrally linked phases: initial partitioning of the original dataset into mutually exclusive subsets via our implemented bagging algorithm; subsequent parallelized training and validation of a quartet of LightGBM models on the segmented data; ultimately, the propagation of Tier-1 confidence scores as transformed inputs to train Tier-2 base learners, thereby enabling hierarchical feature refinement and predictive enhancement.

In this study, we employ bagging to partition the original training set, where each derived subset (containing 63.2% of original samples) trains successive cascade tiers, while the remaining 37.8% out-of-bag data constitutes a validation set that not only evaluates tier performance but also informs subsequent cascade construction. This partitioning yields disjoint datasets: the sampled subset trains Tier-1 base learners, whose predictions on the full training set transform into confidence scores via Equation (8) to serve as Tier-2 inputs; concurrently, the validation set assesses model efficacy and benchmarks against subsequent tiers. In this study, we use Equation (9) to obtain the probabilistic prediction of each level of the cascading framework, and the ST/Non-ST status is further identified by a threshold function, which can be expressed as the following Algorithm 1.

Algorithm 1: Training of the proposed method

Input: A training set $D_{train}=\left\{\right(x_1,y_1),(x_2,y_2),\dots ,(x_m,y_m\left)\right\}$ for financial risk early warning; $\mathrm{A}\mathrm{test}\mathrm{set}{D}_{test}=\left\{\right(x_{m+1},y_{m+1}),(x_{m+2},y_{m+2}),\dots ,(x_n,y_n\left)\right\}$; $\mathrm{LightGBM}\mathrm{as}\mathrm{base}\mathrm{learners}{f}_1,f_2,f_3\mathrm{and}{f}_4$; Round T for Bagging; Output: the proposed method $\mathsf{\Gamma }$ 1: $\mathrm{level}l=1$ 2: $\mathrm{Initialize}\mathrm{validation}\mathrm{accuracy}\mathrm{score}{A}^{\left(0\right)}=0$ 3: $\mathbf{for}t=\mathrm{1,2},\dots ,T\mathbf{do}$ 4: $D_t=\mathit{Boostrap}\left(D_{train}\right)$ 5: $D_{train\backslash }=D_{train\backslash D_t}$ 6: $\mathbf{for}i=\mathrm{1,2},\dots ,4$ do 7: $\mathrm{Train}{f}_i\mathrm{with}{D}_t$ 8: $\mathrm{Get}\mathrm{the}\mathrm{probabilistic}\mathrm{predictions}{p}_t^{\left(f_i\right)}\left(D_{train\backslash }\right)$ 9:   end for 10: $p_i^{\left(f\right)}\left(D_{train\backslash }\right)=\left[p_i^{\left(f_1\right)}\left(D_{train\backslash }\right),p_i^{\left(f_2\right)}\left(D_{train\backslash }\right),p_i^{\left(f_3\right)}\left(D_{train\backslash }\right),p_i^{\left(f_4\right)}\left(D_{train\backslash }\right)\right]$ 11: $\mathrm{Generate}\mathrm{new}\mathrm{training}\mathrm{set}{D}_t^{\left(l\right)}=concat(x_{train\backslash },p_i^{\left(f\right)}(D_{train\backslash }\left)\right)$ for the next level    of the proposed method 12: $A_t^{\left(l\right)}=accuracy\text{\_}score(sgn\left(p_t^{\left(f\right)}\right),y_{train\backslash })$ according to 13:  end for 14: $A^{\left(l\right)}={\displaystyle \frac{1}{T}}{\sum }_{t=1}^T{A}_t^{\left(l\right)}$ 15: $f_{meta}^{\left(l\right)}=\left[f_1,f_2,f_3,f_4\right]$ 16: $\mathbf{if}{A}^{\left(l\right)}>A^{(l-1)}$ then 17: $l=l+1$ 18:   Return to step 4 19:  else 20: $\mathrm{Return}\mathsf{\Gamma }=\left[f_{meta}^{\left(1\right)},f_{meta}^{\left(2\right)},\dots ,f_{meta}^{\left(l\right)}\right]$ 21:  end if

$$C_{test}=\mathit{sgn}(P(D_{test}))=\left\{\begin{array}{c}1ifp\ge \sigma \\ 0ifp<\sigma \end{array}\right.$$

(11)

Validation performance at each cascade tier is quantified by the mean accuracy across four base learners, where label ‘1’ denotes enterprises with financial risk and ‘0’ indicates financially healthy entities. The threshold $\sigma$ governs the discretization of predicted probabilities and ultimately determines three critical evaluation metrics; given the class imbalance inherent in financial risk warnings, we adopt the conventional setting of $\sigma =0.5$ as the optimal operating point.

4. Experimental Settings

4.1. Sample Selection

Corporate financial risk manifests through insufficient cash flow accompanied by surging accounts receivable, inability to service debts, and unsustainable dividend distributions. Prevailing studies on Chinese-listed firms predominantly employ matched-pair designs pairing ST (Special Treatment) and non-ST companies at a 1:1 ratio, which partially mitigates omitted-variable bias yet inherently reduces sample size, compromises generalizability, and introduces pairwise conditional expectations—where risk assessments become relative to matched counterparts. This study analyzes Shanghai/Shenzhen A-share-listed companies from 2000 to 2020, excluding financial sector entities and firms with excessive missing values, yielding a final sample of 2826 enterprises. Under China’s securities regulatory framework, companies typically exhibit financial distress indicators in the audited financial statements of the year preceding their Special Treatment (ST) designation or risk event occurrence (e.g., T−1 for T-year events). These pre-crisis financial data, having undergone rigorous audit procedures, provide reliable representations of the firm’s actual financial condition prior to risk materialization. The methodological approach aligns with established practices in financial risk warning prediction literature [39], where lagged financial variables are systematically employed to capture transitional financial trajectories. This temporal analytical framework particularly enhances the explanatory power for China’s ST mechanism, where regulatory interventions often follow observable financial deterioration patterns. Therefore, our paper prioritizes T−1 financial metrics to capture predictive signals and financial trajectory shifts.

Building upon extant literature, we select 46 indicators spanning solvency, operational efficiency, profitability, growth potential, per-share metrics, and relative valuation to quantify financial health (detailed in

Table 1. Financial indicators of Chinese-listed companies.

Indicator Category	Specific Indicators	Indicator Category	Specific Indicators
solvency	current ratio	Profitability	Return on equity
	quick ratio		Earnings Before Interest and Tax (EBIT)
	cash ratio		Return on invested capital
	working capital		Long-term capital return rate
	Asset liability ratio		Operating cost ratio
	Tangible asset liability ratio		Operating margin
	Equity multiplier		Total operating cost ratio
Business capability	Accounts receivable turnover rate		Asset impairment loss/operating income
	Inventory turnover rate		EBIT margin
	Operating Cycle		Return on assets
	Accounts payable turnover ratio		Net profit margin of total assets
	Operating capital turnover rate		Net profit margin of current assets
	Inventory turnover days	Per share indicator	Earnings per share
	receivables		Net asset value per share
Development capability	Capital accumulation rate		Revenue per share
	Growth rate of owner’s equity		Operating profit per share
	Growth rate of net assets per share		Capital reserve per share
Relative Value Index	Price-sales ratio		Earnings reserve per share
	market-to-book ratio		Undistributed profit per share
	market value		Retained earnings per share
	Market rate		Net cash flow per share
	book-to-market		Earnings per share before interest and tax
	Price-to-Earnings Ratio		Net cash flows from operating activities per share

), with Special Treatment (ST) designation serving as the financial distress criterion. Missing values are handled through median imputation for continuous variables and mode imputation for categorical variables, with missing indicator flags created when >5% of data is absent. Firms receiving ST in year T are labeled ‘1’, others ‘0’, utilizing exclusively CSMAR Database-sourced data (https://data.csmar.com/).

4.2. Implementation Details of the Proposed Method

To obtain the optimal results of financial risk early warning models, we fine-tune the hyper-parameters of financial risk early warning models by grid search methods. In the fine-tuning process of the proposed method, since the proposed method considers LightGBM as base learners, we first fine-tune the hyper-parameters of LightGBM for the proposed method. The detailed hyper-parameter initialization and fine-tune stride of each hyper-parameter are shown in

Table 2. Parameter settings for the proposed method.

Hyper-Parameters	Description	Searching Space	Stride
N_estimators	The number of DTs	[100, 500]	50
Learning_rate	Learning rate that control the optimization step	[0.001, 0.2]	Dichotomy
Max_depth	Maximum depth of DT in each	[3, 11]	1
subsample	Subsample ratio to undersample the training set	[0.6, 1]	0.05
Colsample_bytree	Subsample ratio to undersample the feature set	[0.6, 1]	0.05
$\gamma$	Parameter that specifies the minimum loss function drop required for node splitting	[0, 0.5]	0.10
$\alpha$	A coefficient for the L1 regularization term	[10−5, 10−1]	Dichotomy
$\lambda$	A coefficient for the L2 regularization term	[10−5, 10−1]	Dichotomy
T	The number of rounds for Bagging	[10, 50]	10

.

4.3. Evaluation Metrics

Financial risk early warning is a typical two-class classification problem, which can be modeled as a two-class classification task. As for the two-class classification problem, the original class is ST (positive) and non-ST (negative); according to the real state of the sample and the possible types of the predicted results, the financial risk early warning can be modeled as a two-class classification task, and we can arrange and combine the predictions to obtain four results, as shown in the following

Table 3. Confusion matrix of prediction results.

		Actual
		ST	Non-ST
Predicted	ST	TP	FP
	Non-ST	FN	TN

.

The confusion matrix is an error matrix, which is used to evaluate the performance of the supervised learning algorithm. In this paper, based on the confusion matrix of binary classification, the evaluation indices are introduced. According to the confusion matrix shown in Table 3, we can divide the predictions into four categories: true-positive (TP), false-positive (FP), false-negative (FN), and true-negative (TN).

This paper starts from the confusion matrix to introduce various model evaluation indicators, such as AUC value, precision, recall, F1, ROC curve, and BS.

(1)

Precision (Pre)

The indicator is the percentage of the sample that the model correctly predicted the financial crisis. The indicator measures the accuracy of warnings for the sample that predicted the financial crisis. Its calculation formula is

$$\mathrm{P}\mathrm{r}\mathrm{e}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}}$$

(12)

(2)

Recall (Rec)

The recall is the percentage of the sample that was correctly predicted by the model, of all the samples that had a financial crisis, and it measures the percentage of the sample that was correctly predicted by the model. The specific formula is as follows:

$$\mathrm{R}\mathrm{e}\mathrm{c}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(13)

(3)

F1-score (F1)

F1 is the harmonic mean between precision and recall. The value range of F1 is [0, 1]. The formula for F1 is

$$\mathrm{F}1={\displaystyle \frac{2\times \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\times \mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}+\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}}}$$

(14)

(4)

Brier Score (BS)

The Brier score describes the average error between the predicted result and the actual state. The smaller the score, the better the model. It can be calculated as

$$\mathrm{B}\mathrm{S}={\displaystyle \frac{1}{N}}\sum _{i=1}^N(p_i-y_i{)}^2$$

(15)

where $p_i$ represents the prediction probability of the $i$-th sample, $y_i$ is the true label value of the $i$-th sample, and $N$ is the number of samples.

(5)

ROC curve and AUC

The False-Positive Rate (FPR) represents the probability of incorrectly predicting non-ST samples as ST samples, and is used as the measurement metric of the model’s early warning efficiency. Its formula is

$$\mathrm{F}\mathrm{P}\mathrm{R}={\displaystyle \frac{\mathrm{F}\mathrm{P}}{\mathrm{F}\mathrm{P}+\mathrm{T}\mathrm{N}}}$$

(16)

The True-Positive Rate (TPR) is the percentage of ST samples that are predicted to be ST, also known as ST sample coverage, denoted by Sensitivity. The formula is

$$\mathrm{T}\mathrm{P}\mathrm{R}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(17)

The ROC curve is used to evaluate the quality of the model intuitively. The ROC curve is a curve with the TPR as the ordinate and the FPR as the abscissa. A steeper curve indicates that a higher TPR can be achieved at a lower FPR. According to the change in the threshold, the FPR and TPR of the model change accordingly, forming an ROC curve.

The AUC value is the area under the ROC curve, which is a very good quantifiable evaluation criterion derived from the ROC. The steeper the ROC curve, the better, that is, the larger the AUC, the better. Normally, the AUC value ranges from 0.5 to 1.0, with a larger AUC representing better performance. When the AUC is above 0.8, the model is generally acceptable. AUC is a metric used to evaluate the quality of a classification model.

5. Experimental Results

5.1. Performance Comparison and Analysis

To validate the effectiveness of the proposed algorithm, we initially selected a series of traditional risk early warning models for preliminary comparison, including statistical methods such as LAD and LR, single-machine-learning classifiers like DT, SVM, and NN, classic ensemble-learning techniques such as AdaBoost and RF, as well as advanced ensemble algorithms like XGBoost and LightGBM. As shown in Figure 1, the ROC curves of all risk early warning models lie above the random-guess line, demonstrating the effectiveness of all models and indicating that their overall predictive performance outperforms random guessing. Specifically, Figure 1 reveals that DT performs poorly on this dataset, with its area under the curve (AUC) being smaller than that of other risk early warning models. Furthermore, a comparison between the ROC curves of single-machine-learning classifiers and ensemble algorithms shows that the ensemble algorithms achieve significantly larger AUC values on this dataset compared to single-machine-learning classifiers and traditional statistical methods. Finally, as illustrated in Figure 1, the proposed model in this study exhibits a slightly larger AUC than the advanced ensemble models XGBoost and LightGBM, further validating the effectiveness of the proposed model. All the curves are obtained by 50 times repeated running based on 10-fold cross-validation, with each fold maintaining an 80:20 train-test split ratio to ensure balanced representation across all risk categories.

Table 4. Performance comparison of different classification methods.

Algorithm	AUC	Precision	Recall	F1	BS
LR	0.8932	0.25	0.1667	0.2	0.0104
LDA	0.8991	0.375	0.25	0.3	0.0104
DT	0.8579	0	0	0	0.0088
SVM	0.9119	0	0	0	0.0090
KNN	0.8722	0	0	0	0.0087
NN	0.8880	0.1429	0.1667	0.1538	0.0142
RF	0.9448	0.6735	0.1919	0.2986	0.0304
AdaBoost	0.9191	0.5833	0.3256	0.4179	0.2444
XGBoost	0.9478	0.6538	0.2965	0.4080	0.0323
LightGBM	0.9446	0.6812	0.2733	0.3900	0.0373
Proposed method	0.9502	0.6974	0.3081	0.4274	0.0287

presents the performance of various algorithms on the risk early warning dataset. As shown in Table 4, many single-machine-learning classifiers, such as DT, KNN, and SVM, achieved precision and recall scores of 0 on the risk early warning dataset. This is primarily due to the highly imbalanced nature of the dataset, where the number of ST samples in the test set was limited. The low complexity of single-machine-learning classifiers resulted in poor discrimination between ST and non-ST companies, causing the models to predict predominantly non-ST samples, leading to a correct prediction rate of 0 for ST samples. Compared to single-machine-learning classifiers, traditional statistical risk early warning models performed better, but their precision and recall values remained low. Such limitations could be mitigated through ensemble-learning strategies. As demonstrated in Table 4, ensemble algorithms like AdaBoost, RF, XGBoost, and LightGBM significantly improved AUC values, effectively enhancing precision and recall. In other words, compared to single-risk early warning models, ensemble algorithms improved their predictive capability for ST companies and enhanced prediction performance. Further comparisons revealed that our algorithm achieved optimal performance across metrics such as precision, AUC, and F1-scores, further validating the feasibility of the proposed cascading ensemble algorithm for risk early warning tasks. Additionally, examining the BS scores of single models like DT, SVM, and KNN indicated that single models held a leading advantage in BS metrics. However, their precision and recall scores were 0, as the dataset predominantly consisted of non-ST samples. Single models effectively identified non-ST samples, resulting in smaller overall errors on the risk early warning dataset, yet they exhibited larger overall errors in predicting ST samples.

The superior performance of the proposed model stems from its further cascading on the basis of ensemble strategies, making the proposed framework an “ensemble of ensembles” algorithm. This cascading mechanism not only provides better robustness but also exhibits strong scalability. To further highlight the effectiveness of the proposed cascading structure, we conducted a comparative analysis of the performance under different base learners, with the results presented in

Table 5. Comparison of prediction performance under different base learner cascade mechanisms.

Algorithm	AUC	Precision	Recall	F1	BS
Cascade LR	0.7611	0.5217	0.0698	0.1231	0.0472
Cascade LDA	0.8638	0.5179	0.1686	0.2544	0.0394
Cascade KNN	0.7730	0.5263	0.0581	0.1047	0.0404
Cascade DT	0.9160	0.4946	0.2674	0.3472	0.0327
Cascade RF	0.9477	0.6471	0.1919	0.2960	0.0302
Cascade AdaBoost	0.9350	0.5694	0.2384	0.3361	0.1913
Cascade XGBoost	0.9508	0.5733	0.25	0.3482	0.0333
Cascade LightGBM	0.9502	0.6974	0.3081	0.4274	0.0287

. As shown in Table 5, we employed multiple risk early warning models as base learners in the cascading framework, including LR, LDA, KNN, RF, AdaBoost, XGBoost, and LightGBM. Table 5 reveals that compared to single-machine-learning classifiers, the cascading ensemble models based on traditional statistical methods experienced a decline in AUC. This is because, at each level of the cascading framework, the decisions of the four base learners are made in parallel, and the final performance is the average result of these base learners. Weak base learners at the same level may degrade the overall performance of the cascading ensemble model. In contrast, tree-based cascading ensemble models demonstrated significant performance improvements. Combining the data from Table 4 and Table 5, in terms of AUC, the cascading decision tree model improved by 6.77% compared to the decision tree algorithm, the cascading random forest model improved by 0.31% compared to the random forest model, the cascading AdaBoost improved by 1.73% compared to AdaBoost, the cascading XGBoost improved by 0.319% compared to the XGBoost algorithm, and the cascading LightGBM improved by 0.593% compared to LightGBM. From the BS metric perspective, cascading LightGBM achieved the best BS score, indicating that it could effectively reduce modeling errors in risk early warning tasks. Additionally, integrating Table 4 and Table 5 demonstrates that robust base learners are fundamental to the high performance of cascading ensemble models. To achieve better risk early warning performance, more robust base learners should be the preferred choice for cascading ensemble mechanisms, as weak base learners may lead to performance degradation.

5.2. Sensitivity Analysis

The proposed algorithm is essentially an ensemble, as demonstrated in the cascading ensemble framework, where RF serves as the base learner. Since RF itself is an ensemble of decision trees and the proposed algorithm further ensembles RF, the model can be regarded as an “ensemble of ensembles” algorithm. In Table 4, we summarize the impact of base learner selection on the final model performance. RF, XGBoost, and LightGBM, as representatives of classic and advanced ensemble algorithms, serve as base learners for the proposed model, ensuring high-precision financial risk early warning. RF, XGBoost, and LightGBM themselves are tree-based ensemble algorithms, with RF being a bagging-based algorithm and XGBoost and LightGBM being boosting-based algorithms. As representatives of tree-based ensemble algorithms and base learners for the proposed algorithm, the number of trees in these algorithms is a critical parameter affecting model performance. To investigate the influence of parameters such as the number of trees and the complexity of ensemble base learners on model performance, we further analyzed the model’s performance. Figure 2 illustrates the sensitivity analysis of the model under different parameter settings, with Figure 2a showing the performance curve of LightGBM composed of varying numbers of decision trees and Figure 2b displaying the changes in the AUC metric as the number of leaf nodes in the LightGBM base learner varies. Figure 2a,b indicates that parameters such as the number of trees and leaf nodes in each LightGBM significantly impact the final model performance. A smaller number of decision trees or leaf nodes may lead to underfitting, while excessively increasing these parameters increases model complexity and may result in overfitting. Therefore, careful optimization of these parameters is necessary. On this risk early warning dataset, the optimal AUC is achieved when the number of decision trees is 50 and the number of leaf nodes per regression tree is limited to 70.

To further validate the model’s reliability, this study investigates its detailed performance metrics under varying proportions of training data. As shown in

Table 6. Comparison of the comprehensive performance of the models under different training set ratios.

Proportion of Training Set	Algorithm	AUC	Precision	Recall	F1	BS
0.8	Cascade forest	0.9477	0.6471	0.1919	0.2960	0.0302
	Cascade XGBoost	0.9508	0.5733	0.25	0.3482	0.0333
	Cascade LightGBM	0.9502	0.6974	0.3081	0.4274	0.0287
0.7	Cascade forest	0.9468	0.6327	0.1802	0.2805	0.0303
	Cascade XGBoost	0.9462	0.5595	0.2733	0.3672	0.0347
	Cascade LightGBM	0.9435	0.6452	0.3488	0.4528	0.0303
0.6	Cascade forest	0.9465	0.6327	0.1802	0.2805	0.0303
	Cascade XGBoost	0.9443	0.6098	0.2907	0.3937	0.0335
	Cascade LightGBM	0.9479	0.5625	0.2616	0.3571	0.0314
0.5	Cascade forest	0.9435	0.6304	0.1686	0.2661	0.0304
	Cascade XGBoost	0.9441	0.6420	0.3023	0.4111	0.0332
	Cascade LightGBM	0.9409	0.5641	0.2558	0.3520	0.0321

, the analysis of indicators across different training set proportions reveals a declining trend in AUC as the training data size decreases, indicating a reduction in the model’s discrimination capacity for ST companies. The comparison of BS metrics suggests that increasing the training set proportion or collecting more risk early warning data (financial indicators of ST/non-ST companies) is a viable approach to mitigate the discrepancy between predicted values and true labels. Furthermore, the decline in training data proportion leads to simultaneous degradation in precision and recall, reflecting diminished predictive performance for both ST and non-ST companies, ultimately resulting in a progressively decreasing F1-score. Most notably, the model’s robustness in handling small datasets is enhanced by the bagging algorithm incorporated during the cascading process, which boosts the diversity of each base learner. Remarkably, even with a 30% reduction in training data, the AUC decline remains below 1%, demonstrating sufficient resilience.

6. Discussion

6.1. Limitations

While the proposed ensemble model demonstrates improved robustness through bagging and enhanced generalization via cascade integration, four fundamental limitations require urgent attention in future research. First, the exclusive reliance on financial indicators neglects critical non-financial dimensions like corporate governance structures (e.g., board independence, executive compensation) and external audit opinions, which have proven predictive value in international studies. Second, the geographical restriction to Chinese-listed companies limits the model’s generalizability, particularly given the unique regulatory environment of China’s capital markets. Third, despite algorithmic improvements, key performance metrics (especially recall and F1-scores for minority classes) remain suboptimal for practical deployment, suggesting underlying feature representation or optimization challenges. Most critically, the severe class imbalance (ST/non-ST ratio of 1:31) demands systematic solutions beyond current ensemble techniques—a gap where advanced hybrid sampling strategies (e.g., SMOTE-ENN) or meta-cost-learning frameworks could yield significant improvements.

6.2. Future Research

Future research should prioritize (1) developing multi-modal frameworks integrating financial metrics with ESG factors and governance attributes, (2) conducting cross-market validation using datasets from developed and emerging economies, (3) designing specialized loss functions or attention mechanisms to boost minority class recognition, and (4) establishing standardized evaluation protocols for imbalanced financial prediction tasks. Particularly promising is the exploration of dynamic imbalance adaptation techniques that automatically adjust resampling ratios or cost matrices based on real-time data distributions—an innovation that could bridge the gap between academic metrics and operational requirements in risk management. Meanwhile, systematic comparisons with other state-of-the-art models will further demonstrate the proposed framework’s advantages in terms of generalization capability and operational efficiency, providing valuable benchmarks for both academic research and industry applications. Additionally, future studies should incorporate SHAP (SHapley Additive exPlanations) analysis or other explainable methods to enhance model interpretability, providing insights into feature contributions and decision-making processes. This addition will complement our performance-driven approach with transparent, actionable explanations for stakeholders.

7. Conclusions

In recent years, the gradual maturity of artificial intelligence theory has shifted risk early warning systems toward machine-learning algorithms and deep-learning techniques. Notably, the introduction of ensemble methods has significantly enhanced the robustness of risk early warning models. This study proposed a novel financial risk early warning model based on 46 financial indicators from 2826 A-share-listed companies on the Shanghai and Shenzhen Stock Exchanges in China from 2000 to 2020. In this research, the advanced tree-based ensemble algorithm LightGBM demonstrated high efficiency and precision in financial risk early warning modeling. The proposed algorithm further ensembles LightGBM, leveraging advanced ensemble techniques to enhance enterprise risk early warning capabilities. Additionally, the algorithm employed a cascading approach to increase model complexity, enabling it to adapt to scenarios with insufficient financial data and demonstrating strong scalability. Furthermore, the algorithm improved its generalization performance in risk early warning tasks by leveraging the robustness of tree models and bagging strategies. Experimental results on the financial risk early warning dataset of Chinese-listed companies showed that the proposed highly integrated algorithm effectively outperformed single-machine-learning-classifier models. The AUC and BS values of different base learners in the cascading ensemble indicated that strong base learners are better suited for cascading integration mechanisms, with cascading LightGBM achieving the optimal BS value and effectively reducing modeling errors. Moreover, the robustness of tree-based algorithms and bagging techniques promotes the diversity of base learners, making the proposed algorithm a risk early warning solution that achieves good performance without requiring extensive hyper-parameter tuning. Empirical results demonstrated that the model reached optimal AUC when the number of decision trees was 50 and the number of leaf nodes per tree was limited to 70. Finally, under varying proportions of training data, the cascading ensemble algorithm showed declining trends in AUC, precision, recall, and F1-scores, while the BS value increased. However, the bagging algorithm enhances base learner diversity, limiting the decline in the cascading ensemble model’s AUC value and highlighting its advantage in handling small datasets.

The conclusions of this study offer valuable insights for corporate management and other stakeholders. For business operators, the proposed financial risk early warning model enables them to predict the company’s financial condition for the coming year, allowing for timely and accurate assessment of financial health, facilitating early detection of financial risks, and implementing appropriate measures to avert potential crises. Financial institutions such as banks and bondholders, as well as related investors, can adjust their investment strategies and resource allocations based on the risk early warning results to avoid investment pitfalls. Regulatory bodies like the Securities and Exchange Commission can proactively intervene in listed companies using these early warning signals to prevent chain reactions that could jeopardize the entire financial market. Additionally, other corporate stakeholders, including employees, external customers, and suppliers, can optimize their decision-making based on the financial risk early warning outcomes to maximize their own interests.