Therefore, some key advances in credit risk modeling with SVM are presented. In the third ensemble model, an evolutionary programming (EP) based knowledge ensemble model is proposed for credit risk assessment and analysis.
Introduction
However, in this book we only focus on some topics of credit scoring or credit risk assessment. Compared with the traditional subjective assessment methods, credit risk management using scoring models has the following advantages.
Literature Collection
He mainly discussed the use of statistical techniques in credit scoring and problems in the development of the credit scoring system. Credit Scoring Toolkit: Theory and Practice for Consumer Credit Risk Management and Decision Automation.
Literature Investigation and Analysis
What is Credit Risk Evaluation Problem?
The credit risk assessment problem is to make a classification of good or bad for a particular customer based on the attribute characteristics of a particular customer. To attempt to make a more accurate assessment, many quantitative techniques have been used to develop credit risk assessment models.
Typical Techniques for Credit Risk Analysis
In credit risk assessment problem, set A can be divided into two subsets AG and AB. For example, one simple linear programming model for credit risk assessment problem (Baesen et al., 2003; Thomas et al., 2002) can be formulated as.
Comparisons of Models
Parameters Search Grid Search Grid Search Grid Search Trial and Error Unknown Unknown Particle Swarm Optimization Unknown Unknown Grid Search Grid Search Grid Search. Toolkit Cawley, LS-SVM SVM-light Based Unknown Unknown Unknown Lib-SVM Unknown Unknown Unknown Ls-SVM based Unknown Unknown.
Implications on Valuable Research Topics
Conclusions
In the previous stage, the decision value of the SVM classifiers can be used as a reliability measure in this stage. Using the TS test set, the performance of the SVM-based metamodel can be evaluated.
Introduction
The total error term in the objective function in SVM is weighted by the membership of the data for its class. There are other algorithms for this task such as some fast algorithms (Friess et al., 1998; Joachims, 1998).
SVM with Nearest Point Algorithm
30 2 Credit Risk Assessment Using NPA-based SVM with DOE boundary hyperplanes separating the two classes. Another approach to account for violations is to use the sum of squared violations in the objective function proposed by Friess (1998).
DOE-based Parameter Selection for SVM with NPA
After each iteration, the search area is reset to be centered on the point with the best performance. In this chapter, we use the DOE-based parameter search method to find optimal parameters for SVM with nearest point algorithm.
Experimental Analysis
36 2 Credit Risk Assessment Using an NPA-based SVM with DOE rhythm, some categorical attributes need numerical attributes. Note that the final optimal parameters in the proposed SVM with NVG, C~ and σ, are 45.25 and 32, respectively.
Conclusions
Although the experiments show that the proposed SVM with NPA and DOE is quite promising, the results reported here are still far from sufficient to make a definitive statement on the performance of SVM with NPA and DOE. Since the performance also depends on the characteristics of the datasets, future research is encouraged to identify the performance of the proposed SVM with NPA and DOE and explore the other effective kernel function in this framework.
Introduction
In the field of credit scoring, Van Gestel et al. 2003) mainly discussed the comparative analysis study of different classification techniques on eight real-life credit scoring data sets and also used SVM and Least Square SVM (LSSVM) with linear and RBF kernels and adopted a grid search method to set the hyperparameters. Most of the previous research focuses on grid search (GS), pattern search based on design of experiments (DOE) principles, and genetic algorithm (GA) for parameter selection.
Methodology Description
- Brief Review of LSSVM
- Direct Search for Parameter Selection
In the next subsection, we adopt the direct search method to optimize the parameters of LSSVM. Direct search (DS) methods are a class of simple and direct parameter optimal search method and can be applied almost immediately to many nonlinear optimization problems, especially to lower dimensional search space problems (Hooke and Jeeves, 1961; Mathworks, 2006).
Experimental Study
- Research Data
- Parameter Selection with Genetic Algorithm
- Parameters Selection with Grid Search
- Experimental Results
In the grid search method, each point in the grid is defined by the grid range [(C_min, Sigma_min), (C_max, Sigma_max)] and a unit grid size (Delta_C, Delta_Sigma) evaluated by the objective function f. Network searching can provide some protection against local minimums, but is not very efficient.
Conclusions
The empirical results of the proposed bilateral weighted fuzzy SVM model are described in section 6.3. Common examples of the kernel function are the polynomial kernel K(xi,xj)=(xixTj +1)d and the Gaussian radial basis function K(xi,xj)=exp(−(xi−xj)2/2σ2).
Introduction
In such situations, it is natural to hybridize raw sets and support vector machines because of their complementarity. Different from the previous studies, a new hybrid intelligent mining system is designed by hybridizing raw sets and supporting vector machines from a new perspective.
Preliminaries of Rough Sets and SVM
- Basic Concepts of Rough Sets
- Basic Ideas of Support Vector Machines
Support vector machines (SVM), a class of typical machine learning algorithms, were developed by Vapnik (1995). Support vector machine is a very specific type of learning algorithms characterized by the capacity control of the decision function, the use of kernel functions and the sparsity of the solution (Vapnik Cristianini and Taylor, 2000).
Proposed Hybrid Intelligent Mining System
- General Framework of Hybrid Intelligent Mining System
- Feature Selection by SVM
- Rule Generation by Rough Sets
- General Procedure of the Hybrid Intelligent Mining System
Actually, a reduced decision table can be seen as a set of rules where each rule corresponds to one object of the table. The rule set can be further generalized by applying the rough set reduction method (Li and Wang, 2004).
Experiment Study
- Corporation Credit Dataset
- Consumer Credit Dataset
In the previous four individual methods, SVM and approximate ensemble perform much better than LogR and ANN. In the SVM model, the regularization parameter is 50, and the kernel is the radial basis function with σ2 = 15.
Concluding Remarks
Since the 1960s, many different techniques have appeared, such as discriminant analysis (Altman, 1968), logit analysis (Wiginto, 1980), probit analysis (Grablowsky and Talley, 1981), linear programming (Glover, 1990), integer programming (Mangasarian, 1981) . 1965), k-nearest neighbor (KNN) (Henley and Hand, 1996) and classification tree (Makowski, 1985) have been widely applied to credit risk assessment tasks. The fuzzy SVM (FSVM) was first proposed by Lin and Wang (2002) and is more suitable for credit risk assessment.
Least Squares Fuzzy SVM
- SVM
- FSVM
- Least Squares FSVM
76 5 A Fuzzy Least Squares SVM Approach to Credit Risk Estimation The main problem in (5.5) becomes the task of finding the saddle point of the Lagrangian function, i.e. Once the optimal pair (w, b) is determined, the decision function of the SVM is obtained as.
Experiment Analysis
Moreover, the standard deviation is quite small, which shows that the robustness of the LS-FSVM is good. Meanwhile, the proposed LS-FSVM model appears to be a slightly better LSSVM, which shows that the LS-FSVM is a feasible solution to improve the accuracy of credit risk evaluation.
Conclusions
Lin & Wang's FSVM and LS-FSVM) is better than that of the other listed classifiers, implying that the fuzzy SVM classifier may be more suitable for credit risk assessment tasks than other deterministic classifiers such as LogR. 2) For type II accuracy and total accuracy, LS-FSVM and LSSVM outperform the other five models, implying the strong ability of the least squares version of the SVM model in credit risk assessment. Interestingly, the performance of FSVM is slightly worse than that of LSSVM, the main reasons leading to this phenomenon are worth exploring further.
Introduction
86 6 Evaluation of Credit Risk with a Bilateral Weighted Fuzzy SVM Model The nearest-neighbor approach is a standard non-parametric approach to the classification problem. Its application in the credit risk analysis field can be found in Varetto (1998) and Chen and Huang (2003).
Formulation of the Bilateral-Weighted Fuzzy SVM Model
- Bilateral-Weighting Errors
- Formulation Process of the Bilateral-weighted fuzzy SVM
- Generating Membership
The main drawback of the new bilaterally weighted fuzzy SVM lies in its computational complexity, as it involves a high-dimensional quadratic program. In conclusion, the training of the new fuzzy SVM consists of the following steps:
Empirical Analysis
- Dataset 1: UK Case
- Dataset 2: Japanese Case
- Dataset 3: England Case
As shown in Table 6.1, the new bilateral-weighted FSVM with RBF kernel and logit regression membership generation achieves the best performance. In ANN a two-layer feedforward network with 4 TANSIG neurons in the first layer and one.
Conclusions
So, the kernel and member generation method must be selected properly when the new fuzzy SVM method is used for credit risk analysis. The performance of fuzzy SVM depends greatly on the discriminative power of the member generation method.
Introduction
In this component, two main goals, classification performance (or predictive accuracy) and model complexity (or model interpretability) constitute the suitability evaluation function of GA. In this component, the classification performance or predictive accuracy is used as the GA suitability evaluation function.
SVM and LSSVM
Typical examples of the kernel function are the polynomial kernel Kpoly(xi,xj)=(xTi xj +1)d, the kernel of the radial basis function (RBF): ( , ) exp( 2 2). To overcome the high computational complexity of Vapnik's (1995) SVM, a new technique, least squares SVM (LSSVM) proposed by Suykens (1999) is introduced.
Evolving LSSVM Learning Paradigm
- General Framework of Evolving LSSVM Learning Method .111
- GA-based Parameters Evolution
Regarding the fitness values, the GA distorts its search direction to optimize the evaluation objective. After developing the fitness of the population, the best chromosomes with the highest fitness value are selected using the roulette wheel.
Research Data and Comparable Models
- Research Data
- Overview of Other Comparable Classification Models
To make the numbers of the two classes almost equal, we triple the delinquent data, that is, we add two copies of each delinquent case. For classification purposes, the final computational form of the BPNN model can be written as.
Experimental Results
- Empirical Analysis of GA-based Input Features Evolution
- Empirical Analysis of GA-based Parameters Optimization
- Comparisons with Other Classification Models
In two consumer credit datasets, both applicant's income (the fifth feature for Dataset 2 vs. the seventeenth feature for Dataset 3) and employment status (the sixth feature for Dataset 2 vs. the seventh feature for Dataset 3). First of all, by observing the mixed kernel coefficients, it is easy to find that for all test cases, the proportion of the RBF kernel (ie, the coefficient of λ2) is the highest.
Conclusions
The overall architecture of the multi-stage reliability-based SVM ensemble learning model is illustrated in Figure. In general, the main objectives of the SVM-based metmodeling approach are to improve the classification accuracy.
Introduction
In the fifth stage, the reliability values of the selected SVM models (i.e. ensemble members) are scaled into a unit interval by logistic transformation. In Section 8.3, an overall formulation process of the multistage SVM ensemble learning model is provided in detail.
Previous Studies
138 8 Credit Risk Assessment Using the SVM ensemble learning approach, the classification score and reliability value of the SVM classifier can be obtained. To this end, we attempt to design a complete process model for the SVM ensemble learning paradigm.
Formulation of SVM Ensemble Learning Paradigm
- Partitioning Original Data Set
- Creating Diverse Neural Network Classifiers
- SVM Learning and Confidence Value Generation
- Selecting Appropriate Ensemble Members
- Reliability Value Transformation
- Integrating Multiple Classifiers into an Ensemble Output
144 8 Credit Risk Assessment Using an SVM Ensemble Learning Approach In addition, the decision value f(x) is a good indicator of the confidence level of the ensemble classifiers. To summarize, the reliability-based multistage SVM ensemble learning model can be concluded in the following steps:
Empirical Analysis
- Consumer Credit Risk Assessment
- Corporation Credit Risk Assessment
In the five SVM ensemble models, we can find some similar results with neural network ensemble models. In five neural network ensemble learning models, the minimum strategy achieved the best classification performance, while in the SVM ensemble models, the product strategy and the average strategy achieved the best and second best performance.
Conclusions
154 8 Credit Risk Evaluation Using an SVM Ensemble Learning Approach (3) For the reliability-based neural network ensemble learning model, the performance of product strategy is the best among the five ensemble strategies, followed by mean strategy. These obtained results reveal that the proposed SVM ensemble learning model can provide a promising solution for credit risk analysis, and meanwhile suggest that the proposed multistage SVM ensemble technique has great potential for other binary classification problems.
Introduction
In the final stage, an SVM-based metamodel (i.e. metaclassifier) can be produced by learning from the selected base models with another SVM. 160 9 Credit Risk Analysis with an SVM-based Metamodeling Ensemble The main goals of this chapter are fourfold: (1) to show how an SVM-based metamodel can be constructed; (2) reveal how to evaluate credit risk using the proposed SVM-based metamodel; (3) to show how different methods compare their accuracy in credit risk analysis; and (4) to report how the PCA technique affects the final classification performance of the proposed SVM-based metamodel.
SVM-based Metamodeling Process
- A Generic Metalearning Process
- An Extended Metalearning Process
- SVM-based Metamodeling Process
With different training subsets, the SVM can be trained to form different base classifiers (i.e. base SVM models). 170 9 Credit Risk Analysis with the SVM-based metamodeling ensemble using the PCA technique, we can obtain the appropriate number of base models to generate the metamodels.
Experimental Analyses
- Research Data and Experiment Design
- Experimental Results
In Table 9.1, the (without PCA) refers to the SVM-based metamodeling without PCA, while the (with PCA) refers to the SVM-based metamodeling with PCA. In the four metamodels, the performance of the SVM-based metamodel with PCA is much better than that of the majority voting-based metamodel.
Conclusions
Introduction
But the use of MCDM methods in financial risk forecasting avoids many of the problems that exist when using discriminant analysis (Eisenbeis, 1977; Dimitras et al., 1996). Of the review papers, Dimitras et al. 1996) provided a comprehensive overview of the methods used for predicting the risk of business failure and of new trends in this field.
EP-Based Knowledge Ensemble Methodology
- Brief Introduction of Individual Data Mining Models
- Knowledge Ensemble based on Individual Mining Results . 185
If there exists a kernel function such that K(xi,xj)=(ϕ(xi),ϕ(xj)), it is usually unnecessary to explicitly know what ϕ(x) is, and we only need to work with a core function of the training algorithm, i.e. the optimal classification can be represented by. In the existing literature, majority voting is the most widely used ensemble strategy for
Experiment Results
- Results of Individual Models
- Identification Performance of the Knowledge Ensemble
- Identification Performance Comparisons
From Table 10.3, the best identification performance of the test data is recorded when kernel parameter σ2 is 10 and margin C is 75. As revealed in Table 10.6, the EP-based knowledge ensemble model outperforms four individual models at 10% significance level.
Conclusions
Introduction
Methodology Formulation
Experimental Study
- An Illustrative Numerical Example
- Empirical Comparisons with Different Credit Datasets
Conclusions and Future Directions