Using neural network ensembles for bankruptcy prediction and credit scoring

Bankruptcy prediction and credit scoring have long been regarded as critical topics and have been studied extensively in the accounting and finance literature. Artificial intelligence and machine learning techniques have been used to solve these financial decision-making problems. The multilayer perceptron (MLP) network trained by the back-propagation learning algorithm is the mostly used technique for financial decision-making problems. In addition, it is usually superior to other traditional statistical models. Recent studies suggest combining multiple classifiers (or classifier ensembles) should be better than single classifiers. However, the performance of multiple classifiers in bankruptcy prediction and credit scoring is not fully understood. In this paper, we investigate the performance of a single classifier as the baseline classifier to compare with multiple classifiers and diversified multiple classifiers by using neural networks based on three datasets. By comparing with the single classifier as the benchmark in terms of average prediction accuracy, the multiple classifiers only perform better in one of the three datasets. The diversified multiple classifiers trained by not only different classifier parameters but also different sets of training data perform worse in all datasets. However, for the Type I and Type II errors, there is no exact winner. We suggest that it is better to consider these three classifier architectures to make the optimal financial decision.     

Efficiently processing deterministic approximate aggregation query on massive data

Financial distress prediction is very important to financial institutions who must be able to make critical decisions regarding customer loans. Bankruptcy prediction and credit scoring are the two main aspects considered in financial distress prediction. To assist in this determination, thereby lowering the risk borne by the financial institution, it is necessary to develop effective prediction models for prediction of the likelihood of bankruptcy and estimation of credit risk. A number of financial distress prediction models have been constructed, which utilize various machine learning techniques, such as single classifiers and classifier ensembles, but improving the prediction accuracy is the major research issue. In addition, aside from improving the prediction accuracy, there have been very few studies that specifically consider lowering the Type I error. In practice, Type I errors need to receive careful consideration during model construction because they can affect the cost to the financial institution. In this study, we introduce a classifier ensemble approach designed to reduce the misclassification cost. The outputs produced by multiple classifiers are combined by utilizing the unanimous voting (UV) method to find the final prediction result. Experimental results obtained based on four relevant datasets show that our UV ensemble approach outperforms the baseline single classifiers and classifier ensembles. Specifically, the UV ensemble not only provides relatively good prediction accuracy and minimizes Type I/II errors, but also produces the smallest misclassification cost.     

A comparative study of classifier ensembles for bankruptcy prediction

The aim of bankruptcy prediction in the areas of data mining and machine learning is to develop an effective model which can provide the higher prediction accuracy. In the prior literature, various classification techniques have been developed and studied, in/with which classifier ensembles by combining multiple classifiers approach have shown their outperformance over many single classifiers. However, in terms of constructing classifier ensembles, there are three critical issues which can affect their performance. The first one is the classification technique actually used/adopted, and the other two are the combination method to combine multiple classifiers and the number of classifiers to be combined, respectively. Since there are limited, relevant studies examining these aforementioned disuses, this paper conducts a comprehensive study of comparing classifier ensembles by three widely used classification techniques including multilayer perceptron (MLP) neural networks, support vector machines (SVM), and decision trees (DT) based on two well-known combination methods including bagging and boosting and different numbers of combined classifiers. Our experimental results by three public datasets show that DT ensembles composed of 80–100 classifiers using the boosting method perform best. The Wilcoxon signed ranked test also demonstrates that DT ensembles by boosting perform significantly different from the other classifier ensembles. Moreover, a further study over a real-world case by a Taiwan bankruptcy dataset was conducted, which also demonstrates the superiority of DT ensembles by boosting over the others.     

DF-SVM: a decision forest constructed on artificially enlarged feature space by support vector machine

Enlarging the feature space of the base tree classifiers in a decision forest by means of informative features extracted from an additional predictive model is advantageous for classification tasks. In this paper, we have empirically examined the performance of this type of decision forest with three different base tree classifier models including; (1) the full decision tree, (2) eight-node decision tree and (3) two-node decision tree (or decision stump). The hybrid decision forest with these base classifiers are trained in nine different sized resampled training sets. We have examined the performance of all these ensembles from different point of views; we have studied the bias-variance decomposition of the misclassification error of the ensembles, then we have investigated the amount of dependence and degree of uncertainty among the base classifiers of these ensembles using information theoretic measures. The experiment was designed to find out: (1) optimal training set size for each base classifier and (2) which base classifier is optimal for this kind of decision forest. In the final comparison, we have checked whether the subsampled version of the decision forest outperform the bootstrapped version. All the experiments have been conducted with 20 benchmark datasets from UCI machine learning repository. The overall results clearly point out that with careful selection of the base classifier and training sample size, the hybrid decision forest can be an efficient tool for real world classification tasks.     

A new perspective of performance comparison among machine learning algorithms for financial distress prediction

We set out in this study to review a vast amount of recent literature on machine learning (ML) approaches to predicting financial distress (FD), including supervised, unsupervised and hybrid supervised–unsupervised learning algorithms. Four supervised ML models including the traditional support vector machine (SVM), recently developed hybrid associative memory with translation (HACT), hybrid GA-fuzzy clustering and extreme gradient boosting (XGBoost) were compared in prediction performance to the unsupervised classifier deep belief network (DBN) and the hybrid DBN-SVM model, whereby a total of sixteen financial variables were selected from the financial statements of the publicly-listed Taiwanese firms as inputs to the six approaches. Our empirical findings, covering the 2010–2016 sample period, demonstrated that among the four supervised algorithms, the XGBoost provided the most accurate FD prediction. Moreover, the hybrid DBN-SVM model was able to generate more accurate forecasts than the use of either the SVM or the classifier DBN in isolation.     

A novel hybrid credit scoring model based on ensemble feature selection and multilayer ensemble classification

Credit scoring focuses on the development of empirical models to support the financial decision‐making processes of financial institutions and credit industries. It makes use of applicants' historical data and statistical or machine learning techniques to assess the risk associated with an applicant. However, the historical data may consist of redundant and noisy features that affect the performance of credit scoring models. The main focus of this paper is to develop a hybrid model, combining feature selection and a multilayer ensemble classifier framework, to improve the predictive performance of credit scoring. The proposed hybrid credit scoring model is modeled in three phases. The initial phase constitutes preprocessing and assigns ranks and weights to classifiers. In the next phase, the ensemble feature selection approach is applied to the preprocessed dataset. Finally, in the last phase, the dataset with the selected features is used in a multilayer ensemble classifier framework. In addition, a classifier placement algorithm based on the Choquet integral value is designed, as the classifier placement affects the predictive performance of the ensemble framework. The proposed hybrid credit scoring model is validated on real‐world credit scoring datasets, namely, Australian, Japanese, German‐categorical, and German‐numerical datasets.     

Financial decision support using neural networks and support vector machines

Abstract: Bankruptcy prediction and credit scoring are the two important problems facing financial decision support. The multilayer perceptron (MLP) network has shown its applicability to these problems and its performance is usually superior to those of other traditional statistical models. Support vector machines (SVMs) are the core machine learning techniques and have been used to compare with MLP as the benchmark. However, the performance of SVMs is not fully understood in the literature because an insufficient number of data sets is considered and different kernel functions are used to train the SVMs. In this paper, four public data sets are used. In particular, three different sizes of training and testing data in each of the four data sets are considered (i.e. 3:7, 1:1 and 7:3) in order to examine and fully understand the performance of SVMs. For SVM model construction, the linear, radial basis function and polynomial kernel functions are used to construct the SVMs. Using MLP as the benchmark, the SVM classifier only performs better in one of the four data sets. On the other hand, the prediction results of the MLP and SVM classifiers are not significantly different for the three different sizes of training and testing data.     

Listed companies’ financial distress prediction based on weighted majority voting combination of multiple classifiers

How to effectively predict financial distress is an important problem in corporate financial management. Though much attention has been paid to financial distress prediction methods based on single classifier, its limitation of uncertainty and benefit of multiple classifier combination for financial distress prediction has also been neglected. This paper puts forward a financial distress prediction method based on weighted majority voting combination of multiple classifiers. The framework of multiple classifier combination system, model of weighted majority voting combination, basic classifiers’ voting weight model and basic classifiers’ selection principles are discussed in detail. Empirical experiment with Chinese listed companies’ real world data indicates that this method can greatly improve the average prediction accuracy and stability, and it is more suitable for financial distress prediction than single classifiers.     

The effects of combining classifiers with the same training statistics using Bayesian decision rules

Multiple classifier systems (MCS) are attracting increasing interest in the field of pattern recognition and machine learning. Recently, MCS are also being introduced in the remote sensing field where the importance of classifier diversity for image classification problems has not been examined. In this article, Satellite Pour l'Observation de la Terre (SPOT) IV panchromatic and multispectral satellite images are classified into six land cover classes using five base classifiers: contextual classifier, k-nearest neighbour classifier, Mahalanobis classifier, maximum likelihood classifier and minimum distance classifier. The five base classifiers are trained with the same feature sets throughout the experiments and a posteriori probability, derived from the confusion matrix of these base classifiers, is applied to five Bayesian decision rules (product rule, sum rule, maximum rule, minimum rule and median rule) for constructing different combinations of classifier ensembles. The performance of these classifier ensembles is evaluated for overall accuracy and kappa statistics. Three statistical tests, the McNemar's test, the Cochran's Q test and the Looney's F-test, are used to examine the diversity of the classification results of the base classifiers compared to the results of the classifier ensembles. The experimental comparison reveals that (a) significant diversity amongst the base classifiers cannot enhance the performance of classifier ensembles; (b) accuracy improvement of classifier ensembles can only be found by using base classifiers with similar and low accuracy; (c) increasing the number of base classifiers cannot improve the overall accuracy of the MCS and (d) none of the Bayesian decision rules outperforms the others.     

Aggregating multiple classification results using Choquet integral for financial distress early warning

Financial distress prediction methods based on combination classifier become a rising trend in this field. This paper applies Choquet integral to ensemble single classifiers and proposes a Choquet integral-based combination classifier for financial distress early warning. Also, as the conditions between training and pattern recognition cannot be completely consistent, so this paper proposes an adaptive fuzzy measure by using the dynamic information in the single classifier pattern recognition results which is more reasonable than the static prior fuzzy density. Finally, a comparative analysis based on Chinese listed companies’ real data is conducted to verify prediction accuracy and stability of the combination classifier. The experiment results indicate that financial distress prediction using Choquet integral-based combination classifier has higher average accuracy and stability than single classifiers.     

Soft computing system for bank performance prediction

This paper presents a soft computing based bank performance prediction system. It is an ensemble system whose constituent models are a multi-layered feed forward neural network trained with backpropagation (MLFF-BP), a probabilistic neural network (PNN) and a radial basis function neural network (RBFN), support vector machine (SVM), classification and regression trees (CART) and a fuzzy rule based classifier. Further, principal component analysis (PCA) based hybrid neural networks, viz. PCA-MLFF-BP, PCA-PNN and PCA-RBF are also included as constituents of the ensemble. Moreover, GRNN and PNN were trained with a genetic algorithm to optimize the smoothing factors. Two ensembles (i) simple majority voting based and (ii) weightage based are implemented. This system predicts the performance of a bank in the coming financial year based on its previous 2-years’ financial data. Ten-fold cross-validation is performed in the training sessions and results are validated with an independent production set. It is demonstrated that the ensemble is able to yield lower Type I and Type II errors compared to its constituent models. Further, the ensemble also outperformed an earlier study [P.G. Swicegood, Predicting poor bank profitability: a comparison of neural network, discriminant analysis and professional human judgement, Ph.D. Thesis, Department of Finance, Florida State University, 1998] that used multivariate discriminant analysis (MDA), MLFF-BP and human judgment.     

Two-level classifier ensembles for credit risk assessment

Many techniques have been proposed for credit risk assessment, from statistical models to artificial intelligence methods. During the last few years, different approaches to classifier ensembles have successfully been applied to credit scoring problems, demonstrating to be generally more accurate than single prediction models. The present paper goes one step beyond by introducing composite ensembles that jointly use different strategies for diversity induction. Accordingly, the combination of data resampling algorithms (bagging and AdaBoost) and attribute subset selection methods (random subspace and rotation forest) for the construction of composite ensembles is explored with the aim of improving the prediction performance. The experimental results and statistical tests show that this new two-level classifier ensemble constitutes an appropriate solution for credit scoring problems, performing better than the traditional single ensembles and very significantly better than individual classifiers.     

Unsupervised feature selection and general pattern discovery using Self-Organizing Maps for gaining insights into the nature of seismic wavefields

This study presents an unsupervised feature selection and learning approach for the discovery and intuitive imaging of significant temporal patterns in seismic single-station or network recordings. For this purpose, the data are parametrized by real-valued feature vectors for short time windows using standard analysis tools for seismic data, such as frequency-wavenumber, polarization, and spectral analysis. We use Self-Organizing Maps (SOMs) for a data-driven feature selection, visualization and clustering procedure, which is in particular suitable for high-dimensional data sets. Our feature selection method is based on significance testing using the Wald–Wolfowitz runs test for individual features and on correlation hunting with SOMs in feature subsets. Using synthetics composed of Rayleigh and Love waves and real-world data, we show the robustness and the improved discriminative power of that approach compared to feature subsets manually selected from individual wavefield parametrization methods. Furthermore, the capability of the clustering and visualization techniques to investigate the discrimination of wave phases is shown by means of synthetic waveforms and regional earthquake recordings.     

AptaCDSS-E: A classifier ensemble-based clinical decision support system for cardiovascular disease level prediction

Conventional clinical decision support systems are generally based on a single classifier or a simple combination of these models, showing moderate performance. In this paper, we propose a classifier ensemble-based method for supporting the diagnosis of cardiovascular disease (CVD) based on aptamer chips. This AptaCDSS-E system overcomes conventional performance limitations by utilizing ensembles of different classifiers. Recent surveys show that CVD is one of the leading causes of death and that significant life savings can be achieved if precise diagnosis can be made. For CVD diagnosis, our system combines a set of four different classifiers with ensembles. Support vector machines and neural networks are adopted as base classifiers. Decision trees and Bayesian networks are also adopted to augment the system. Four aptamer-based biochip data sets including CVD data containing 66 samples were used to train and test the system. Three other supplementary data sets are used to alleviate data insufficiency. We investigated the effectiveness of the ensemble-based system with several different aggregation approaches by comparing the results with single classifier-based models. The prediction performance of the AptaCDSS-E system was assessed with a cross-validation test. The experimental results show that our system achieves high diagnosis accuracy (>94%) and comparably small prediction difference intervals (<6%), proving its usefulness in the clinical decision process of disease diagnosis. Additionally, 10 possible biomarkers are found for further investigation.     

A comparative study on base classifiers in ensemble methods for credit scoring

In the last years, the application of artificial intelligence methods on credit risk assessment has meant an improvement over classic methods. Small improvements in the systems about credit scoring and bankruptcy prediction can suppose great profits. Then, any improvement represents a high interest to banks and financial institutions. Recent works show that ensembles of classifiers achieve the better results for this kind of tasks. In this paper, it is extended a previous work about the selection of the best base classifier used in ensembles on credit data sets. It is shown that a very simple base classifier, based on imprecise probabilities and uncertainty measures, attains a better trade-off among some aspects of interest for this type of studies such as accuracy and area under ROC curve (AUC). The AUC measure can be considered as a more appropriate measure in this grounds, where the different type of errors have different costs or consequences. The results shown here present to this simple classifier as an interesting choice to be used as base classifier in ensembles for credit scoring and bankruptcy prediction, proving that not only the individual performance of a classifier is the key point to be selected for an ensemble scheme.     

An experimental study on diversity for bagging and boosting with linear classifiers

In classifier combination, it is believed that diverse ensembles have a better potential for improvement on the accuracy than non-diverse ensembles. We put this hypothesis to a test for two methods for building the ensembles: Bagging and Boosting, with two linear classifier models: the nearest mean classifier and the pseudo-Fisher linear discriminant classifier. To estimate diversity, we apply nine measures proposed in the recent literature on combining classifiers. Eight combination methods were used: minimum, maximum, product, average, simple majority, weighted majority, Naive Bayes and decision templates. We carried out experiments on seven data sets for different sample sizes, different number of classifiers in the ensembles, and the two linear classifiers. Altogether, we created 1364 ensembles by the Bagging method and the same number by the Boosting method. On each of these, we calculated the nine measures of diversity and the accuracy of the eight different combination methods, averaged over 50 runs. The results confirmed in a quantitative way the intuitive explanation behind the success of Boosting for linear classifiers for increasing training sizes, and the poor performance of Bagging in this case. Diversity measures indicated that Boosting succeeds in inducing diversity even for stable classifiers whereas Bagging does not.     

Ensemble approach based on bagging,boosting and stacking for short-term prediction in agribusiness time series

The investigation of the accuracy of methods employed to forecast agricultural commodities prices is an important area of study. In this context, the development of effective models is necessary. Regression ensembles can be used for this purpose. An ensemble is a set of combined models which act together to forecast a response variable with lower error. Faced with this, the general contribution of this work is to explore the predictive capability of regression ensembles by comparing ensembles among themselves, as well as with approaches that consider a single model (reference models) in the agribusiness area to forecast prices one month ahead. In this aspect, monthly time series referring to the price paid to producers in the state of Parana, Brazil for a 60 kg bag of soybean (case study 1) and wheat (case study 2) are used. The ensembles bagging (random forests — RF), boosting (gradient boosting machine — GBM and extreme gradient boosting machine — XGB), and stacking (STACK) are adopted. The support vector machine for regression (SVR), multilayer perceptron neural network (MLP) and K-nearest neighbors (KNN) are adopted as reference models. Performance measures such as mean absolute percentage error (MAPE), root mean squared error (RMSE), mean absolute error (MAE), and mean squared error (MSE) are used for models comparison. Friedman and Wilcoxon signed rank tests are applied to evaluate the models’ absolute percentage errors (APE). From the comparison of test set results, MAPE lower than 1% is observed for the best ensemble approaches. In this context, the XGB/STACK (Least Absolute Shrinkage and Selection Operator-KNN-XGB-SVR) and RF models showed better performance for short-term forecasting tasks for case studies 1 and 2, respectively. Better APE (statistically smaller) is observed for XGB/STACK and RF in relation to reference models. Besides that, approaches based on boosting are consistent, providing good results in both case studies. Alongside, a rank according to the performances is: XGB, GBM, RF, STACK, MLP, SVR and KNN. It can be concluded that the ensemble approach presents statistically significant gains, reducing prediction errors for the price series studied. The use of ensembles is recommended to forecast agricultural commodities prices one month ahead, since a more assertive performance is observed, which allows to increase the accuracy of the constructed model and reduce decision-making risk.     

Exploring the synergetic effects of sample types on the performance of ensembles for credit risk and corporate bankruptcy prediction

Credit risk and corporate bankruptcy prediction has widely been studied as a binary classification problem using both advanced statistical and machine learning models. Ensembles of classifiers have demonstrated their effectiveness for various applications in finance using data sets that are often characterized by imperfections such as irrelevant features, skewed classes, data set shift, and missing and noisy data. However, there are other corruptions in the data that might hinder the prediction performance mainly on the default or bankrupt (positive) cases, where the misclassification costs are typically much higher than those associated to the non-default or non-bankrupt (negative) class. Here we characterize the complexity of 14 real-life financial databases based on the different types of positive samples. The objective is to gain some insight into the potential links between the performance of classifier ensembles (BAGGING, AdaBoost, random subspace, DECORATE, rotation forest, random forest, and stochastic gradient boosting) and the positive sample types. Experimental results reveal that the performance of the ensembles indeed depends on the prevalent type of positive samples.     

Diversity-based combination of non-parametric classifiers for EMG signal decomposition

Non-parametric classification procedures based on a certainty measure and nearest neighbour rule for motor unit potential classification (MUP) during electromyographic (EMG) signal decomposition were explored. A diversity-based classifier fusion approach is developed and evaluated to achieve improved classification performance. The developed system allows the construction of a set of non-parametric base classifiers and then automatically chooses, from the pool of base classifiers, subsets of classifiers to form candidate classifier ensembles. The system selects the classifier ensemble members by exploiting a diversity measure for selecting classifier teams. The kappa statistic is used as the diversity measure to estimate the level of agreement between base classifier outputs, i.e., to measure the degree of decision similarity between base classifiers. The pool of base classifiers consists of two kinds of classifiers: adaptive certainty-based classifiers (ACCs) and adaptive fuzzy k-NN classifiers (AFNNCs) and both utilize different types of features. Once the patterns are assigned to their classes, by the classifier fusion system, firing pattern consistency statistics for each class are calculated to detect classification errors in an adaptive fashion. Performance of the developed system was evaluated using real and simulated EMG signals and was compared with the performance of the constituent base classifiers and the performance of the fixed ensemble containing the full set of base classifiers. Across the EMG signal data sets used, the diversity-based classifier fusion approach had better average classification performance overall, especially in terms of reducing classification errors.