# Toward an Efficient and Effective Credit Scorer for Cross-Border E-Commerce Enterprises

Authors: Chang Xu; Ruize Guo; Yulai Zhang; Xinyuan Luo
Journal: Scientific Programming
 (2023)

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## Abstract

Building an efficient and effective credit scorer for enterprises is an important and urgent demand in the cross-border e-commerce industry. In this paper, we present a framework to build a credit scorer using e-commerce data integrated from various sources. First, an improved dependency graph approach is proposed to recognize distinct records in the dataset. Then, we apply logistic regression using a prejudice remover regularizer to train the model, preceded by predictor preparation through binning and evaluating their information value. Lastly, we build the credit scorer according to the coefficients of the model. We implement our framework on a dataset from the official customs database and a large cross-border e-commerce platform. The empirical results demonstrate that the scorer built by our methodology can be used to effectively evaluate enterprises, while also removing prejudice against small and medium enterprises to a certain extent.


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## Body

## 1. Introduction

E-commerce has become a new business mode with the rapid influence of the Internet and wireless communications technology. As the world’s largest exporter and second-largest importer, there are hundreds of thousands of cross-border enterprises in China, making trades with foreign partners and customers on global e-commerce platforms such as Amazon and Alibaba. Unlike the traditional offline mode, the main body of e-commerce is composed of a large number of small- and medium-sized enterprises (SMEs), which render conventional credit assessment methods, such as authorized enterprise organization (AEO), inapplicable. Both the government and the e-commerce platforms need a new efficient credit score method to evaluate these enterprises according to the multifarious data produced from their trades.Meanwhile, the COVID-19 pandemic has severely impacted global imports and exports. As the world’s second-largest economy, China’s import and export trade has also been greatly affected, and SMEs are the most affected. To ease the pressure on these SMEs and speed up the flow of goods, the Chinese administration needs to establish an efficient, effective, and nondiscriminatory credit evaluation system.Although various credit evaluation methods have been applied in many industries, there remains a lack of effective credit assessment approaches for cross-border e-commerce companies. There are a number of challenges posed here. First, the enterprises’ trade-related data are scattered across multiple isolated data sources, each of which shapes the data in its own format. Integrating these heterogeneous data (in particular, distinguishing repeated records from distinct data) is not an easy job. Second, official Chinese policies advocate the development of SMEs, whereas huge, multinational corporations have overwhelming advantages in the cross-border trade business. Thus, an effective model should consciously restrain the underlying advantages of large-scale enterprises, which obviously exist in the traditional credit score evaluation. Third, the current research study on cross-border e-commerce credit methods mainly focuses on the internal business information of enterprises, by third-party research institutions, without considering the research from the perspective of supervision units [1, 2]. Lastly, we assert that an applicable model here is not only effective and extensible but also explicable, making the model suitable for regulated e-commerce services.In this paper, we propose an efficient framework to build a credit scorer for cross-border e-commerce enterprises. We first integrate the e-commerce data from various sources using an improved record reconciliation approach, with the aim of recognizing and refining the entities in the heterogeneous data. Then, we train a classifier model using logistic regression, preceded by predictor selection through binning and evaluating their information value (IV). In order to eliminate the model’s prejudice against SMEs, we also implement a prejudice remover regularizer in the training. Lastly, we build the credit scorer from the model coefficients. We apply our framework to the data provided by the official customs database and a large Chinese cross-border e-commerce platform. The original dataset includes about 1,400,000 records on over 4000 companies. The results indicate that the proposed scorer is effective for evaluating enterprises and is relatively friendly to SMEs.The remainder of the paper is organized as follows: in Section2, we discuss related work; in Section 3, we describe the details of our framework; in Section 4, we present our evaluation and the corresponding results; and lastly, we conclude our work in Section 5.


## 2. Related Work

The credit scoring problem initially originated in the banking industry [3]. In earlier years, it relied on using questionnaire data and the applicant’s credit history. With the popularization of information technology, people began to explore the truth about credit from transaction data using statistical learning methods. These approaches included logistic regression [4, 5], decision trees [6, 7], SVM [8–11], nearest neighbor [12], and neural networks [13–16]. However, most of the abovementioned studies are oriented toward personal credit issues in financial applications. In recent decades, on the basis of personal credit research, experts and scholars began to study how to evaluate enterprise credit from the perspective of enterprise operation information, from the initial expert system to the later classical machine learning methods and then to the recently popular deep learning methods [17]. Compared with several different credit evaluation methods, logistic regression performs well in most cases [18]. Therefore, this study will be mainly based on logistic regression.In recent years, some researchers have paid considerable attention to the credit score problem in e-commerce, especially for the C2C e-commerce type [19–21]. We noted that these studies always focused on transaction data, while ignoring the data on other elements of the cross-border trade chain. For example, in reference [22], the author selected some objective values from the data of a single e-commerce website as indicators and admitted that the data for logistics were not sufficient for an evaluation. Therefore, a complete assessment for cross-border enterprises needs comprehensive data from various sources, which brings another problem, i.e., record reconciliation.Record reconciliation is one of the major problems in data integration [23]. When combining data from multiple sources, we need to recognize the various references to the same real-world entity on an individual level. The approaches include merging/purging [24], record linkage [25], hardening soft databases [26], reference matching [27], deduplication [28], object identification [29], and identity uncertainty [30]. In reference [31], the authors proposed a novel method based on propagating reference similarity decisions in a dependency graph. The information is enriched and propagated in the process of calculating the nodes of the graph. This method is extremely suitable for the scenario of our research, but its performance exhibits a severe bottleneck in practice.It is important in machine learning to choose an appropriate penalty term to prevent overfitting. One of the main problems is removing the prejudice against SMEs. The authors of reference [32, 33] focused on evaluating and reducing indirect prejudice through a statistical dependence between sensitive features and other information. A prejudice remover regularizer was proposed to enforce the determination’s independence from sensitive information, which is considered to be the underlying cause of the disadvantages of SMEs.


## 3. Framework

The experiments described in this section are performed on a cloud server with the Linux operating system. In terms of hardware, the server memory is 8 GB and the CPU is an e5-2680 v4. In terms of software, the Sklearn 1.0.1 framework is used and the programming language is Python 3.7.We propose a framework to build a credit scorer for cross-border e-commerce enterprises using their trade-related data, which are collected and integrated from multiple data sources. First, we refine the integrated dataset to eliminate the redundant records, which would otherwise distort the learning process. Then, we implement logistic regression using a prejudice remover regularizer to train the model, preceded by predictor preparation through binning and evaluating their information value. Lastly, we build the credit scorer according to the coefficients of the model we trained. The details of the abovementioned steps are described in the sections below.


### 3.1. Record Reconciliation

#### 3.1.1. Problem Description

Record reconciliation is one of the major problems when integrating data from multiple sources. As different sources have their own data formats, there exist duplicate records referring to the same real-world entity. In our research, this entity may be trade records, transport records, check records, or administrative penalty records. Furthermore, there exist unavoidable inconsistencies in business systems, such as misspellings, heterogeneous use of abbreviations, discrepancies in particular attributes, and errors in data transforming/formatting. For example, in Figure1(a), we list three trade records T1, T2, and T3 with their reference enterprise records E1 and E2 and area records A1 and A2, where T1 is from the official customs database and T2 and T3 are from an e-commerce platform’s database. While they seem to be three different trades of two enterprises, they are actually the same.Figure 1
Example of dependency graph approach. (a) Three trade recordsT1, T2, and T3 and their related records. T1 is from the official customs database; T2 and T3 are from an e-commerce platform database. (b) The dependency graph of the example. Due to space limitations, we only show the atomic attribute nodes of T2 and T3 in the graph.
(a)(b)Obviously, this kind of data mistake will produce phantom data for subsequent model training, causing unpredictable errors. In order to improve data quality, we first need to combine these records. The dependency graph approach proposed in reference [27] is suitable for this problem. However, in practice, we found it to be extremely computationally expensive and memory-intensive. Thus, we modified the original approach for our case to improve its efficiency.


#### 3.1.2. The Original Dependency Graph Approach

The approach begins by constructing the dependency graph of all records. One node in the graph marks a similarity between a pair of records or a pair of atomic attributes (whose values are of a simple type, such as string or numeric). There exists an edge from noden to m if, and only if, the similarity of m truly depends on the similarity of n. According to the different types of dependency, the edges can be classified as strong Boolean-valued, weak Boolean-valued, and real-valued. Figure 1(b) depicts a part of the dependency graph using the data in Figure 1(a).The second step of the approach is to iteratively recompute the scores on the nodes to propagate similarity decisions in the graph. This step starts by computing the similarity scores of the atomic attribute nodes and then their neighbors, using different strategies according to the type of edge. During the propagation, when two nodes are merged, their neighbors need to be concurrently recomputed, thereby enriching the information about the record. After all record nodes are computed, we can then compute the transitive closure for the final reconciliation results. Due to space limitations, we do not describe all details of the approach here; instead, the reader is referred to reference [27].The dependency graph approach is novel and powerful as it not only employs the similarity between atomic attributes but also explores the similarity dependency in complex information spaces. For example, in the data of Figure1(a), if we merge E1 and E2, the similarity between T1 and T2 is certainly increased. We adopted this approach in our research. Unfortunately, we found the computational cost and memory consumption to be extensive when using our dataset. Thus, we optimize the original algorithm to improve its efficiency for our case, as described in Section 3.1.3.


#### 3.1.3. Improvement

Using performance analytics, we identified two major performance bottlenecks in the original approach:(i)
Gigantic graph volume: As described in Section3.1.2, the approach needs to first construct a complete graph, in which each node represents a pair of records and their attributes. Therefore, theoretically, it needs to allocate at most m+1Cn2 nodes for n records with m attributes. Although the original paper optimized this case by omitting the nodes with an initial similarity lower than an empirical threshold, it still consumed too much memory in practice. In addition to the serious computational burden, as the physical memory cannot accommodate the full graph structure, the huge mass of I/Os prevents the calculation from being completed in an acceptable time.(ii)
Frequent computation on merge: When two records are merged, all nodes connected to them need to be checked, some need to be recomputed, and their neighbors need to be reconnected [27]. This involves many search and update operations, which represent a heavy burden in a large graph structure.The reason for these bottlenecks is that the original approach is symmetric, whereby all records need to be compared with each other and verified at each iteration. However, in reality, many datasets are asymmetric. In our scenario, the data from the official customs database can be considered exact. Thus, we can use these data as thebase set, whereas data from other sources can be seen as candidates for reconciliation. Therefore, the original approach can be improved as outlined in Algorithm 1.Algorithm 1: Reconcile (Rb, Rc).
//Rb is the base set, while Rc is the candidate record set to be reconciled into Rb.Rc′ ⟵ Rc;for each record r in RbG ⟵ construct dependency graph of r and each record in Rc′;R′ ← do reconciliation on G;Rc′ ⟵ Rc′ − R′;end forG′ ⟵ construct dependency graph of Rc′;R′ ⟵ do reconciliation on G′returnRb ∪ R′The key point of Algorithm1 is that we change the original symmetric approach to a progressive one. In each loop, we pick one record from the base set and reconcile it with the remaining records in the candidate dataset. We need not consider the reconciliation between the records in the base set as we assume them to be exact. Then, we remove records recognized as repeated from the candidate set to reduce unnecessary computation in the next loop. Lastly, we reconcile the remaining records in the candidate dataset and then merge them into the final dataset. In this way, we reduce the upper bound size of the dependency graph to the volume of the candidate dataset, which greatly improves the efficiency of the original approach.


### 3.2. Model Training

We apply logistic regression for model training because of its efficiency and explicability. To choose the appropriate predictors for each feature, we first discretize the values into several bins and then calculate the weight of evidence (WOE) for each bin. Second, we calculate the information value (IV) of each feature to choose the most powerful ones. Lastly, we train the model by applying logistic regression using a prejudice remover regularizer.


#### 3.2.1. Binning and WOE

For each feature, we choose the corresponding binning method as a matter of experience. The methods include equal-width, equal-frequency, and k-means clustering. It is unnecessary to consider more complicated binning methods, such as supervised binning, as most features are evenly distributed.After binning, we obtain a series of discrete values for each feature; then, we need to calculate the WOE for each bin as follows:(1)WOEi=lnGi/GtotalBi/Btotal,where Gi represents the number of good enterprises in each bin and Gtotal represents the total number of good enterprises. Accordingly, Bi represents the number of bad enterprises in each bin and Btotal represents the total number of bad enterprises. Thus, the WOE of the ith bin denotes the discrepancy in the proportion of good/bad enterprises in this bin, which represents its distinguishability.Table1 lists the WOE of each bin for the “average age of the customers”.Table 1
WOE for the “average age of the customers.” The values are binned using equal-frequency clustering and then normalized.
BinWOE1: [0, 0.0028]−1.46332: [0.0028, 0.0061]−0.6393: [0.0061, 0.0082]−0.49334: [0.0082, 0.0149]0.02765: [0.0149, 0.0215]0.54896: [0.0215, 0.048]0.58027: [0.048, 0.0607]0.80218: [0.0607, 1]0.9527


#### 3.2.2. Information Value

The information value (IV) of a feature is one of the most widely used indicators to pick predictors in credit score models. The formula for IV is as follows:(2)IV=∑inBiBtotal−GiGtotal×WOEi.We can see that IV is simply the weighted sum of WOE values. A larger IV denotes that the feature is more likely to be picked as a predictor. Table2 lists the IV values for some of the features.Table 2
IV coefficient values andP value for some features.
FeatureIVCoefficient value in final modelP valueInspection hit rate of goods0.9251.2453<0.01Percentage of related tiny transport enterprises0.7941.2921<0.01High amount from the same payer0.7661.1201<0.01Record of execution on dishonesty0.7010.64630.0512Average age of the buyer0.5630.69980.0295Consistency of the buyer and payer0.3430.65250.0242Abnormal contact details0.004−1.02020.0139Related transport enterprise has a record of dishonesty0.1211.43090.0332P value is the significance level of the features calculated according to the actual statistics, and a value lower than 0.05 indicates a significant difference.


#### 3.2.3. Prejudice Remover Regularizer

As mentioned in Section1, our aim was to eliminate the prejudice against SMEs. The authors of reference [28] proposed the prejudice index (PI) to quantify the degree of indirect prejudice, which is straightforwardly defined as the mutual information between Y and Xa:(3)PI=∑Y,XaPY,XalnPY,XaPXaPy,where Y represents the target result and Xa represents the value of feature a. Obviously, a larger PI indicates that a is a more sensitive feature. Thus, the regularizer can be formulated as follows:(4)minLfX,Y+ƞ×PI,where f (X) is the loss function and ƞ is used to control the degree of prejudice removal. Accordingly, this regularizer can help to weaken the prejudice toward SMEs in the logistic regression. After training, we obtain the coefficient value of each predictor, as shown in Table 2.


### 3.3. The Credit Card Scorer

The last step is to build a credit card scorer from the model. We define the probability that an enterprise’s credit score is bad asp. Then, lnp/1−p is the relative probability (₨) that the enterprise’s credit score is bad. The credit card score can be defined as the linear expression of ₨. Subsequently, we can calculate the scale for each bin by substituting some known scores obtained from experts.Table3 lists the scale for “the average age of the buyer.”Table 3
Final scale on “the average age of the buyers.”
BinScale1: [0, 0.0028]972: [0.0028, 0.0061]563: [0.0061, 0.0082]524: [0.0082, 0.0149]215: [0.0149, 0.0215]−26: [0.0215, 0.048]−117: [0.048, 0.0607]−128: [0.0607, 1]−32


## 3.1. Record Reconciliation

### 3.1.1. Problem Description

Record reconciliation is one of the major problems when integrating data from multiple sources. As different sources have their own data formats, there exist duplicate records referring to the same real-world entity. In our research, this entity may be trade records, transport records, check records, or administrative penalty records. Furthermore, there exist unavoidable inconsistencies in business systems, such as misspellings, heterogeneous use of abbreviations, discrepancies in particular attributes, and errors in data transforming/formatting. For example, in Figure1(a), we list three trade records T1, T2, and T3 with their reference enterprise records E1 and E2 and area records A1 and A2, where T1 is from the official customs database and T2 and T3 are from an e-commerce platform’s database. While they seem to be three different trades of two enterprises, they are actually the same.Figure 1
Example of dependency graph approach. (a) Three trade recordsT1, T2, and T3 and their related records. T1 is from the official customs database; T2 and T3 are from an e-commerce platform database. (b) The dependency graph of the example. Due to space limitations, we only show the atomic attribute nodes of T2 and T3 in the graph.
(a)(b)Obviously, this kind of data mistake will produce phantom data for subsequent model training, causing unpredictable errors. In order to improve data quality, we first need to combine these records. The dependency graph approach proposed in reference [27] is suitable for this problem. However, in practice, we found it to be extremely computationally expensive and memory-intensive. Thus, we modified the original approach for our case to improve its efficiency.


### 3.1.2. The Original Dependency Graph Approach

The approach begins by constructing the dependency graph of all records. One node in the graph marks a similarity between a pair of records or a pair of atomic attributes (whose values are of a simple type, such as string or numeric). There exists an edge from noden to m if, and only if, the similarity of m truly depends on the similarity of n. According to the different types of dependency, the edges can be classified as strong Boolean-valued, weak Boolean-valued, and real-valued. Figure 1(b) depicts a part of the dependency graph using the data in Figure 1(a).The second step of the approach is to iteratively recompute the scores on the nodes to propagate similarity decisions in the graph. This step starts by computing the similarity scores of the atomic attribute nodes and then their neighbors, using different strategies according to the type of edge. During the propagation, when two nodes are merged, their neighbors need to be concurrently recomputed, thereby enriching the information about the record. After all record nodes are computed, we can then compute the transitive closure for the final reconciliation results. Due to space limitations, we do not describe all details of the approach here; instead, the reader is referred to reference [27].The dependency graph approach is novel and powerful as it not only employs the similarity between atomic attributes but also explores the similarity dependency in complex information spaces. For example, in the data of Figure1(a), if we merge E1 and E2, the similarity between T1 and T2 is certainly increased. We adopted this approach in our research. Unfortunately, we found the computational cost and memory consumption to be extensive when using our dataset. Thus, we optimize the original algorithm to improve its efficiency for our case, as described in Section 3.1.3.


### 3.1.3. Improvement

Using performance analytics, we identified two major performance bottlenecks in the original approach:(i)
Gigantic graph volume: As described in Section3.1.2, the approach needs to first construct a complete graph, in which each node represents a pair of records and their attributes. Therefore, theoretically, it needs to allocate at most m+1Cn2 nodes for n records with m attributes. Although the original paper optimized this case by omitting the nodes with an initial similarity lower than an empirical threshold, it still consumed too much memory in practice. In addition to the serious computational burden, as the physical memory cannot accommodate the full graph structure, the huge mass of I/Os prevents the calculation from being completed in an acceptable time.(ii)
Frequent computation on merge: When two records are merged, all nodes connected to them need to be checked, some need to be recomputed, and their neighbors need to be reconnected [27]. This involves many search and update operations, which represent a heavy burden in a large graph structure.The reason for these bottlenecks is that the original approach is symmetric, whereby all records need to be compared with each other and verified at each iteration. However, in reality, many datasets are asymmetric. In our scenario, the data from the official customs database can be considered exact. Thus, we can use these data as thebase set, whereas data from other sources can be seen as candidates for reconciliation. Therefore, the original approach can be improved as outlined in Algorithm 1.Algorithm 1: Reconcile (Rb, Rc).
//Rb is the base set, while Rc is the candidate record set to be reconciled into Rb.Rc′ ⟵ Rc;for each record r in RbG ⟵ construct dependency graph of r and each record in Rc′;R′ ← do reconciliation on G;Rc′ ⟵ Rc′ − R′;end forG′ ⟵ construct dependency graph of Rc′;R′ ⟵ do reconciliation on G′returnRb ∪ R′The key point of Algorithm1 is that we change the original symmetric approach to a progressive one. In each loop, we pick one record from the base set and reconcile it with the remaining records in the candidate dataset. We need not consider the reconciliation between the records in the base set as we assume them to be exact. Then, we remove records recognized as repeated from the candidate set to reduce unnecessary computation in the next loop. Lastly, we reconcile the remaining records in the candidate dataset and then merge them into the final dataset. In this way, we reduce the upper bound size of the dependency graph to the volume of the candidate dataset, which greatly improves the efficiency of the original approach.


## 3.1.1. Problem Description

Record reconciliation is one of the major problems when integrating data from multiple sources. As different sources have their own data formats, there exist duplicate records referring to the same real-world entity. In our research, this entity may be trade records, transport records, check records, or administrative penalty records. Furthermore, there exist unavoidable inconsistencies in business systems, such as misspellings, heterogeneous use of abbreviations, discrepancies in particular attributes, and errors in data transforming/formatting. For example, in Figure1(a), we list three trade records T1, T2, and T3 with their reference enterprise records E1 and E2 and area records A1 and A2, where T1 is from the official customs database and T2 and T3 are from an e-commerce platform’s database. While they seem to be three different trades of two enterprises, they are actually the same.Figure 1
Example of dependency graph approach. (a) Three trade recordsT1, T2, and T3 and their related records. T1 is from the official customs database; T2 and T3 are from an e-commerce platform database. (b) The dependency graph of the example. Due to space limitations, we only show the atomic attribute nodes of T2 and T3 in the graph.
(a)(b)Obviously, this kind of data mistake will produce phantom data for subsequent model training, causing unpredictable errors. In order to improve data quality, we first need to combine these records. The dependency graph approach proposed in reference [27] is suitable for this problem. However, in practice, we found it to be extremely computationally expensive and memory-intensive. Thus, we modified the original approach for our case to improve its efficiency.


## 3.1.2. The Original Dependency Graph Approach

The approach begins by constructing the dependency graph of all records. One node in the graph marks a similarity between a pair of records or a pair of atomic attributes (whose values are of a simple type, such as string or numeric). There exists an edge from noden to m if, and only if, the similarity of m truly depends on the similarity of n. According to the different types of dependency, the edges can be classified as strong Boolean-valued, weak Boolean-valued, and real-valued. Figure 1(b) depicts a part of the dependency graph using the data in Figure 1(a).The second step of the approach is to iteratively recompute the scores on the nodes to propagate similarity decisions in the graph. This step starts by computing the similarity scores of the atomic attribute nodes and then their neighbors, using different strategies according to the type of edge. During the propagation, when two nodes are merged, their neighbors need to be concurrently recomputed, thereby enriching the information about the record. After all record nodes are computed, we can then compute the transitive closure for the final reconciliation results. Due to space limitations, we do not describe all details of the approach here; instead, the reader is referred to reference [27].The dependency graph approach is novel and powerful as it not only employs the similarity between atomic attributes but also explores the similarity dependency in complex information spaces. For example, in the data of Figure1(a), if we merge E1 and E2, the similarity between T1 and T2 is certainly increased. We adopted this approach in our research. Unfortunately, we found the computational cost and memory consumption to be extensive when using our dataset. Thus, we optimize the original algorithm to improve its efficiency for our case, as described in Section 3.1.3.


## 3.1.3. Improvement

Using performance analytics, we identified two major performance bottlenecks in the original approach:(i)
Gigantic graph volume: As described in Section3.1.2, the approach needs to first construct a complete graph, in which each node represents a pair of records and their attributes. Therefore, theoretically, it needs to allocate at most m+1Cn2 nodes for n records with m attributes. Although the original paper optimized this case by omitting the nodes with an initial similarity lower than an empirical threshold, it still consumed too much memory in practice. In addition to the serious computational burden, as the physical memory cannot accommodate the full graph structure, the huge mass of I/Os prevents the calculation from being completed in an acceptable time.(ii)
Frequent computation on merge: When two records are merged, all nodes connected to them need to be checked, some need to be recomputed, and their neighbors need to be reconnected [27]. This involves many search and update operations, which represent a heavy burden in a large graph structure.The reason for these bottlenecks is that the original approach is symmetric, whereby all records need to be compared with each other and verified at each iteration. However, in reality, many datasets are asymmetric. In our scenario, the data from the official customs database can be considered exact. Thus, we can use these data as thebase set, whereas data from other sources can be seen as candidates for reconciliation. Therefore, the original approach can be improved as outlined in Algorithm 1.Algorithm 1: Reconcile (Rb, Rc).
//Rb is the base set, while Rc is the candidate record set to be reconciled into Rb.Rc′ ⟵ Rc;for each record r in RbG ⟵ construct dependency graph of r and each record in Rc′;R′ ← do reconciliation on G;Rc′ ⟵ Rc′ − R′;end forG′ ⟵ construct dependency graph of Rc′;R′ ⟵ do reconciliation on G′returnRb ∪ R′The key point of Algorithm1 is that we change the original symmetric approach to a progressive one. In each loop, we pick one record from the base set and reconcile it with the remaining records in the candidate dataset. We need not consider the reconciliation between the records in the base set as we assume them to be exact. Then, we remove records recognized as repeated from the candidate set to reduce unnecessary computation in the next loop. Lastly, we reconcile the remaining records in the candidate dataset and then merge them into the final dataset. In this way, we reduce the upper bound size of the dependency graph to the volume of the candidate dataset, which greatly improves the efficiency of the original approach.


## 3.2. Model Training

We apply logistic regression for model training because of its efficiency and explicability. To choose the appropriate predictors for each feature, we first discretize the values into several bins and then calculate the weight of evidence (WOE) for each bin. Second, we calculate the information value (IV) of each feature to choose the most powerful ones. Lastly, we train the model by applying logistic regression using a prejudice remover regularizer.


### 3.2.1. Binning and WOE

For each feature, we choose the corresponding binning method as a matter of experience. The methods include equal-width, equal-frequency, and k-means clustering. It is unnecessary to consider more complicated binning methods, such as supervised binning, as most features are evenly distributed.After binning, we obtain a series of discrete values for each feature; then, we need to calculate the WOE for each bin as follows:(1)WOEi=lnGi/GtotalBi/Btotal,where Gi represents the number of good enterprises in each bin and Gtotal represents the total number of good enterprises. Accordingly, Bi represents the number of bad enterprises in each bin and Btotal represents the total number of bad enterprises. Thus, the WOE of the ith bin denotes the discrepancy in the proportion of good/bad enterprises in this bin, which represents its distinguishability.Table1 lists the WOE of each bin for the “average age of the customers”.Table 1
WOE for the “average age of the customers.” The values are binned using equal-frequency clustering and then normalized.
BinWOE1: [0, 0.0028]−1.46332: [0.0028, 0.0061]−0.6393: [0.0061, 0.0082]−0.49334: [0.0082, 0.0149]0.02765: [0.0149, 0.0215]0.54896: [0.0215, 0.048]0.58027: [0.048, 0.0607]0.80218: [0.0607, 1]0.9527


### 3.2.2. Information Value

The information value (IV) of a feature is one of the most widely used indicators to pick predictors in credit score models. The formula for IV is as follows:(2)IV=∑inBiBtotal−GiGtotal×WOEi.We can see that IV is simply the weighted sum of WOE values. A larger IV denotes that the feature is more likely to be picked as a predictor. Table2 lists the IV values for some of the features.Table 2
IV coefficient values andP value for some features.
FeatureIVCoefficient value in final modelP valueInspection hit rate of goods0.9251.2453<0.01Percentage of related tiny transport enterprises0.7941.2921<0.01High amount from the same payer0.7661.1201<0.01Record of execution on dishonesty0.7010.64630.0512Average age of the buyer0.5630.69980.0295Consistency of the buyer and payer0.3430.65250.0242Abnormal contact details0.004−1.02020.0139Related transport enterprise has a record of dishonesty0.1211.43090.0332P value is the significance level of the features calculated according to the actual statistics, and a value lower than 0.05 indicates a significant difference.


### 3.2.3. Prejudice Remover Regularizer

As mentioned in Section1, our aim was to eliminate the prejudice against SMEs. The authors of reference [28] proposed the prejudice index (PI) to quantify the degree of indirect prejudice, which is straightforwardly defined as the mutual information between Y and Xa:(3)PI=∑Y,XaPY,XalnPY,XaPXaPy,where Y represents the target result and Xa represents the value of feature a. Obviously, a larger PI indicates that a is a more sensitive feature. Thus, the regularizer can be formulated as follows:(4)minLfX,Y+ƞ×PI,where f (X) is the loss function and ƞ is used to control the degree of prejudice removal. Accordingly, this regularizer can help to weaken the prejudice toward SMEs in the logistic regression. After training, we obtain the coefficient value of each predictor, as shown in Table 2.


## 3.2.1. Binning and WOE

For each feature, we choose the corresponding binning method as a matter of experience. The methods include equal-width, equal-frequency, and k-means clustering. It is unnecessary to consider more complicated binning methods, such as supervised binning, as most features are evenly distributed.After binning, we obtain a series of discrete values for each feature; then, we need to calculate the WOE for each bin as follows:(1)WOEi=lnGi/GtotalBi/Btotal,where Gi represents the number of good enterprises in each bin and Gtotal represents the total number of good enterprises. Accordingly, Bi represents the number of bad enterprises in each bin and Btotal represents the total number of bad enterprises. Thus, the WOE of the ith bin denotes the discrepancy in the proportion of good/bad enterprises in this bin, which represents its distinguishability.Table1 lists the WOE of each bin for the “average age of the customers”.Table 1
WOE for the “average age of the customers.” The values are binned using equal-frequency clustering and then normalized.
BinWOE1: [0, 0.0028]−1.46332: [0.0028, 0.0061]−0.6393: [0.0061, 0.0082]−0.49334: [0.0082, 0.0149]0.02765: [0.0149, 0.0215]0.54896: [0.0215, 0.048]0.58027: [0.048, 0.0607]0.80218: [0.0607, 1]0.9527


## 3.2.2. Information Value

The information value (IV) of a feature is one of the most widely used indicators to pick predictors in credit score models. The formula for IV is as follows:(2)IV=∑inBiBtotal−GiGtotal×WOEi.We can see that IV is simply the weighted sum of WOE values. A larger IV denotes that the feature is more likely to be picked as a predictor. Table2 lists the IV values for some of the features.Table 2
IV coefficient values andP value for some features.
FeatureIVCoefficient value in final modelP valueInspection hit rate of goods0.9251.2453<0.01Percentage of related tiny transport enterprises0.7941.2921<0.01High amount from the same payer0.7661.1201<0.01Record of execution on dishonesty0.7010.64630.0512Average age of the buyer0.5630.69980.0295Consistency of the buyer and payer0.3430.65250.0242Abnormal contact details0.004−1.02020.0139Related transport enterprise has a record of dishonesty0.1211.43090.0332P value is the significance level of the features calculated according to the actual statistics, and a value lower than 0.05 indicates a significant difference.


## 3.2.3. Prejudice Remover Regularizer

As mentioned in Section1, our aim was to eliminate the prejudice against SMEs. The authors of reference [28] proposed the prejudice index (PI) to quantify the degree of indirect prejudice, which is straightforwardly defined as the mutual information between Y and Xa:(3)PI=∑Y,XaPY,XalnPY,XaPXaPy,where Y represents the target result and Xa represents the value of feature a. Obviously, a larger PI indicates that a is a more sensitive feature. Thus, the regularizer can be formulated as follows:(4)minLfX,Y+ƞ×PI,where f (X) is the loss function and ƞ is used to control the degree of prejudice removal. Accordingly, this regularizer can help to weaken the prejudice toward SMEs in the logistic regression. After training, we obtain the coefficient value of each predictor, as shown in Table 2.


## 3.3. The Credit Card Scorer

The last step is to build a credit card scorer from the model. We define the probability that an enterprise’s credit score is bad asp. Then, lnp/1−p is the relative probability (₨) that the enterprise’s credit score is bad. The credit card score can be defined as the linear expression of ₨. Subsequently, we can calculate the scale for each bin by substituting some known scores obtained from experts.Table3 lists the scale for “the average age of the buyer.”Table 3
Final scale on “the average age of the buyers.”
BinScale1: [0, 0.0028]972: [0.0028, 0.0061]563: [0.0061, 0.0082]524: [0.0082, 0.0149]215: [0.0149, 0.0215]−26: [0.0215, 0.048]−117: [0.048, 0.0607]−128: [0.0607, 1]−32


## 4. Evaluation and Results

### 4.1. Evaluation

The experimental data for our research were obtained from the official customs database and a large Chinese e-commerce platform. We selected more than 4000 active enterprises on the platform and collected their related data from both the platform’s database and the official customs data cloud, which consists of different government databases, including the Tax Bureau, Statistics Bureau, and Ministry of Industry and Information Technology. The data we chose were created between July, 2020, and December, 2020. For each enterprise, we obtained at least 35 transaction data records and other records related to transport information, payment information, etc. After integration, the number of features was more than 500. We classified them into different categories as shown in Table4.Table 4
Feature categories of the dataset.
Feature categoryDescriptionProportion (%)Enterprise informationThe static information of the enterprises6Transaction informationData about the trade20Transport informationData about the transport14Clearance informationData about the clearance process in customs, e.g., declaration and examination14Credit historyIdentification of any historical bad credit records12CooperatorsRelations to other entities10Comments in customs databaseComments in the official customs database8Comments on platformComments on the e-commerce website8OthersOthers8The indicators in the paper are classified as discrete and continuous, both of which are based on discussions with experts who have hands-on case-handling experience within the supervision unit.As can be seen from Table4, customs clearance information, transportation information, partners, customs database remarks, and platform remarks are all new credit indicator categories constructed in this work which meet the needs of supervision units.We evaluated our framework from three perspectives. First, we measured the efficiency and results of our improved record reconciliation approach. Then, we evaluated the classification quality of the scorer. Lastly, we conducted experiments to verify the effect of the prejudice remover regularizer.


### 4.2. Results

#### 4.2.1. Improved Record Reconciliation Approach

As described in Section3.1, we improved the original dependency graph approach to meet our dataset’s requirements. The motivation of our work is that the original approach could not be completed in an acceptable time when the dataset contained more than 100,000 records. In our improved approach, the algorithm becomes progressive and deals with only part of data in each iteration, thereby reducing both the computational cost and the memory consumption.To measure the performance improvement of our approach, we applied the original approach and our improved one to datasets of various sizes. The full dataset consisted of about 1,400,000 records on over 4000 enterprises. In this step, we needed to characterize the transaction data, payment data, transport data, and partner data. For comparison, we divided the full dataset into various subsets, as described in Table5.Table 5
Various datasets for performance evaluation.
Data set# of enterprises# of recordsDS110037,699DS220072,804DS3500194,206DS41000402,152DS52000800,422DSfull40251,424,228Figure2 depicts the computational cost and memory consumption for each dataset using the original approach and our improved approach. We can see that the original approach exhibited an exponential increase in computational cost with the increase in dataset size, as each pair of records needed to be theoretically compared. In fact, we could not obtain a valid output for datasets larger than DS3 due to surpassing the memory requirement. In comparison, our improved approach exhibited good scalability with the dataset size, as it only computed the similarity of candidate records to one record in each iteration, thus linearizing the complexity of the algorithm.Figure 2
Computation cost and memory consumption comparison for original approach and improved approach. (a) Computational cost comparations on different data sets. (b) Memory consumption comparison on different data sets.
(a)(b)Although the performance of the approach was considerably improved, we were still concerned about the effect of the reconciliation. We evaluated the effects on DS1, DS2, and DS3 as a function of precision, recall, and the reported F-measure, defined as follows:(5)F−measure=2×precision×recallprecision+recall,Table6 lists the average precision/recall and F-measure for all classes of records involved in the reconciliation. We found that the improved approach outperformed the original approach for all three datasets. Specifically, upon increasing the size of the dataset, this advantage was also increased. For example, the recall for DS1 was improved by 5.4%, while it was improved by 17.8% for DS3. This is because the improved approach avoids unnecessary similarity computations between records from the exact base set, which may result in incorrect reconciliation and a decrease in recall.Table 6
Comparison of the original and improved approach.
Data setOriginalImprovedPrecision/recallF measurePrecision/recallF measureDS10.954/0.9210.9370.999/0.9750.989DS20.922/0.9050.9130.988/0.9700.979DS30.892/0.7450.8120989/0.9230.955


#### 4.2.2. Quality of Scorer

Referring to the FICO credit score rule and experts’ suggestions from customs, we mapped the credit score of cross-border e-commerce enterprises within a range of 200 to 950, categorized into five levels, as defined in Table7.Table 7
Credit levels and their corresponding score intervals.
Credit levelHighest scoreLowest scoreBB347200BBB497348A653498AA801654AAA950802A score lower than 200 is scaled to 200 and a score greater than 950 is scaled to 950.We selected and integrated records of 500 enterprises from the customs database and platform as the validation dataset. For comparison, we trained the model using datasets DS1 to DSfull, and then, we built the scorers individually using the method described in Sections 3.2 and 3.3. Then, we scored the enterprises and determined their credit level. Lastly, we compared the results to those manually crafted by experts to obtain the AUC value.Figure3 describes the learning curves of our model with/without new indicators on training datasets of different sizes. We can see that the AUC increases with the size of the data set, indicating our method’s correctness and effectiveness. When the number of records exceeded 0.8 million, the quality of the classification stabilized at an AUC value of 0.89, representing an empirically qualified score to deploy in production. The AUC value of the classification quality of the model without the new indicators is only 0.82, which indicates that the new index added here improves the quality of the model.Figure 3
The learning curve on training datasets of various sizes.In view of the ineluctable discrepancy in human recognition that exists in manual grading, we conducted another validation test by selecting 50 enterprises on each level from the results of the validation dataset. Consequently, the experts assigned each case a binary remark (qualified/unqualified) according to their behavior. The results are summarized in Table8. We can see that our model score and the qualified ratio from the experts exhibited a strong convergence, again indicating the correctness of our model.Table 8
Qualified/unqualified results for enterprises on different levels.
Credit levelQualifiedUnqualifiedQualified ratio (%)BB113922BBB292158A401080AA48296AAA500100


#### 4.2.3. Effect of the Prejudice Remover Regularizer

In order to evaluate the effect of the prejudice remover regularizer, we used the disparate impact (DI) [28], which is defined as follows:(6)DIX=PY=BX=0PY=BX=1.DI is calculated by dividing the conditional probability of the positive result given a sensitiveX value by that given a nonsensitive X value. A DI value nearer to 1 denotes that the predictor is more insensitive to the score result.Several potentially sensitive predictors were chosen according to the experts’ advice and classified into three categories: penalty, capital, and profit. Figure4(a) demonstrates the DI for the three categories of predictors with/without the regularizer. We can see that the DI with the regularizer was nearer to 1 than that without the regularizer, indicating its ability to remove certain prejudices originally existing toward SMEs. In the three categories, the effect on capital was the weakest, suggesting a potentially strong correlation between capital-related features and credit score in cross-border e-commerce transactions.Figure 4
DI evaluation on (a) different categories of predictors and (b) various values ofƞ for category profit.
(a)(b)Figure4(b) depicts the effect of prejudice removal on various values of ƞ as calculated in equation (4). We can see that when the value of ƞ was equal to 14, the effect of prejudice removal was best. The category we used in this experiment was profit.


## 4.1. Evaluation

The experimental data for our research were obtained from the official customs database and a large Chinese e-commerce platform. We selected more than 4000 active enterprises on the platform and collected their related data from both the platform’s database and the official customs data cloud, which consists of different government databases, including the Tax Bureau, Statistics Bureau, and Ministry of Industry and Information Technology. The data we chose were created between July, 2020, and December, 2020. For each enterprise, we obtained at least 35 transaction data records and other records related to transport information, payment information, etc. After integration, the number of features was more than 500. We classified them into different categories as shown in Table4.Table 4
Feature categories of the dataset.
Feature categoryDescriptionProportion (%)Enterprise informationThe static information of the enterprises6Transaction informationData about the trade20Transport informationData about the transport14Clearance informationData about the clearance process in customs, e.g., declaration and examination14Credit historyIdentification of any historical bad credit records12CooperatorsRelations to other entities10Comments in customs databaseComments in the official customs database8Comments on platformComments on the e-commerce website8OthersOthers8The indicators in the paper are classified as discrete and continuous, both of which are based on discussions with experts who have hands-on case-handling experience within the supervision unit.As can be seen from Table4, customs clearance information, transportation information, partners, customs database remarks, and platform remarks are all new credit indicator categories constructed in this work which meet the needs of supervision units.We evaluated our framework from three perspectives. First, we measured the efficiency and results of our improved record reconciliation approach. Then, we evaluated the classification quality of the scorer. Lastly, we conducted experiments to verify the effect of the prejudice remover regularizer.


## 4.2. Results

### 4.2.1. Improved Record Reconciliation Approach

As described in Section3.1, we improved the original dependency graph approach to meet our dataset’s requirements. The motivation of our work is that the original approach could not be completed in an acceptable time when the dataset contained more than 100,000 records. In our improved approach, the algorithm becomes progressive and deals with only part of data in each iteration, thereby reducing both the computational cost and the memory consumption.To measure the performance improvement of our approach, we applied the original approach and our improved one to datasets of various sizes. The full dataset consisted of about 1,400,000 records on over 4000 enterprises. In this step, we needed to characterize the transaction data, payment data, transport data, and partner data. For comparison, we divided the full dataset into various subsets, as described in Table5.Table 5
Various datasets for performance evaluation.
Data set# of enterprises# of recordsDS110037,699DS220072,804DS3500194,206DS41000402,152DS52000800,422DSfull40251,424,228Figure2 depicts the computational cost and memory consumption for each dataset using the original approach and our improved approach. We can see that the original approach exhibited an exponential increase in computational cost with the increase in dataset size, as each pair of records needed to be theoretically compared. In fact, we could not obtain a valid output for datasets larger than DS3 due to surpassing the memory requirement. In comparison, our improved approach exhibited good scalability with the dataset size, as it only computed the similarity of candidate records to one record in each iteration, thus linearizing the complexity of the algorithm.Figure 2
Computation cost and memory consumption comparison for original approach and improved approach. (a) Computational cost comparations on different data sets. (b) Memory consumption comparison on different data sets.
(a)(b)Although the performance of the approach was considerably improved, we were still concerned about the effect of the reconciliation. We evaluated the effects on DS1, DS2, and DS3 as a function of precision, recall, and the reported F-measure, defined as follows:(5)F−measure=2×precision×recallprecision+recall,Table6 lists the average precision/recall and F-measure for all classes of records involved in the reconciliation. We found that the improved approach outperformed the original approach for all three datasets. Specifically, upon increasing the size of the dataset, this advantage was also increased. For example, the recall for DS1 was improved by 5.4%, while it was improved by 17.8% for DS3. This is because the improved approach avoids unnecessary similarity computations between records from the exact base set, which may result in incorrect reconciliation and a decrease in recall.Table 6
Comparison of the original and improved approach.
Data setOriginalImprovedPrecision/recallF measurePrecision/recallF measureDS10.954/0.9210.9370.999/0.9750.989DS20.922/0.9050.9130.988/0.9700.979DS30.892/0.7450.8120989/0.9230.955


### 4.2.2. Quality of Scorer

Referring to the FICO credit score rule and experts’ suggestions from customs, we mapped the credit score of cross-border e-commerce enterprises within a range of 200 to 950, categorized into five levels, as defined in Table7.Table 7
Credit levels and their corresponding score intervals.
Credit levelHighest scoreLowest scoreBB347200BBB497348A653498AA801654AAA950802A score lower than 200 is scaled to 200 and a score greater than 950 is scaled to 950.We selected and integrated records of 500 enterprises from the customs database and platform as the validation dataset. For comparison, we trained the model using datasets DS1 to DSfull, and then, we built the scorers individually using the method described in Sections 3.2 and 3.3. Then, we scored the enterprises and determined their credit level. Lastly, we compared the results to those manually crafted by experts to obtain the AUC value.Figure3 describes the learning curves of our model with/without new indicators on training datasets of different sizes. We can see that the AUC increases with the size of the data set, indicating our method’s correctness and effectiveness. When the number of records exceeded 0.8 million, the quality of the classification stabilized at an AUC value of 0.89, representing an empirically qualified score to deploy in production. The AUC value of the classification quality of the model without the new indicators is only 0.82, which indicates that the new index added here improves the quality of the model.Figure 3
The learning curve on training datasets of various sizes.In view of the ineluctable discrepancy in human recognition that exists in manual grading, we conducted another validation test by selecting 50 enterprises on each level from the results of the validation dataset. Consequently, the experts assigned each case a binary remark (qualified/unqualified) according to their behavior. The results are summarized in Table8. We can see that our model score and the qualified ratio from the experts exhibited a strong convergence, again indicating the correctness of our model.Table 8
Qualified/unqualified results for enterprises on different levels.
Credit levelQualifiedUnqualifiedQualified ratio (%)BB113922BBB292158A401080AA48296AAA500100


### 4.2.3. Effect of the Prejudice Remover Regularizer

In order to evaluate the effect of the prejudice remover regularizer, we used the disparate impact (DI) [28], which is defined as follows:(6)DIX=PY=BX=0PY=BX=1.DI is calculated by dividing the conditional probability of the positive result given a sensitiveX value by that given a nonsensitive X value. A DI value nearer to 1 denotes that the predictor is more insensitive to the score result.Several potentially sensitive predictors were chosen according to the experts’ advice and classified into three categories: penalty, capital, and profit. Figure4(a) demonstrates the DI for the three categories of predictors with/without the regularizer. We can see that the DI with the regularizer was nearer to 1 than that without the regularizer, indicating its ability to remove certain prejudices originally existing toward SMEs. In the three categories, the effect on capital was the weakest, suggesting a potentially strong correlation between capital-related features and credit score in cross-border e-commerce transactions.Figure 4
DI evaluation on (a) different categories of predictors and (b) various values ofƞ for category profit.
(a)(b)Figure4(b) depicts the effect of prejudice removal on various values of ƞ as calculated in equation (4). We can see that when the value of ƞ was equal to 14, the effect of prejudice removal was best. The category we used in this experiment was profit.


## 4.2.1. Improved Record Reconciliation Approach

As described in Section3.1, we improved the original dependency graph approach to meet our dataset’s requirements. The motivation of our work is that the original approach could not be completed in an acceptable time when the dataset contained more than 100,000 records. In our improved approach, the algorithm becomes progressive and deals with only part of data in each iteration, thereby reducing both the computational cost and the memory consumption.To measure the performance improvement of our approach, we applied the original approach and our improved one to datasets of various sizes. The full dataset consisted of about 1,400,000 records on over 4000 enterprises. In this step, we needed to characterize the transaction data, payment data, transport data, and partner data. For comparison, we divided the full dataset into various subsets, as described in Table5.Table 5
Various datasets for performance evaluation.
Data set# of enterprises# of recordsDS110037,699DS220072,804DS3500194,206DS41000402,152DS52000800,422DSfull40251,424,228Figure2 depicts the computational cost and memory consumption for each dataset using the original approach and our improved approach. We can see that the original approach exhibited an exponential increase in computational cost with the increase in dataset size, as each pair of records needed to be theoretically compared. In fact, we could not obtain a valid output for datasets larger than DS3 due to surpassing the memory requirement. In comparison, our improved approach exhibited good scalability with the dataset size, as it only computed the similarity of candidate records to one record in each iteration, thus linearizing the complexity of the algorithm.Figure 2
Computation cost and memory consumption comparison for original approach and improved approach. (a) Computational cost comparations on different data sets. (b) Memory consumption comparison on different data sets.
(a)(b)Although the performance of the approach was considerably improved, we were still concerned about the effect of the reconciliation. We evaluated the effects on DS1, DS2, and DS3 as a function of precision, recall, and the reported F-measure, defined as follows:(5)F−measure=2×precision×recallprecision+recall,Table6 lists the average precision/recall and F-measure for all classes of records involved in the reconciliation. We found that the improved approach outperformed the original approach for all three datasets. Specifically, upon increasing the size of the dataset, this advantage was also increased. For example, the recall for DS1 was improved by 5.4%, while it was improved by 17.8% for DS3. This is because the improved approach avoids unnecessary similarity computations between records from the exact base set, which may result in incorrect reconciliation and a decrease in recall.Table 6
Comparison of the original and improved approach.
Data setOriginalImprovedPrecision/recallF measurePrecision/recallF measureDS10.954/0.9210.9370.999/0.9750.989DS20.922/0.9050.9130.988/0.9700.979DS30.892/0.7450.8120989/0.9230.955


## 4.2.2. Quality of Scorer

Referring to the FICO credit score rule and experts’ suggestions from customs, we mapped the credit score of cross-border e-commerce enterprises within a range of 200 to 950, categorized into five levels, as defined in Table7.Table 7
Credit levels and their corresponding score intervals.
Credit levelHighest scoreLowest scoreBB347200BBB497348A653498AA801654AAA950802A score lower than 200 is scaled to 200 and a score greater than 950 is scaled to 950.We selected and integrated records of 500 enterprises from the customs database and platform as the validation dataset. For comparison, we trained the model using datasets DS1 to DSfull, and then, we built the scorers individually using the method described in Sections 3.2 and 3.3. Then, we scored the enterprises and determined their credit level. Lastly, we compared the results to those manually crafted by experts to obtain the AUC value.Figure3 describes the learning curves of our model with/without new indicators on training datasets of different sizes. We can see that the AUC increases with the size of the data set, indicating our method’s correctness and effectiveness. When the number of records exceeded 0.8 million, the quality of the classification stabilized at an AUC value of 0.89, representing an empirically qualified score to deploy in production. The AUC value of the classification quality of the model without the new indicators is only 0.82, which indicates that the new index added here improves the quality of the model.Figure 3
The learning curve on training datasets of various sizes.In view of the ineluctable discrepancy in human recognition that exists in manual grading, we conducted another validation test by selecting 50 enterprises on each level from the results of the validation dataset. Consequently, the experts assigned each case a binary remark (qualified/unqualified) according to their behavior. The results are summarized in Table8. We can see that our model score and the qualified ratio from the experts exhibited a strong convergence, again indicating the correctness of our model.Table 8
Qualified/unqualified results for enterprises on different levels.
Credit levelQualifiedUnqualifiedQualified ratio (%)BB113922BBB292158A401080AA48296AAA500100


## 4.2.3. Effect of the Prejudice Remover Regularizer

In order to evaluate the effect of the prejudice remover regularizer, we used the disparate impact (DI) [28], which is defined as follows:(6)DIX=PY=BX=0PY=BX=1.DI is calculated by dividing the conditional probability of the positive result given a sensitiveX value by that given a nonsensitive X value. A DI value nearer to 1 denotes that the predictor is more insensitive to the score result.Several potentially sensitive predictors were chosen according to the experts’ advice and classified into three categories: penalty, capital, and profit. Figure4(a) demonstrates the DI for the three categories of predictors with/without the regularizer. We can see that the DI with the regularizer was nearer to 1 than that without the regularizer, indicating its ability to remove certain prejudices originally existing toward SMEs. In the three categories, the effect on capital was the weakest, suggesting a potentially strong correlation between capital-related features and credit score in cross-border e-commerce transactions.Figure 4
DI evaluation on (a) different categories of predictors and (b) various values ofƞ for category profit.
(a)(b)Figure4(b) depicts the effect of prejudice removal on various values of ƞ as calculated in equation (4). We can see that when the value of ƞ was equal to 14, the effect of prejudice removal was best. The category we used in this experiment was profit.


## 5. Conclusions

In this paper, we propose a framework for building an effective credit scorer for cross-border e-commerce enterprises. The contributions of this paper are as follows: first, we introduced a better dependency graph approach to reconcile the redundancy of records from multiple data sources, which improved the data quality for consequent model training. Compared with the original algorithm, our method could save considerable computational cost and memory consumption, making it applicable for large datasets. Second, we used logistic regression for data training, preceded by predictor preparation through binning and evaluating the information value, which was maturely adopted to personal credit applications. The advantage of this approach is its efficiency and explicability. Third, we used a prejudice remover regularizer to weaken the excessive advantage of large enterprises, in response to the official policy to advocate the development of small and medium e-commerce enterprises. Experiments on real datasets demonstrated both the effectiveness and efficiency of our framework.In the future, our aim is to try other kinds of regularizers for prejudice removal, which would help us better understand the underlying clues related to the credit score of cross-border e-commerce enterprises. Furthermore, our aim is to integrate additional data from other sources, especially related to enterprises’ daily activities, to improve the model’s precision. Building a credit score system is extremely important for cross-border e-commerce; accordingly, we anticipate further challenges in the foreseeable future.



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*Source: 5281050-2023-01-12.xml*