An experimental comparison of ensemble of classifiers for bankruptcy prediction and credit scoring

In this paper, we investigate the performance of several systems based on ensemble of classifiers for bankruptcy prediction and credit scoring.The obtained results are very encouraging, our results improved the performance obtained using the stand-alone classifiers. We show that the method “Random Subspace” outperforms the other ensemble methods tested in this paper. Moreover, the best stand-alone method is the multi-layer perceptron neural net, while the best method tested in this work is the Random Subspace of Levenberg–Marquardt neural net.In this work, three financial datasets are chosen for the experiments: Australian credit, German credit, and Japanese credit.     

Exploring the behaviour of base classifiers in credit scoring ensembles

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 more accurate than single prediction models. However, it is still a question what base classifiers should be employed in each ensemble in order to achieve the highest performance. Accordingly, the present paper evaluates the performance of seven individual prediction techniques when used as members of five different ensemble methods. The ultimate aim of this study is to suggest appropriate classifiers for each ensemble approach in the context of credit scoring. The experimental results and statistical tests show that the C4.5 decision tree constitutes the best solution for most ensemble methods, closely followed by the multilayer perceptron neural network and logistic regression, whereas the nearest neighbour and the naive Bayes classifiers appear to be significantly the worst.     

A new hybrid ensemble credit scoring model based on classifiers consensus system approach

During the last few years there has been marked attention towards hybrid and ensemble systems development, having proved their ability to be more accurate than single classifier models. However, among the hybrid and ensemble models developed in the literature there has been little consideration given to: 1) combining data filtering and feature selection methods 2) combining classifiers of different algorithms; and 3) exploring different classifier output combination techniques other than the traditional ones found in the literature. In this paper, the aim is to improve predictive performance by presenting a new hybrid ensemble credit scoring model through the combination of two data pre-processing methods based on Gabriel Neighbourhood Graph editing (GNG) and Multivariate Adaptive Regression Splines (MARS) in the hybrid modelling phase. In addition, a new classifier combination rule based on the consensus approach (ConsA) of different classification algorithms during the ensemble modelling phase is proposed. Several comparisons will be carried out in this paper, as follows: 1) Comparison of individual base classifiers with the GNG and MARS methods applied separately and combined in order to choose the best results for the ensemble modelling phase; 2) Comparison of the proposed approach with all the base classifiers and ensemble classifiers with the traditional combination methods; and 3) Comparison of the proposed approach with recent related studies in the literature. Five of the well-known base classifiers are used, namely, neural networks (NN), support vector machines (SVM), random forests (RF), decision trees (DT), and naïve Bayes (NB). The experimental results, analysis and statistical tests prove the ability of the proposed approach to improve prediction performance against all the base classifiers, hybrid and the traditional combination methods in terms of average accuracy, the area under the curve (AUC) H-measure and the Brier Score. The model was validated over seven real world credit datasets.     

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.     

A comparative assessment of ensemble learning for credit scoring

Both statistical techniques and Artificial Intelligence (AI) techniques have been explored for credit scoring, an important finance activity. Although there are no consistent conclusions on which ones are better, recent studies suggest combining multiple classifiers, i.e., ensemble learning, may have a better performance. In this study, we conduct a comparative assessment of the performance of three popular ensemble methods, i.e., Bagging, Boosting, and Stacking, based on four base learners, i.e., Logistic Regression Analysis (LRA), Decision Tree (DT), Artificial Neural Network (ANN) and Support Vector Machine (SVM). Experimental results reveal that the three ensemble methods can substantially improve individual base learners. In particular, Bagging performs better than Boosting across all credit datasets. Stacking and Bagging DT in our experiments, get the best performance in terms of average accuracy, type I error and type II error.     

Fusion of multiple diverse predictors in stock market

Forecasting stock returns and their risk represents one of the most important concerns of market decision makers. Although many studies have examined single classifiers of stock returns and risk methods, fusion methods, which have only recently emerged, require further study in this area. The main aim of this paper is to propose a fusion model based on the use of multiple diverse base classifiers that operate on a common input and a Meta classifier that learns from base classifiers’ outputs to obtain more precise stock return and risk predictions. A set of diversity methods, including Bagging, Boosting and AdaBoost, is applied to create diversity in classifier combinations. Moreover, the number and procedure for selecting base classifiers for fusion schemes is determined using a methodology based on dataset clustering and candidate classifiers’ accuracy. The results demonstrate that Bagging exhibited superior performance within the fusion scheme and could achieve a maximum of 83.6% accuracy with Decision Tree, LAD Tree and Rep Tree for return prediction and 88.2% accuracy with BF Tree, DTNB and LAD Tree in risk prediction. For feature selection part, a wrapper-GA algorithm is developed and compared with the fusion model. This paper seeks to help researcher select the best individual classifiers and fuse the proper scheme in stock market prediction. To illustrate the approach, we apply it to Tehran Stock Exchange (TSE) data for the period from 2002 to 2012.     

Ensemble classification based on generalized additive models

Generalized additive models (GAMs) are a generalization of generalized linear models (GLMs) and constitute a powerful technique which has successfully proven its ability to capture nonlinear relationships between explanatory variables and a response variable in many domains. In this paper, GAMs are proposed as base classifiers for ensemble learning. Three alternative ensemble strategies for binary classification using GAMs as base classifiers are proposed: (i) GAMbag based on Bagging, (ii) GAMrsm based on the Random Subspace Method (RSM), and (iii) GAMens as a combination of both. In an experimental validation performed on 12 data sets from the UCI repository, the proposed algorithms are benchmarked to a single GAM and to decision tree based ensemble classifiers (i.e. RSM, Bagging, Random Forest, and the recently proposed Rotation Forest). From the results a number of conclusions can be drawn. Firstly, the use of an ensemble of GAMs instead of a single GAM always leads to improved prediction performance. Secondly, GAMrsm and GAMens perform comparably, while both versions outperform GAMbag. Finally, the value of using GAMs as base classifiers in an ensemble instead of standard decision trees is demonstrated. GAMbag demonstrates performance comparable to ordinary Bagging. Moreover, GAMrsm and GAMens outperform RSM and Bagging, while these two GAM ensemble variations perform comparably to Random Forest and Rotation Forest. Sensitivity analyses are included for the number of member classifiers in the ensemble, the number of variables included in a random feature subspace and the number of degrees of freedom for GAM spline estimation.     

Combining cluster analysis with classifier ensembles to predict financial distress

The ability to accurately predict business failure is a very important issue in financial decision-making. Incorrect decision-making in financial institutions is very likely to cause financial crises and distress. Bankruptcy prediction and credit scoring are two important problems facing financial decision support. As many related studies develop financial distress models by some machine learning techniques, more advanced machine learning techniques, such as classifier ensembles and hybrid classifiers, have not been fully assessed. The aim of this paper is to develop a novel hybrid financial distress model based on combining the clustering technique and classifier ensembles. In addition, single baseline classifiers, hybrid classifiers, and classifier ensembles are developed for comparisons. In particular, two clustering techniques, Self-Organizing Maps (SOMs) and k-means and three classification techniques, logistic regression, multilayer-perceptron (MLP) neural network, and decision trees, are used to develop these four different types of bankruptcy prediction models. As a result, 21 different models are compared in terms of average prediction accuracy and Type I & II errors. By using five related datasets, combining Self-Organizing Maps (SOMs) with MLP classifier ensembles performs the best, which provides higher predication accuracy and lower Type I & II errors.     

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.     

A variant of Rotation Forest for constructing ensemble classifiers

Rotation Forest, an effective ensemble classifier generation technique, works by using principal component analysis (PCA) to rotate the original feature axes so that different training sets for learning base classifiers can be formed. This paper presents a variant of Rotation Forest, which can be viewed as a combination of Bagging and Rotation Forest. Bagging is used here to inject more randomness into Rotation Forest in order to increase the diversity among the ensemble membership. The experiments conducted with 33 benchmark classification data sets available from the UCI repository, among which a classification tree is adopted as the base learning algorithm, demonstrate that the proposed method generally produces ensemble classifiers with lower error than Bagging, AdaBoost and Rotation Forest. The bias–variance analysis of error performance shows that the proposed method improves the prediction error of a single classifier by reducing much more variance term than the other considered ensemble procedures. Furthermore, the results computed on the data sets with artificial classification noise indicate that the new method is more robust to noise and kappa-error diagrams are employed to investigate the diversity–accuracy patterns of the ensemble classifiers.     

A fast ensemble pruning algorithm based on pattern mining process

Ensemble pruning deals with the reduction of base classifiers prior to combination in order to improve generalization and prediction efficiency. Existing ensemble pruning algorithms require much pruning time. This paper presents a fast pruning approach: pattern mining based ensemble pruning (PMEP). In this algorithm, the prediction results of all base classifiers are organized as a transaction database, and FP-Tree structure is used to compact the prediction results. Then a greedy pattern mining method is explored to find the ensemble of size k. After obtaining the ensembles of all possible sizes, the one with the best accuracy is outputted. Compared with Bagging, GASEN, and Forward Selection, experimental results show that PMEP achieves the best prediction accuracy and keeps the size of the final ensemble small, more importantly, its pruning time is much less than other ensemble pruning algorithms.     

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.     

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.     

Neural network ensemble strategies for financial decision applications

Considerable research effort has been expended to identify more accurate models for decision support systems in financial decision domains including credit scoring and bankruptcy prediction. The focus of this earlier work has been to identify the “single best” prediction model from a collection that includes simple parametric models, nonparametric models that directly estimate data densities, and nonlinear pattern recognition models such as neural networks. Recent theories suggest this work may be misguided in that ensembles of predictors provide more accurate generalization than the reliance on a single model. This paper investigates three recent ensemble strategies: crossvalidation, bagging, and boosting. We employ the multilayer perceptron neural network as a base classifier. The generalization ability of the neural network ensemble is found to be superior to the single best model for three real world financial decision applications.     

基于装袋GEP分类器集成的信用评估

为提高信用评估的预测精度,提出一种基于装袋的基因表达式编程(GEP)多分类器集成算法。该算法采用Bagging方法将GEP产生的多个差异基分类器进行集成。在德国信用数据库真实数据集上的实验及性能分析表明,该算法较SVM算法的预测精度提高约2.7%;较KNN(K=17)算法的预测精度提高约7.93%;较单GEP分类算法的预测精度提高约1.1%。     

基于DESMID-AD动态选择的类别不平衡信用评估模型

针对现实信用评估业务中样本类别不平衡和代价敏感的情况,为降低信用风险评估的误分类损失,提出一种基于DESMID-AD动态选择的信用评估集成模型,根据每一个测试样本的特点动态地选择合适的基分类器对其进行信用预测.为提高模型对信用差客户(小类)的识别能力,在基分类器训练前使用过采样的方法对训练数据作类别平衡,采用元学习的方式基于多个指标进行基分类器的性能评估并在此阶段设计权重机制增强小类的影响.在三个公开信用评估数据集上,以AUC、一型、二型错误率以及误分类代价作为评价指标,与九种信用评估常用模型做比较,证明了该方法在信用评估领域的有效性和可行性.     

Using a Neural Network to Approximate an Ensemble of Classifiers

Several methods (e.g., Bagging, Boosting) of constructing and combining an ensemble of classifiers have recently been shown capable of improving accuracy of a class of commonly used classifiers (e.g., decision trees, neural networks). The accuracy gain achieved, however, is at the expense of a higher requirement for storage and computation. This storage and computation overhead can decrease the utility of these methods when applied to real-world situations. In this Letter, we propose a learning approach which allows a single neural network to approximate a given ensemble of classifiers. Experiments on a large number of real-world data sets show that this approach can substantially save storage and computation while still maintaining accuracy similar to that of the entire ensemble.     

基于支持向量机集成的故障诊断

为提高故障诊断的准确性,提出了一种基于遗传算法的支持向量机集成学习方法,定义了相应的遗传操作算子,并探讨了集成下的分类器的构造策略。对汽轮机转子不平衡故障诊断的仿真实验结果表明,集成学习方法的性能通常优于单个支持向量机,而所提方法性能则优于Bagging与Boosting等传统集成学习方法,获得的集成所包括的分类器数目更少,而且结合多种分类器构造策略可提高分类器的多样性。该方法能容易地推广到神经网络、决策树等其他学习算法。     

Feature selection in single and ensemble learning‐based bankruptcy prediction models

Feature selection is an important data preprocessing step for the construction of an effective bankruptcy prediction model. The prediction performance can be affected by the employed feature selection and classification techniques. However, there have been very few studies of bankruptcy prediction that identify the best combination of feature selection and classification techniques. In this study, two types of feature selection methods, including filter‐ and wrapper‐based methods, are considered, and two types of classification techniques, including statistical and machine learning techniques, are employed in the development of the prediction methods. In addition, bagging and boosting ensemble classifiers are also constructed for comparison. The experimental results based on three related datasets that contain different numbers of input features show that the genetic algorithm as the wrapper‐based feature selection method performs better than the filter‐based one by information gain. It is also shown that the lowest prediction error rates for the three datasets are provided by combining the genetic algorithm with the naïve Bayes and support vector machine classifiers without bagging and boosting.     

基于旋转森林的分类器集成算法研究

为提高决策树的集成分类精度,介绍了一种基于特征变换的旋转森林分类器集成算法,通过对数据属性集的随机分割,并在属性子集上对抽取的子样本数据进行主成分分析,以构造新的样本数据,达到增大基分类器差异性及提高预测准确率的目的。在Weka平台下,分别采用Bagging、AdaBoost及旋转森林算法对剪枝与未剪枝的J48决策树分类算法进行集成的对比试验,以10次10折交叉验证的平均准确率为比较依据。结果表明旋转森林算法的预测精度优于其他两个算法,验证了旋转森林是一种有效的决策树分类器集成算法。