Ensemble Learning with Support Vector Machines for Bond Rating

Bond rating is regarded as an important event for measuring financial risk of companies and for determining the investment returns of investors. As a result, it has been a popular research topic for researchers to predict companies' credit ratings by applying statistical and machine learning techniques. The statistical techniques, including multiple regression, multiple discriminant analysis (MDA), logistic models (LOGIT), and probit analysis, have been traditionally used in bond rating. However, one major drawback is that it should be based on strict assumptions. Such strict assumptions include linearity, normality, independence among predictor variables and pre-existing functional forms relating the criterion variablesand the predictor variables. Those strict assumptions of traditional statistics have limited their application to the real world. Machine learning techniques also used in bond rating prediction models include decision trees (DT), neural networks (NN), and Support Vector Machine (SVM). Especially, SVM is recognized as a new and promising classification and regression analysis method. SVM learns a separating hyperplane that can maximize the margin between two categories. SVM is simple enough to be analyzed mathematical, and leads to high performance in practical applications. SVM implements the structuralrisk minimization principle and searches to minimize an upper bound of the generalization error. In addition, the solution of SVM may be a global optimum and thus, overfitting is unlikely to occur with SVM. In addition, SVM does not require too many data sample for training since it builds prediction models by only using some representative sample near the boundaries called support vectors. A number of experimental researches have indicated that SVM has been successfully applied in a variety of pattern recognition fields. However, there are three major drawbacks that can be potential causes for degrading SVM's performance. First, SVM is originally proposed for solving binary-class classification problems. Methods for combining SVMs for multi-class classification such as One-Against-One, One-Against-All have been proposed, but they do not improve the performance in multi-class classification problem as much as SVM for binary-class classification. Second, approximation algorithms (e.g. decomposition methods, sequential minimal optimization algorithm) could be used for effective multi-class computation to reduce computation time, but it could deteriorate classification performance. Third, the difficulty in multi-class prediction problems is in data imbalance problem that can occur when the number of instances in one class greatly outnumbers the number of instances in the other class. Such data sets often cause a default classifier to be built due to skewed boundary and thus the reduction in the classification accuracy of such a classifier. SVM ensemble learning is one of machine learning methods to cope with the above drawbacks. Ensemble learning is a method for improving the performance of classification and prediction algorithms. AdaBoost is one of the widely used ensemble learning techniques. It constructs a composite classifier by sequentially training classifiers while increasing weight on the misclassified observations through iterations. The observations that are incorrectly predicted by previous classifiers are chosen more often than examples that are correctly predicted. Thus Boosting attempts to produce new classifiers that are better able to predict examples for which the current ensemble's performance is poor. In this way, it can reinforce the training of the misclassified observations of the minority class. This paper proposes a multiclass Geometric Mean-based Boosting (MGM-Boost) to resolve multiclass prediction problem. Since MGM-Boost introduces the notion of geometric mean into AdaBoost, it can perform learning process considering the geometric mean-based accuracy and errors of multiclass. This study applies MGM-Boost to the real-world bond rating case for Korean companies to examine the feasibility of MGM-Boost. 10-fold cross validations for threetimes with different random seeds are performed in order to ensure that the comparison among three different classifiers does not happen by chance. For each of 10-fold cross validation, the entire data set is first partitioned into tenequal-sized sets, and then each set is in turn used as the test set while the classifier trains on the other nine sets. That is, cross-validated folds have been tested independently of each algorithm. Through these steps, we have obtained the results for classifiers on each of the 30 experiments. In the comparison of arithmetic mean-based prediction accuracy between individual classifiers, MGM-Boost (52.95%) shows higher prediction accuracy than both AdaBoost (51.69%) and SVM (49.47%). MGM-Boost (28.12%) also shows the higher prediction accuracy than AdaBoost (24.65%) and SVM (15.42%)in terms of geometric mean-based prediction accuracy. T-test is used to examine whether the performance of each classifiers for 30 folds is significantly different. The results indicate that performance of MGM-Boost is significantly different from AdaBoost and SVM classifiers at 1% level. These results mean that MGM-Boost can provide robust and stable solutions to multi-classproblems such as bond rating.

회사채 신용등급 예측을 위한 SVM 앙상블학습

회사채 신용등급은 투자자의 입장에서는 수익률 결정의 중요한 요소이며 기업의 입장에서는 자본비용 및 기업 가치와 관련된 중요한 재무의사결정사항으로 정교한 신용등급 예측 모형의 개발은 재무 및 회계 분야에서 오랫동안 전통적인 연구 주제가 되어왔다. 그러나, 회사채 신용등급 예측 모형의 성과와 관련된 가장 중요한 문제는 등급별 데이터의 불균형 문제이다. 예측 문제에 있어서 데이터 불균형(Data imbalance) 은 사용되는 표본이 특정 범주에 편중되었을 때 나타난다. 데이터 불균형이 심화됨에 따라 범주 사이의 분류경계영역이 왜곡되므로 분류자의 학습성과가 저하되게 된다. 본 연구에서는 데이터 불균형 문제가 존재하는 다분류 문제를 효과적으로 해결하기 위한 다분류 기하평균 부스팅 기법 (Multiclass Geometric Mean-based Boosting MGM-Boost)을 제안하고자 한다. MGM-Boost 알고리즘은 부스팅 알고리즘에 기하평균 개념을 도입한 것으로 오분류된 표본에 대한 학습을 강화할 수 있으며 불균형 분포를 보이는 각 범주의 예측정확도를 동시에 고려한 학습이 가능하다는 장점이 있다. 회사채 신용등급 예측문제를 활용하여 MGM-Boost의 성과를 검증한 결과 SVM 및 AdaBoost 기법과 비교하여 통계적으로 유의적인 성과개선 효과를 보여주었으며 데이터 불균형 하에서도 벤치마킹 모형과 비교하여 견고한 학습성과를 나타냈다.