A Sequential Probabilistic System for Bankruptcy Data Classification

Introduction

Business failure prediction is of major importance for financial institutions and governments for making correct business decision (Thomas et, 2002; Huang et al, 2004; Khashman, 2010; Chen et al, 2013). Indeed, the increase of financial failure accelerates the economic deterioration and yields a lot of social problems (Chen et al, 2013). Thus, the problem of business failure affects investors, creditors, shareholders, and employees (Horta & AS Camanho, 2013). This highlights the importance of developing bankruptcy prediction models to serve as early warning and decision support systems (Thomas et, 2002; Huang et al, 2004; Khashman, 2010; Chen et al, 2013). Indeed, the benefits of using a business failure prediction model include reducing the cost of credit analysis, enabling faster decision, insuring credit collections, and diminishing possible risk (West, 2000). In addition, accurate bankruptcy prediction usually leads to better credit risk monitoring, and an increased debt collection rate (Lee & Wu, 2013). In general, the main characteristics of a good bankruptcy prediction model are as follows (Brezigar-Masten & Masten, 2012): reliability and robustness, ease of implementation, high degree of prediction accuracy and clear interpretability and transparency of decision making process.

The purpose of this paper is to present a two-stage probabilistic system to the problem of bankruptcy prediction. In the first stage, a set of initial features (inputs) is processed to select features that affect most probably the class label by using a logistic regression. Indeed, feature selection plays an important role in classification (Luukka, 2011); for instance, it allows simplifying the model, reducing computational cost, removing insignificant features, making the model more transparent and more comprehensible, providing better explanation, and reducing noise. As a result, feature selection may help enhancing the classification accuracy (Luukka, 2011). Logistic regression (Hilbe, 2009) is chosen in this study thanks to its ability to evaluate marginal probability contribution of each feature on class label. In particular, high uncertainty is expected to be related with low marginal probability contribution. Thus, the feature with the lowest probability significance is removed from the initial inputs set. In the second stage, the probabilistic neural network (PNN) (Specht, 1990) is adopted for classification task. It provides a general solution to pattern classification problems based on Bayesian theory. It is able to classify a new sample with the maximum probability of success given a large training set using prior knowledge. As a result, a sequential probabilistic system based on logistic regression for features selection and probabilistic neural network for data classification may achieve high accuracy thanks to marginal probability used for features selection and the learning ability of probabilistic neural networks. For comparison purpose, a bankruptcy classification system based on a conventional neural network trained with the initial features set is adopted as a reference model. The performance of each approach is evaluated in terms of correct classification rate (accuracy), sensitivity and specificity.