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![The function max(0,z) is a surrogate function aiming to maximize the AUROC. However, this function is non-differentiable when z = 0. Thus, we replace it with the differentiable ε-smoothed function, hεz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${h}_{\varepsilon }\left(z\right)$$\end{document}](publication/352062156/figure/fig4/AS:1036653166612480@1624168783182/The-function-max0-z-is-a-surrogate-function-aiming-to-maximize-the-AUROC-However-this.png)
The function max(0,z) is a surrogate function aiming to maximize the AUROC. However, this function is non-differentiable when z = 0. Thus, we replace it with the differentiable ε-smoothed function, hεz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${h}_{\varepsilon }\left(z\right)$$\end{document}
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In this paper, we estimate coefficients of bankruptcy forecasting models, such as logistic and neural network models, by maximizing their discriminatory power as measured by the Area Under Receiver Operating Characteristics (AUROC) curve. A method is introduced and compared with traditional logistic and neural network models, using out-of-sample an...
Citations
The article examines the applicability of existing bankruptcy prediction models in the food retail sector. The industry has been chosen for analysis due to the fact, that according to official statistics, it has been significantly affected by the events of recent years (Covid-19 epidemic and economic crisises). For the study, a database was created with all firms that had ceased to operate in the sector over an 11-year period in 3 counties. The main objectives of the study were: 1) to check whether there are differences in the reliability of the models and which models are most applicable to the selected sector; 2) to investigate the accuracy of the models over the time horizons of bankruptcy; 3) to check the accuracy of forecasting models by type of bankruptcy completion procedure; 4) provide suggestions on the possibilities of applying bankruptcy forecasting models and indicate directions for further research. During the research, it was found that not all considered models are suitable for accurate forecasting. Two of the five models have very low prediction accuracy (Virág-Hajdu model and Tafler model). Assessment of model accuracy across bankruptcy time horizons showed that there is little variation in short-term forecast accuracy, with a slight decrease in the reliability of the models in the long term. Examining the predictive accuracy of the models by completion procedure type revealed that the types of procedures affected the prediction. The most accurate results were obtained for liquidation, while voluntary liquidation was the least accurate in several cases. The use of bankruptcy prediction models is important for an enterprise because they are a key tool for reducing its operational risk and preventing financial problems. The study can provide information for businesses in the food retail sector and the results can be used for further research. There are additional opportunities for expanding the enterprise database, transferring the research to other sectors of the economy, and expanding the number of bankruptcy models to study the suitability of their application to enterprises of various industries
Recently, ensemble-based machine learning models have been widely used and have demonstrated their efficiency in bankruptcy prediction. However, these algorithms are black box models and people cannot understand why they make their forecasts. This explains why interpretability methods in machine learning attract attention from many artificial intelligence researchers. In this paper, we evaluate the prediction performance of Random Forest, LightGBM, XGBoost, and NGBoost (Natural Gradient Boosting for probabilistic prediction) for French firms from different industries with the horizon of 1–5 years. We then use Shapley Additive Explanations (SHAP), a model-agnostic method to explain XGBoost, one of the best models for our data. SHAP can show how each feature impacts the output from XGBoost. Furthermore, single prediction can also be explained, thus allowing black box models to be used in credit risk management.
The study presents a systematic review of 232 studies on various aspects of the use of artificial intelligence methods for identification of financial distress (such as bankruptcy or insolvency). We follow the guidelines of the PRISMA methodology for performing the systematic reviews. The study discusses bankruptcy-related financial datasets, data imbalance, feature dimensionality reduction in financial datasets, financial distress prediction, data pre-processing issues, non-financial indicators, frequently used machine-learning methods, performance evolution metrics, and other related issues of machine-learning-based workflows. The study findings revealed the necessity of data balancing, dimensionality reduction techniques in data preprocessing, and allow researchers to identify new research directions that have not been analyzed yet.
Full text available at SSRN: http://dx.doi.org/10.2139/ssrn.3911490
In this paper, we test alternative feature selection methods for bankruptcy prediction and illustrate their superiority versus popular models used in the literature. We test these methods using a comprehensive dataset of more than one million financial statements from privately held Norwegian SMEs in 2006-2017. Our methods are allowed to choose among 155 accounting-based input variables derived from prior literature. We find that the input variables chosen by an embedded least absolute shrinkage and selection operator (LASSO) feature selection method yield the best in-sample fit, out-of-sample performance, and stability. Our findings are robust to using discrete hazard models with either a deep artificial neural network (DNN) or logistic regression (LR) in the estimation and hold across different time periods. We show in a simulation which mimics a real-world competitive credit market that using LASSO to choose bankruptcy predictors improves credit risk pricing and decision making, resulting in significantly higher bank profits.
