Credit Scoring: A Constrained Optimization Framework With Hybrid Evolutionary Feature Selection

Introduction

One of the most important developments in the field of risk management is financial risk management (Verbano & Venturini, 2011). An important type of financial risk is credit risk which is defined as the probability that a customer will default on a loan; namely, the potential failure of meeting his/her loan obligations (Thomas et al., 2002). Credit scoring is an important topic in the credit risk management and has been the major focus of the banking industry, especially in the aftermath of 2008 crisis.

Usually, data collected by banks include a large amount of features. Some of them may be inconsistent or redundant due to their high inter-correlation (Liu & Schumann, 2005). Therefore, a considerable effort in cleansing or pre-selection is needed to make the collected data useful for credit scoring. Choosing the feature subset that maximizes a chosen classification measure is an essential and crucial step of a typical credit scoring process. Data mining techniques such as feature selection are used due to the abundance of data and the imperative to discover knowledge from raw data (Liu & Motoda, 2012). Feature selection can be viewed as a dimensionality reduction technique where the number of features in a specific dataset is reduced to the minimum, while the performance of the data mining classification task is maximized (Wang et al., 2015).

The nowadays multi-dimensional nature of a customer’s characteristics, the subjective judgment of a financial analyst (ad hoc decisions based on experience), as well as the complexity that occurs from designing with a high predictive performance necessitate the interaction of credit scoring with scientific areas such as statistics, machine learning, operations research and decision making.

The main objective of this chapter is to propose an accurate two-phase credit scoring model with a high predictive performance. Particularly, data mining feature selection techniques, supervised machine learning algorithms and an evolutionary optimization algorithm are used in hybrid synthesis to develop an optimal credit scoring model. In the first phase, the Minimum Redundancy Maximum Relevance (MRMR) algorithm is applied to find an optimal set of features that is mutually and maximally dissimilar and can represent the response variable effectively (Ding & Peng, 2005). Therefore, features can be ordered by their feature importance. Based on that, a financial analyst is allowed, according to his/her experience, to select an initial subset of features and define constraints (e.g., pairs of features of equal importance) so as to proceed to the second phase of the solution approach. The second phase is associated with an iterative procedure where supervised machine learning algorithms such as Logistic Regression (LR) and Linear Discriminant Analysis (LDA) are combined with an evolutionary optimization algorithm such as the Genetic Algorithm (GA) to choose the feature subset that maximizes a chosen classification measure according to the predefined features and subject to the predefined constraints.

The remainder of the chapter is organized as follows: Section 2 provides a brief of literature review of credit scoring problem and solution approaches applied to feature selection problems. A mathematical formulation of the feature selection problem, as well as some basic concepts regarding the MRMR, LR, LDA and GA are presented in Section 3. Section 4 introduces the proposed hybrid scheme based on supervised learning and evolutionary learning. In section 5, the authors illustrate the performance of the proposed scheme in terms of numerical experiments using standard credit scoring datasets. Section 6 concludes the chapter and provides directions for future work.