# Machine Learning for Bankruptcy Prediction in the American Stock Market: Dataset and Benchmarks
## 2 Related Works  
The recent advancements in machine learning (ML) led to new, innovative, and functional approaches [8; 9]. Moreover, they have enabled the development of intelligent models that try to assess the likelihood of companies' default by looking for relationships among different types of financial data, and the financial status of a firm in the future [10; 11; 12; 13; 14; 15; 16; 17]. Different ML algorithms and techniques such as Support Vector Machine (SVM) [18], boost ing techniques [19], discriminant analysis [20], and Neural Networks [5] have been used in the literature for this task. Moreover, different architectures have been evaluated to identify effective decision boundaries for this binary classification problem, such as the least absolute shrinkage and selection operator [21], dynamic slacks-based model [22], and two-stage classification [13]. However, although default prediction models have been studied for decades, several issues remain. Interestingly, some new issues have even been introduced with the recently increased exploitation of machine-learning models. Indeed, since the Z-Score model was proposed by [PERSON] in 1968 [23], research mainly focused on accounting-based ratios as markers to detect and understand if a firm is likely to face financial difficulties, such as bankruptcy. Scoring-based models use discriminant analysis to provide ordinal rankings of default risk but are often computed from small datasets using statistical and probabilistic models that focus more on explainability and explicability but miss generalization over time and across different sectors [24]. Other examples are the Kralicek quick test [25] and the Taffler model [26]. In [27], a step towards modern machine learning was made by introducing a binary response model that uses explanatory variables and applies a logistic function for bankruptcy prediction [28]. However, the main goal of these models' class is not to identify a decision boundary in the feature space but only to select a decision based on an output threshold that was statistically significant in the past for the specific sector. For example, [PERSON] suggested two thresholds, 1.81 and 2.99. Specifically, an [PERSON]'s Z-score above the 2.99 threshold means that firms are not expected to default in the next two years, below 1.81 that they are expected to default, while the interval between the two thresholds is named the \"zone of ignorance\" where no clear decision can be taken. However, even though many practitioners use this threshold, in [PERSON]'s view, this is an unfortunate practice since over the past 50 years, credit-worthiness dynamics and trends have changed so dramatically that the original zone cutoffs are no longer relevant [24]. Moreover, we still lack a definite theory for the bankruptcy prediction task [18; 29] and in particular, a generally accepted performance metric is missing along with a formal theoretical framework. As a consequence, the most common methodology in bankruptcy prediction tasks is identifying discriminant features using a trial and error approach with various accounting-based ratios [15; 16]. Machine-learning models usually need large datasets to be trained and suffer when class imbalance is strong as in bankruptcy, since default events are quite rare. Learning from imbalanced data requires dealing with several challenges, especially when the most important class that should be recognized is exactly the one that is least represented in the dataset. This issue is strongly related to the lack of a general performance metric. Machine-learning techniques like ensemble methods were firstly explored for default prediction by [PERSON] et al. [30]. [PERSON] et al. showed a much better performance for the ensembles compared to standalone classifiers, while their results were also confirmed by [PERSON] et al. [31]. [PERSON] et al. further analyzed the performance of ensemble models, finding that bagging outperformed boosting for all credit databases in terms of average accuracy, as well as type I and type II error [32].