A new approach in reject inference of using ensemble learning based on global semi-supervised framework

Highlights

• A novel global semi-supervised framework for reject inference is proposed.

• A novel algorithm that combine multiple classifiers and clustering algorithms is introduced.

• The framework is proved to outperform several normal techniques.

• The framework is validated on the real data set.

Abstract

Credit scoring in online Peer-to-Peer (P2P) lending faces a huge challenge, which is the credit scoring models discard rejected applicants. This selective discarding leads to bias in the parameters of the models and ultimately affects the performance of credit evaluation. One approach for handling this problem is to adopt reject inference, which is a technique that infer the status of rejected samples and incorporate the results into credit scoring models. The most popular practice of reject inference is to use a credit scoring model that is only built on accepted samples to directly predict the status of rejected samples. However, the distribution of accepted samples in online P2P lending is different from rejected samples. We propose SSL-EC3, a global semi-supervised framework that merges multiple classifiers and clustering algorithms together to make better use of the information of rejected samples. It uses multiple unsupervised models (clustering algorithms) to explore the internal relationships of all samples, and then incorporates the information into the ensemble of supervised models (classifiers) to help correct initial classification results of rejected samples. In addition, we try to use a dynamic ensemble selection (DES) to select the appropriate ensemble of classifiers for each sample to be classified. Experimental results on the real data sets demonstrate the benefits of the proposed methods over conventional methods based on the reject inference.

Introduction

Credit scoring is an effective tool for assessing the potential default risks of borrowers, which guarantees the interests of platforms and investors [1]. According to borrower history records including personal information and payment records, credit scoring roughly divides borrowers into two classes, good or bad. Traditional credit scoring models use only accepted applicants and ignore rejected since the rejected applicants have no classes labels. This fact leads to sample selection bias problem and even affect the performance of the models. It is unreasonable to use these models to predict the status of all unknown borrowers.

Online Peer-to-Peer (P2P) lending provides a convenient service that allow users to trade directly. One drawback of this convenience is that investors cannot accurately assess the credit of borrowers, and the interests of platforms and investors face enormous challenges. In order to protect the interests, platforms and investors usually set high thresholds for borrowers, which has led to a large number of applicants being rejected. Thus, traditional credit scoring models have biased results in predicting borrowers’ default risks under such case. How to add rejected applicants to credit scoring models has become a big challenge, especially in online P2P lending.

Reject inference technology refers to the use of an approach to infer the status (good or bad) of rejected applicants, and add the results to the establishment process of the credit scoring models [2]. Sohn et al. [3], [4] believe that the nature of reject inference is to solve the data missing problem. They divide the data missing mechanism into three categories, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). Different types of data missing have different approaches to deal with. Furthermore, the emergence of reject inference technology avoids the waste of resources and improves the stability of credit scoring models [5], [6], [7].

In recent years, many methods based on reject inference have emerged and successfully applied to the area of credit scoring. Like extrapolation and augmentation [8]. Machine learning models have attracted researchers’ attention.

Machine learning models based on reject inference are roughly divided into two types, supervised models and semi-supervised models. Supervised models have strong predictive power, but cannot exploit the potential information of unlabeled samples [4], [9]. Recently, researches have focused on semi-supervised models [10], [11], [12]. Semi-supervised models simultaneously model both labeled and unlabeled samples. They seem to be naturally designed to reject inference [13]. However, there are many restrictions on semi-supervised in practical applications. For example, the classes of labeled samples should be correct, the distribution of unlabeled samples should be the same or similar to that of labeled samples, etc. The real situations are often not ideal, especially for online P2P lending. As shown in Table 2, we clearly see a obvious difference between accepted (labeled) and rejected (unlabeled) samples in Lending Club.

We focus on how to fully exploit the predictive power of classifiers and the internal relationships between rejected and accepted samples. There are many works have shown that combining multiple classifiers and clustering algorithms can get more stable classification results and play the role of rejected samples [14], [15], [16], [17]. We introduce an ensemble learning by maximizing the consensus among the output of multiple classifiers and clustering algorithms.

In this work, a particular version of combining clustering and classification for ensemble learning (EC3) framework [18] is integrated into an global semi-supervised learning (SSL) to perform reject inference, namely SSL-EC3. We use classifiers combined with clustering algorithms to obtain a better credit scoring model. SSL-EC3 is built on two fundamental hypotheses: (i) the ensemble of classifiers have powerful classification capabilities, which ensure the accuracy of credit scoring models; (ii) the integration of clustering methods can explore the inherent relationships between accepted and rejected samples, which ensure the generalization ability of credit scoring models. Furthermore, we try to adopt a dynamic ensemble selection (DES) automatically select the appropriate classifier for samples [19]. DES is a Python library that implement the advanced dynamic classifier and ensemble selection techniques. Our experimental results show that SSL-EC3 is helpful for reject inference in online P2P lending.

The structure of this paper is as follows. Section 2 gives an overview of various methods based on reject inference in credit scoring models. Based on the existing methods, we describe the proposed SSL-EC3 framework in Section 3. Section 4 describes the data needed for our experiment and necessary preparations. Section 5 describes and discusses the experimental results in detail. Finally, we conclude the paper.