Credit risk prediction method and device, program product and storage medium

By using graph neural network technology in the credit risk prediction model, weighted calculations are performed based on the similarity of customer information feature vectors, the problem of difficulty in identifying credit risks in credit services is solved, and high-accurate credit risk prediction is achieved, supporting the risk management and operating efficiency improvement of credit institutions.

CN119648383APending Publication Date: 2025-03-18AGRICULTURAL BANK OF CHINA
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Patent Information

Application Number
CN202411738854.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-29
Publication Date
2025-03-18

AI Technical Summary

Technical Problem

How to effectively identify and manage credit risks in credit services such as Internet finance and credit cards, especially when the number of users and market participants increase.

Method used

By constructing a credit risk prediction model, the model uses graph neural network technology to weight the similarity between the customer information feature vector of the customer to be predicted and the feature vector of the historical credit customers, and generates a customer information feature weighted graph to predict the customer's credit risk.

Benefits of technology

This method can effectively explore the implicit relationships between credit customers, improve the accuracy of credit risk prediction, help credit institutions identify and manage risks, reduce operating costs, and increase operating scale and profits.

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Abstract

The embodiment of the invention discloses a credit risk prediction method and device, a program product and a storage medium. The method comprises the following steps: inputting a first customer information feature vector of a to-be-predicted customer into a credit risk prediction model; the credit risk prediction model is obtained by training a second customer information feature vector of a historical credit customer; performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature map; obtaining a first customer information feature weighted graph based on the first customer information feature graph and the weight parameter matrix; and obtaining a first prediction result based on the first customer information feature weighted graph. According to the credit risk prediction model obtained through pre-training, the implicit relationship between the credit customers can be effectively mined, the accuracy of credit risk prediction is improved, and the credit risk is effectively identified.
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Description

Technical Field

[0001] The present application relates to the field of computer technology, and more specifically, to a credit risk prediction method, device, program product and storage medium. Background Art

[0002] In the past few years, with the rapid development of Internet finance and credit services such as bank credit cards, convenient financial solutions have been provided to the majority of users, greatly enriching the market's financial service system.

[0003] However, with the expansion of the scope of credit services and the increase in market participants, while credit services such as Internet finance and credit cards have brought convenience to users, the risk management challenges faced by credit institutions have gradually increased. How to identify credit risks has become a technical problem that needs to be solved urgently. Summary of the invention

[0004] In view of this, the embodiments of the present application disclose a credit risk prediction method, device, program product and storage medium to achieve effective identification of credit risk.

[0005] The technical solutions provided by the embodiments of this application are as follows:

[0006] In a first aspect, an embodiment of the present application provides a credit risk prediction method, the method comprising:

[0007] Inputting the first customer information feature vector of the customer to be predicted into a credit risk prediction model; the credit risk prediction model is obtained by training the second customer information feature vector of historical credit customers;

[0008] Calculating similarity between the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph;

[0009] Based on the first customer information feature graph and the weight parameter matrix, obtaining a first customer information feature weighted graph;

[0010] Based on the first customer information feature weighted graph, a first prediction result is obtained.

[0011] In combination with the first aspect, in a possible implementation manner of the first aspect, the performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain the first customer information feature graph includes:

[0012] Based on a similarity calculation formula, similarity calculation is performed on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph; the similarity calculation formula includes at least two of the following: a cosine similarity calculation formula, a Euclidean distance calculation formula, and a Pearson correlation coefficient calculation formula.

[0013] In combination with the first aspect, in a possible implementation of the first aspect, there are multiple historical credit customers, there are multiple second customer information feature vectors, and the similarity calculation of the first customer information feature vector and the second customer information feature vector is performed to obtain a first customer information feature graph, including:

[0014] Calculating similarities between the first customer information feature vector and the plurality of second customer information feature vectors to obtain a plurality of first similarities;

[0015] Determine the first similarity greater than the similarity threshold as the second similarity;

[0016] Sorting the second similarities to obtain a sorting result;

[0017] Based on the sorting result, a first customer information feature graph is obtained.

[0018] In combination with the first aspect, in a possible implementation of the first aspect, the credit risk prediction model includes a first graph attention network, a second graph attention network, and a normalized inactivation activation block, and the first prediction result is obtained based on the first customer information feature weighted graph, including:

[0019] Inputting the first customer information feature weighted graph into the first graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first customer information feature weighted graph to obtain a first attention feature;

[0020] Inputting the first attention feature into the second graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first attention feature to obtain a second attention feature;

[0021] The second attention feature is input into the normalized inactivation activation block, and batch normalization, random inactivation, and nonlinear transformation are performed on the second attention feature to obtain the first prediction result.

[0022] In combination with the first aspect, in a possible implementation manner of the first aspect, the method further includes:

[0023] Fine-tuning the credit risk prediction model using the first customer information feature vector to obtain a fine-tuned credit risk prediction model;

[0024] The step of inputting the first customer information feature vector of the customer to be predicted into the credit risk prediction model comprises:

[0025] The first customer information feature vector is input into the fine-tuned credit risk prediction model.

[0026] In combination with the first aspect, in a possible implementation manner of the first aspect, there are multiple second customer information feature vectors, and the method further includes:

[0027] Inputting a plurality of the second customer information feature vectors into a training model;

[0028] Performing similarity calculation on a plurality of the second customer information feature vectors to obtain a second customer information feature graph;

[0029] Based on the second customer information feature graph and the weight parameter matrix, obtaining a second customer information feature weighted graph;

[0030] Obtaining a second prediction result based on the second customer information feature weighted graph;

[0031] Obtaining a loss value based on the second prediction result and the credit risk label corresponding to the historical credit customer;

[0032] The training model is iteratively trained based on the loss value to obtain the credit risk prediction model.

[0033] In combination with the first aspect, in a possible implementation of the first aspect, the credit information of the customer to be predicted includes: first credit information of a floating point type, second credit information of an integer type, and third credit information of a discrete type, and the method further includes:

[0034] Processing the first credit information using a maximum-minimum normalization method to obtain a first sub-feature vector;

[0035] Processing the second credit information using an equal frequency binning method to obtain a second sub-feature vector;

[0036] Numerically encoding the third credit information to obtain a third sub-feature vector;

[0037] A first customer information feature vector is obtained based on the first sub-feature vector, the second sub-feature vector, and the third sub-feature vector.

[0038] In a second aspect, an embodiment of the present application provides a credit risk prediction device, the device comprising:

[0039] An input module, used to input a first customer information feature vector of a customer to be predicted into a credit risk prediction model; the credit risk prediction model is obtained by training a second customer information feature vector of a historical credit customer;

[0040] a calculation module, configured to perform similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph;

[0041] The calculation module is further used to obtain a first customer information feature weighted graph based on the first customer information feature graph and the weight parameter matrix;

[0042] A prediction module is used to obtain a first prediction result based on the first customer information feature weighted graph.

[0043] The credit risk prediction device has the function of implementing the credit risk prediction method in the first aspect or any possible implementation of the first aspect. The function can be implemented by hardware or by hardware executing corresponding software, and the hardware or software includes one or more modules corresponding to the above functions.

[0044] In a third aspect, an embodiment of the present application provides a credit risk prediction device, which may include at least one processor, and the processor is used to call computer instructions in a memory so that the credit risk prediction device executes the credit risk prediction method in the above-mentioned first aspect or any optional embodiment of the first aspect.

[0045] In combination with the third aspect, in a possible implementation of the third aspect, the credit risk prediction device may further include a memory.

[0046] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, which may include instructions. When the instructions are executed on a computer, the computer executes the credit risk prediction method in the above-mentioned first aspect or any optional embodiment of the first aspect.

[0047] In a fifth aspect, an embodiment of the present application provides a computer program product, which may include instructions. When the instructions are executed on a computer, the computer executes the credit risk prediction method in the above-mentioned first aspect or any optional embodiment of the first aspect.

[0048] In a sixth aspect, an embodiment of the present application provides a chip system, which includes a processor for supporting the device to implement the functions involved in the above aspects, for example, sending or processing the data and / or information involved in the above methods. In one possible design, the chip system also includes a memory, which is used to store program instructions and data necessary for the device. The chip system can be composed of chips, or it can include chips and other discrete devices.

[0049] In the seventh aspect, an embodiment of the present application provides a chip, comprising one or more interface circuits and one or more processors; the interface circuit is used to receive signals from a memory of an electronic device and send signals to the processor, the signals including computer instructions stored in the memory; when the processor executes the computer instructions, the electronic device executes the credit risk prediction method in the first aspect or any optional implementation of the first aspect.

[0050] Based on the above technical solution, this application has the following beneficial effects:

[0051] The embodiment of the present application discloses a credit risk prediction method, device, program product and storage medium. Among them, the method includes: inputting the first customer information feature vector of the customer to be predicted into the credit risk prediction model; the credit risk prediction model is obtained by training the second customer information feature vector of the historical credit customer; performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain the first customer information feature graph; based on the first customer information feature graph and the weight parameter matrix, obtaining the first customer information feature weighted graph; based on the first customer information feature weighted graph, obtaining the first prediction result. It can be seen that the credit risk prediction model obtained by pre-training in the embodiment of the present application can predict the credit risk of the customer to be predicted, so that the credit institution can provide corresponding credit services for the customer to be predicted in combination with the predicted credit risk. Moreover, the credit risk prediction model in the embodiment of the present application is a graph neural network, which takes the customer information feature weighted graph as input, and the customer information feature weighted graph can characterize the correlation between the customer to be predicted and the historical credit customer, so that the implicit relationship between credit customers can be effectively mined, the accuracy of credit risk prediction can be improved, and the credit risk can be effectively identified. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can also be obtained based on the disclosed drawings.

[0053] Figure 1 A flowchart of a credit risk prediction method disclosed in an embodiment of the present application;

[0054] Figure 2 A flowchart of another credit risk prediction method disclosed in an embodiment of the present application;

[0055] Figure 3 A flowchart of another credit risk prediction method disclosed in an embodiment of the present application;

[0056] Figure 4 A schematic diagram of the structure of a credit risk prediction device disclosed in an embodiment of the present application. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. The embodiments based on the present application are all within the scope of protection of the present application.

[0058] The following is an explanation of some professional terms involved in the embodiments of the present application.

[0059] (1) Graph Neural Networks (GNN): A type of deep learning model designed to process graph-structured data. GNNs use nodes and edges to represent entities and their relationships in the data, and use message passing mechanisms to pass information between nodes to update node states. GNNs can learn the deep structural features of graphs through techniques such as node embedding, aggregating neighbor information, and updating node states, capture complex patterns and dependencies in graphs, and provide effective feature representation and prediction capabilities for graph data, making GNNs suitable for scenarios such as social network analysis and recommendation systems.

[0060] (2) Adjacency matrix: The adjacency matrix is ​​a method of representing a graph in graph theory, which is used to describe the connection relationship between nodes in the graph. In the adjacency matrix, the rows and columns represent the nodes in the graph, and the elements in the matrix indicate whether there is an edge between the nodes. For an unweighted graph, 0 can be used to represent no edge connection, and 1 can be used to represent an edge connection; for a weighted graph, a specific weight value can be used to represent the strength of the edge. The adjacency matrix allows the structural properties of the graph and the relationship between nodes to be intuitively analyzed and processed through matrix operations.

[0061] (3) Attention Mechanism: It is an important technology in the field of deep learning, which is used to enhance the model's ability to selectively focus on information. The attention mechanism imitates the working principle of human attention, allowing the model to prioritize the most critical information when processing a large amount of input data. By calculating the weight distribution of input features, the attention mechanism can dynamically focus on the most important information for the current task, thereby improving the performance and efficiency of the model. The attention mechanism has shown a wide range of application value in many fields such as natural language processing, image recognition, and recommendation systems. In particular, it has played a key role in improving the accuracy and efficiency of tasks such as sequence to sequence models (Seq2Seq), language translation, and text summarization. By giving the model the ability to "pay attention" to key information, the attention mechanism greatly enhances the ability of deep learning models to process complex data.

[0062] In the past few years, with the rapid development of credit services such as Internet finance and bank credit cards, convenient financial solutions have been provided to the majority of users, greatly enriching the financial service system of the market. However, all this convenience has not reduced the importance of risk control. With the expansion of the scope of credit services and the increase in market participants, higher requirements have been placed on the risk management capabilities of credit institutions. Whether it is a traditional bank, an Internet financial company or a microfinance institution, they all face a common challenge: how to effectively identify and control credit risks while providing credit services to maximize profits and maintain sustainable development. A key issue is that the existence of bad customers will not only directly lead to economic losses, but also increase the difficulty of subsequent risk control and collection work, posing a threat to the long-term profitability of the enterprise. At the same time, if high-quality customers cannot be accurately identified, the enterprise will miss the opportunity to expand its customer base and increase revenue. Therefore, being able to effectively distinguish between potential normal customers and potential defaulting customers is crucial to improving the competitiveness of banks and financial institutions and ensuring their long-term stable development.

[0063] Traditional credit risk assessment methods rely on linear models and shallow data analysis, which cannot fully utilize the deep relationships and patterns contained in large-scale complex data, resulting in inaccurate identification of potential risks and limited risk control effects. In addition, existing risk assessment models usually lack flexibility and adaptability, making it difficult to respond to market changes and emerging risks in a timely manner, which in turn affects the competitiveness and long-term stable development of financial institutions.

[0064] To this end, the embodiments of the present application disclose a credit risk prediction method, device, program product and storage medium. The credit risk prediction model obtained through pre-training can predict the credit risk of the customer to be predicted, so that the credit institution can provide corresponding credit services to the customer to be predicted in combination with the predicted credit risk, so as to reduce risks and operating costs, and at the same time bring a larger operating scale and benefits to the credit structure, supporting the credit institution to achieve the goal of maximizing benefits. Moreover, the credit risk prediction model in the embodiments of the present application is a graph neural network, and the weighted graph of customer information features can characterize the correlation between the customer to be predicted and the historical credit customers. In this way, through deep learning and complex network analysis technology, the implicit and complex relationships between credit customers can be effectively mined, the accuracy of credit risk prediction can be improved, and effective identification of credit risks can be achieved.

[0065] See also Figure 1 , a flowchart of a credit risk prediction method disclosed in an embodiment of the present application, the credit risk prediction method may include the following steps:

[0066] S101. Inputting a first customer information feature vector of a customer to be predicted into a credit risk prediction model.

[0067] Among them, the credit risk prediction model can be obtained by training the second customer information feature vector of historical credit customers, and the credit risk prediction model is a graph neural network.

[0068] The customer to be predicted in the embodiment of the present application may be a credit applicant. The first customer information feature vector may be obtained by preprocessing the credit information of the customer to be tested, and the second customer information feature vector may be obtained by preprocessing the credit information of historical credit customers. The credit information may include gender, marital status, working hours, age, education level, total loan amount, etc.

[0069] S102: Calculate the similarity between the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph.

[0070] Among them, the first customer information feature map is used to characterize the correlation between the customer to be predicted and the historical credit customers.

[0071] S103: Obtain a first customer information feature weighted graph based on the first customer information feature graph and the weight parameter matrix.

[0072] The weight parameter matrix in the embodiment of the present application can be a learnable weight parameter matrix. Among them, the learnable weight parameter matrix refers to a parameter matrix that can be adjusted and optimized during the training process. These parameters are the core components of the model and are used to extract features from input data and make predictions.

[0073] S104: Obtain a first prediction result based on the first customer information feature weighted graph.

[0074] Among them, the first prediction result can be used to characterize whether the customer to be predicted defaults.

[0075] In a possible implementation, the first prediction result may be any one of the following: default, no default. Correspondingly, the credit risk label corresponding to the historical credit customer may be any one of the following: default, no default.

[0076] In another possible implementation, the first prediction result may be any one of the following: high default probability, medium default probability, low default probability, no default. Correspondingly, the credit risk label corresponding to the historical credit customer may be any one of the following: high default probability, medium default probability, low default probability, no default.

[0077] It can be seen that the credit risk prediction model obtained by pre-training in the embodiment of the present application can predict the credit risk of the customer to be predicted, so that the credit institution can provide corresponding credit services to the customer to be predicted in combination with the predicted credit risk. Moreover, the credit risk prediction model in the embodiment of the present application is a graph neural network, which takes the weighted graph of customer information features as input, and the weighted graph of customer information features can characterize the correlation between the customer to be predicted and the historical credit customers, so that the implicit relationship between credit customers can be effectively mined, the accuracy of credit risk prediction can be improved, and the credit risk can be effectively identified.

[0078] See also Figure 2 , a flow chart of another credit risk prediction method provided for the implementation of this application. First, the embodiment of this application needs to pre-process the credit information of the customer to obtain the information feature vector of each customer; then use the model to construct multiple customer information feature graphs through various similarity calculation formulas such as cosine similarity, Euclidean distance, and Pearson correlation from the customer information feature vector; then use the model to integrate multiple customer information feature graphs through a learnable weight parameter matrix to obtain a customer information feature weighted graph; then input the customer information feature weighted graph into the two-layer graph attention network of the model, perform linear transformation, attention mechanism operation, normalization, and feature aggregation, so that the information between adjacent nodes in the customer information feature weighted graph is fully propagated and flowed, and the attention feature is obtained; finally, the attention feature is batch normalized (Batch Norm), randomly inactivated (Drop out), and nonlinearly transformed using the activation function (Activation) to obtain the final prediction result. It can be understood that the customers here include: customers to be predicted and historical credit customers. During the model training process, the true labels and prediction results can be iteratively trained using the loss function to obtain the final model parameters, and then the credit risk prediction model can be expressed; during the model application process, when there are new credit customers, that is, customers to be predicted, incremental learning is used to freeze some layers of the credit risk prediction model, and credit risk prediction is performed after fine-tuning the credit risk prediction model.

[0079] See also Figure 3 , a flow chart of another credit risk prediction method provided for the implementation of this application, Figure 3 exist Figure 1 , Figure 2 Based on the corresponding provided credit risk prediction method, the credit risk prediction method is described in more detail. The credit risk prediction method provided in the embodiment of the present application may include the following steps:

[0080] S301. Preprocess the credit information of a plurality of historical credit customers to obtain a plurality of second customer information feature vectors.

[0081] In the embodiment of the present application, a historical credit information set can be obtained by collecting and collating the credit data of multiple historical credit customers. The historical credit information set includes the credit information of multiple historical credit customers, and the credit information of historical credit customers can be composed of two parts: basic attribute information of historical credit customers and transaction behavior information of historical credit customers. Among them, the basic attribute information may include: gender, marital status, working hours, age, education level, insurance, whether to buy a house, whether to buy a car, total loan amount, etc. Transaction behavior information may include: transaction time, transaction amount, transaction classification code and other attributes. For each historical credit customer, there can also be a variable to identify whether it has defaulted, such as 0 for non-default and 1 for default.

[0082] The target variable of the embodiment of the present application is to determine whether a default will occur. The target variable will be affected by a variety of characteristic variables, such as floating-point continuous values ​​such as transaction amount, integer continuous values ​​such as age, number of debit cards held, years of work experience, and discrete values ​​such as gender and education level. These characteristic variables often differ in dimension and value. For this reason, the embodiment of the present application needs to preprocess the historical credit information set to obtain the second customer information characteristic vector of each historical credit customer.

[0083] The preprocessing process of the embodiment of the present application may include the following: For the case of invalid values ​​in the historical credit information set, a null value replacement or 0 filling method can be uniformly adopted. For floating-point continuous value features, the maximum-minimum normalization method is applied for processing; for integer continuous value features, the equal frequency binning method is adopted; for discrete features, the LabelEncoder in the sklearn.preprocessing library in python is used for numerical encoding, and unique numbers are assigned to different category values. In this way, the influence weights of each feature variable on the model objective function are unified, while enhancing the stability and interpretability of the model and accelerating the convergence speed of the iterative solution of the model.

[0084] Among them, the maximum-minimum normalization method is a commonly used data preprocessing technique, which maps the original data to a specified range, usually the [0,1] interval, through linear transformation. The purpose of this method is to eliminate the dimensional influence between different features, so that the data can be compared and analyzed on the same scale, while retaining the distribution relationship of the original data. The equal frequency binning method is a data binning technique that divides the data into several intervals so that the number of data in each interval is roughly equal. This method is particularly suitable for processing skewed distributed data and reducing the impact of outliers. It is also commonly used in feature engineering for building machine learning models such as decision trees. LabelEncoder is a tool provided by the sklearn.preprocessing module in Python, which is used to convert classification labels into different numerical values. This conversion is very useful in machine learning because most machine learning algorithms require numerical input.

[0085] In the embodiment of the present application, the second customer information feature vector obtained after preprocessing can also be subjected to feature extraction and creation to obtain the final second customer information feature vector. For example, the transaction amount is taken as the logarithm (log) value, grouped and counted according to the transaction classification code, the number of transactions and the total amount in each group are counted, the total amount in the past 3 days and the past 7 days is counted, the maximum and minimum amounts are counted, the total expenditure is counted, etc. In this way, the content of the second customer information feature vector can be enriched, and the classification accuracy of the model can be improved.

[0086] Among them, taking log of transaction amount is a commonly used data preprocessing method, especially in the fields of financial data analysis and machine learning. Taking log can help stabilize the variance of data, reduce the impact of extreme values, and make the data distribution closer to normal distribution.

[0087] It is understandable that other methods may be used in the embodiments of the present application to pre-process the credit information of historical credit customers, and the embodiments of the present application are not limited to this.

[0088] S302: Input a plurality of second customer information feature vectors into a training model.

[0089] In the embodiment of the present application, multiple historical credit customers may correspond to multiple second customer information feature vectors.

[0090] S303: Perform similarity calculation on multiple second customer information feature vectors to obtain a second customer information feature graph.

[0091] Multiple second customer information feature vectors can be combined to obtain the information feature vector matrix X∈R N×F, where N represents the number of nodes, that is, the number of historical credit customers, and F represents the characteristic dimension of the node. The second information feature graph can be constructed by a variety of similarity calculation methods. The second information feature graph can be constructed using the adjacency matrix A∈R N×N It means that A∈R N×N It can represent the connection between nodes and the correlation between historical customer credit.

[0092] In the embodiment of the present application, the similarity calculation can be performed on the second customer information feature vectors of two historical credit customers by three similarity calculation methods: cosine similarity, Euclidean distance, and Pearson correlation coefficient. Among them, the second customer information feature vector of a historical credit customer will include multiple sub-feature vectors, such as gender corresponding to a sub-feature vector, marital status corresponding to a sub-feature vector, and so on. The following illustrates the similarity calculation by taking the second customer information feature vector of a historical credit customer as A, A including i sub-feature vectors, and the second customer information feature vector of another historical credit customer as B, B including i sub-feature vectors.

[0093] ①The cosine similarity calculation formula is as follows:

[0094]

[0095] Among them, A and B represent the second customer information feature vectors of historical credit customers, Cosine Similarity(A, B) represents the cosine similarity between A and B, and A i , B i represents the ith sub-feature vector of the historical credit customer, and n represents the number of sub-feature vectors. If Cosine Similarity(A, B) is greater than the similarity threshold, such as 0.8, 0.85, etc., it is determined that there is an undirected edge between the historical credit customer corresponding to A and the historical credit customer corresponding to B.

[0096] It should be noted that, in the embodiment of the present application, the number of historical credit customers is N, and the cosine similarity between each historical credit customer and other N-1 historical credit customers needs to be calculated to obtain N-1 cosine similarities corresponding to each customer, and finally the N-1 cosine similarities corresponding to each customer are used to obtain the second customer information feature graph under the cosine similarity calculation, and the second customer information feature graph can be represented by the adjacency matrix G1∈R N×N express.

[0097] ②The Euclidean distance calculation formula is as follows:

[0098]

[0099] Where A and B represent the second customer information feature vectors of historical credit customers, Euclidean Distance (A, B) represents the Euclidean distance between A and B, and A i , B i represents the ith sub-feature vector of the historical credit customer, and n represents the number of sub-feature vectors. If Euclidean Distance (A, B) is greater than the similarity threshold, such as the similarity threshold is 0.8, 0.85, etc., it is determined that there is an undirected edge between the historical credit customer corresponding to A and the historical credit customer corresponding to B.

[0100] It should be noted that, in the embodiment of the present application, the number of historical credit customers is N, and the Euclidean distance between each historical credit customer and other N-1 historical credit customers needs to be calculated to obtain the N-1 Euclidean distances corresponding to each customer. Finally, the N-1 Euclidean distances corresponding to each customer are used to obtain the second customer information feature graph under the Euclidean distance calculation. The second customer information feature graph can be represented by the adjacency matrix G2∈R N×N express.

[0101] ③The calculation formula of Pearson correlation coefficient is as follows:

[0102]

[0103] Among them, A and B represent the second customer information feature vectors of historical credit customers, Euclidean Distance (A, B) represents the Pearson correlation coefficient between A and B, and A i , B i represents the ith sub-feature vector of the historical credit customer, and n represents the number of sub-feature vectors. If Pearson Correlation (A, B) is greater than the similarity threshold, such as the similarity threshold is 0.8, 0.85, etc., it is determined that there is an undirected edge between the historical credit customer corresponding to A and the historical credit customer corresponding to B.

[0104] It should be noted that in the embodiment of the present application, the number of historical credit customers is N, and the Pearson correlation coefficient between each historical credit customer and other N-1 historical credit customers needs to be calculated to obtain the N-1 Pearson correlation coefficients corresponding to each customer. Finally, the N-1 Euclidean distances corresponding to each customer are used to obtain the second customer information feature graph under the Pearson correlation coefficient calculation. The second customer information feature graph can be represented by the adjacency matrix G3∈R N×N express.

[0105] In a possible implementation, in the embodiment of the present application, only the nodes with the top M similarities can be retained for each credit customer, such as M is 10, 11, etc., to construct the second customer information feature graph. In this way, the size of the second customer information feature graph can be reduced and the amount of calculation can be reduced. Among them, the closer the distance between two nodes, the higher the similarity.

[0106] S304: Obtain a second customer information feature weighted graph based on the second customer information feature graph and the weight parameter matrix.

[0107] In the embodiment of the present application, the second customer information feature graphs G1, G2, and G3 obtained in S303 can be transformed into the second customer information feature graphs G1, G2, and G3 through a learnable weight parameter matrix W i The second customer information feature weighted graph is obtained by integration, and the second customer information feature weighted graph can be represented by an adjacency matrix G4.

[0108] Among them, the calculation formula of G4 can be as follows:

[0109] G4=W1G1+W2*G2+W3*G3;

[0110] W1, W2, and W3 represent learnable weight parameter matrices, and W1, W2, and W3 can all be initialized using Xavier.

[0111] S305: Obtain a second prediction result based on the second customer information feature weighted graph.

[0112] The training model in the embodiment of the present application may include a two-layer graph attention network, and the second customer information feature weighted graph may be input into the graph attention network for processing. Among them, for each pair of nodes i and node represented by the second customer information feature weighted graph, the graph attention network first calculates an attention coefficient, which indicates the importance of the features of node i and node j to node i, and then obtains the new features of node i based on the attention coefficient. The calculation process can be as follows:

[0113] 1) Linear transformation: A shared linear transformation is applied to the second eigenvector of each node, and the weight matrix is F c represents the transformed feature dimension, and the transformed second feature vector is represented as h′ i =Wx i , x i represents the i-th sub-eigenvector before transformation.

[0114] 2) Attention mechanism operation: For node i and each neighbor node j of node i, calculate the initial attention coefficient in represents the parameters of the attention mechanism, and || represents the connection operation.

[0115] 3) Normalization: Use the softmax function to normalize all initial attention coefficients corresponding to node i to ensure that the final output attention coefficient can be interpreted as a probability: in, represents the set of neighbor nodes of node i, exp(e ij ) indicates e ij Take the natural exponential function with base e, e ij represents the initial attention coefficient of node i and node j, exp(e ik ) indicates e ik Take the natural exponential function with base e, e ik Represents the initial attention coefficients of nodes i and k.

[0116] 4) Feature aggregation: using attention coefficient α ij As the weight, the transformed features of the neighboring nodes are aggregated together to obtain the new features of node i. The new features of node i can be expressed as Among them, σ represents a nonlinear activation function, and the nonlinear activation function can be a ReLu activation function, etc.

[0117] It should be noted that each layer of the graph attention network in the embodiment of the present application will perform linear transformation, attention mechanism operation, normalization processing and feature aggregation, and the output of the previous layer of the graph attention network is used as the input of the next layer of the graph attention network, and is calculated in sequence. Among them, the attention mechanism operation is the attention calculation.

[0118] The graph attention network in the embodiment of the present application adopts a multi-head attention mechanism, that is, the above 1)-4) processes are repeated K times in parallel, and then the results are averaged. The input is sent to the subsequent normalization inactivation activation block for batch normalization, random inactivation, and nonlinear transformation to obtain the final prediction result. In the embodiment of the present application, nonlinear transformation is performed by an activation function.

[0119] It can be understood that S303 to S305 are all implemented through training models.

[0120] S306: Obtain a loss value based on the second prediction result and the credit risk labels corresponding to the historical credit customers.

[0121] In the embodiment of the present application, a cross entropy loss function can be used to calculate the loss value of the second prediction result and the credit risk label, and then the parameters of the entire training model are updated by back propagation based on the loss value.

[0122] For a single sample, the cross entropy loss can be expressed as:

[0123] L(Y,P)=-[Ylog(P)+(1-Y)log(1-P)]

[0124] Among them, L(Y,P) represents the loss value, Y is the credit risk label, that is, the actual label, and P is the second prediction result, that is, the result predicted by the training model.

[0125] S307. Iteratively train the training model based on the loss value to obtain a credit risk prediction model.

[0126] In the embodiment of the present application, the credit information of historical credit customers is preprocessed to obtain a second customer information feature vector, and then a risk prediction model is trained based on the second information feature vector. This facilitates the subsequent use of the trained risk prediction model to predict the risk of credit applicants, thereby improving the accuracy of risk prediction.

[0127] S308 , pre-processing the credit information of the customer to be predicted to obtain a first customer information feature vector.

[0128] The credit information of the customer to be predicted in the embodiment of the present application includes: first credit information of floating point type, second credit information of integer type, and third credit information of discrete type. Correspondingly, S308 may include: using the maximum-minimum normalization method to process the first credit information to obtain a first sub-feature vector; using the equal frequency binning method to process the second credit information to obtain a second sub-feature vector; numerically encoding the third credit information to obtain a third sub-feature vector; based on the first sub-feature vector, the second sub-feature vector, and the third sub-feature vector, obtaining the first customer information feature vector. In this way, different processing methods are used for different types of credit information, which facilitates the subsequent use of the first customer information feature vector for credit risk prediction, can unify the weights of the influence of each feature on the objective function of the credit risk prediction model, and at the same time enhance the stability and interpretability of the credit risk prediction model, and accelerate the convergence speed of the iterative solution of the credit risk prediction model.

[0129] It can be understood that the method of obtaining the first customer information feature vector in the embodiment of the present application is similar to the method of obtaining the second customer information feature vector in the above S301, so it will not be repeated here.

[0130] S309: Input the first customer information feature vector into the credit risk prediction model.

[0131] It can be understood that S309 is similar to S101 in the above embodiment, and similar parts are not described again here.

[0132] In a possible implementation, in the embodiment of the present application, the first customer information feature vector can be used to fine-tune the credit risk prediction model to obtain a fine-tuned credit risk prediction model; accordingly, S309 may include: inputting the first customer information feature vector into the fine-tuned credit risk prediction model. In this way, the credit risk prediction is performed only after the credit risk prediction model is fine-tuned using the new credit information, which can improve the accuracy of the credit risk prediction.

[0133] S310 , performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph.

[0134] S310 in the embodiment of the present application may include: based on a similarity calculation formula, performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature map; the similarity calculation formula includes at least two of the following: a cosine similarity calculation formula, an Euclidean distance calculation formula, and a Pearson correlation coefficient calculation formula. In this way, the correlation between new credit applicants and historical credit customers can be better captured through the similarity calculation formula, thereby improving the accuracy of credit risk prediction. Moreover, the first customer information feature map is constructed through at least two similarity calculation formulas, which can enrich the feature content used for credit risk prediction and further improve the accuracy of credit risk prediction.

[0135] S310 in the embodiment of the present application may include: calculating the similarity between the first customer information feature vector and multiple second customer information feature vectors to obtain multiple first similarities; determining the first similarities greater than the similarity threshold as the second similarities; sorting the second similarities to obtain a sorting result; and obtaining the first customer information feature graph based on the sorting result. In this way, the calculation amount of the model can be reduced while retaining important features, thereby improving the speed of credit risk prediction.

[0136] It should be noted that in the embodiment of the present application, for different similarity calculation formulas, the first customer information feature graph corresponding to the similarity calculation formula is obtained. Based on the similarity calculation formula, similarity calculation can be performed on the first customer information feature vector and multiple second customer information feature vectors to obtain multiple first similarities.

[0137] It is understandable that the method of obtaining the first customer information feature map in the embodiment of the present application is similar to the method of obtaining the second customer information feature map in the above S303, so it is not repeated here. In the embodiment of the present application, the second customer information feature map can be modified based on the sorting result, that is, the first customer information feature vector is integrated into the second customer information feature map to obtain the first customer information feature map.

[0138] S311. Obtain a first customer information feature weighted graph based on the first customer information feature graph and the weight parameter matrix.

[0139] It can be understood that the method of obtaining the first customer information feature weighted graph in the embodiment of the present application is similar to the method of obtaining the second customer information feature weighted graph in the above S304, so it will not be repeated here.

[0140] S312: Obtain a first prediction result based on the first customer information feature weighted graph.

[0141] The credit risk prediction model in the embodiment of the present application may include a first graph attention network, a second graph attention network and a normalized inactivation activation block. Accordingly, S312 may include: inputting the first customer information feature weighted graph into the first graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first customer information feature weighted graph to obtain a first attention feature; inputting the first attention feature into the second graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first attention feature to obtain a second attention feature; inputting the second attention feature into the normalized inactivation activation block, performing batch normalization, random inactivation and nonlinear transformation on the second attention feature to obtain a first prediction result. In this way, the attention mechanism is used to focus on analyzing key nodes and edge connections, so that the credit risk prediction model can identify and emphasize the key factors affecting credit risk, thereby improving the accuracy of credit risk prediction.

[0142] It can be understood that the method of obtaining the first prediction result in the embodiment of the present application is similar to the method of obtaining the second prediction result in the above S305, so it will not be repeated here.

[0143] In the embodiment of the present application, when new customer data comes in, that is, when there is a customer to be predicted, the credit information of the customer to be predicted is first preprocessed to obtain the first customer information feature vector. This step is consistent with the preprocessing step during the original model training. Using the same similarity calculation formula as that used in model training, the first customer information feature vector is integrated into the existing customer information feature map to obtain the first customer information feature map. Then the first customer information feature weighted map corresponding to the first customer information feature map is input into the graph attention network, and only the new customer data is used to fine-tune the model parameters. During the fine-tuning process, other layers are frozen, and only the learnable weight parameter matrix is ​​trained, that is, only the weight parameter matrix related to a specific task is trained, such as the learnable parameters in the fully connected layer or the attention layer, wherein layers such as the feature extraction layer can be frozen, and the feature extraction layer can be used to obtain the customer information feature weighted map, etc.; then the fine-tuned credit risk prediction model is used for the prediction of new customer data to obtain the prediction result, that is, whether the customer to be predicted defaults.

[0144] It can be understood that S310 to S312 in the embodiment of the present application can be implemented by a credit risk prediction model or a fine-tuned credit risk prediction model.

[0145] It can be seen that the credit risk prediction method based on graph neural network in the embodiment of the present application regards the construction of graph network and label prediction as a complete structure, builds an end-to-end learnable network model, deeply integrates and analyzes the transaction behavior, credit history and social network information of bank customers, effectively constructs customer credit portraits, and introduces the attention mechanism in the network model to enable the information between adjacent nodes to fully propagate and flow, and can identify and emphasize the key factors affecting credit risk, such as the impact of sudden economic events on customer credit, which significantly improves the accuracy of model prediction. Moreover, through meticulous network structure design, it can better capture nonlinear and complex customer behavior patterns, and greatly improves the recognition accuracy compared to traditional methods. Especially when processing large-scale data, its excellent computing efficiency and scalability make credit risk prediction more real-time and accurate, thereby providing financial institutions with more effective risk prevention and control measures.

[0146] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

[0147] In order to better implement the above-mentioned solution of the embodiment of the present application, relevant devices for implementing the above-mentioned solution are also provided below.

[0148] See also Figure 4 , a schematic diagram of the structure of a credit risk prediction device disclosed in an embodiment of the present application, the credit risk prediction device 400 comprises:

[0149] An input module 401 is used to input a first customer information feature vector of a customer to be predicted into a credit risk prediction model; the credit risk prediction model is obtained by training a second customer information feature vector of a historical credit customer;

[0150] A calculation module 402 is used to calculate the similarity between the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph;

[0151] The calculation module 402 is further used to obtain a first customer information feature weighted graph based on the first customer information feature graph and the weight parameter matrix;

[0152] The prediction module 403 is used to obtain a first prediction result based on the first customer information feature weighted graph.

[0153] In one possible implementation, the calculation module 402 in the credit risk prediction device provided in the embodiment of the present application is specifically used to perform similarity calculation on the first customer information feature vector and the second customer information feature vector based on a similarity calculation formula to obtain a first customer information feature map; the similarity calculation formula includes at least two of the following: cosine similarity calculation formula, Euclidean distance calculation formula, and Pearson correlation coefficient calculation formula.

[0154] In a possible implementation, in the credit risk prediction device provided in the embodiment of the present application, there are multiple historical credit customers, there are multiple second customer information feature vectors, and the calculation module 402 includes:

[0155] A first calculation unit, configured to perform similarity calculation on the first customer information feature vector and a plurality of the second customer information feature vectors to obtain a plurality of first similarities;

[0156] a determining unit, configured to determine the first similarity greater than a similarity threshold as a second similarity;

[0157] A sorting unit, used for sorting the second similarities to obtain a sorting result;

[0158] The determination unit is further used to obtain a first customer information feature map based on the sorting result.

[0159] In a possible implementation, the credit risk prediction model in the credit risk prediction device provided in the embodiment of the present application includes a first graph attention network, a second graph attention network and a normalized inactivation activation block, and the prediction module 403 includes:

[0160] an attention unit, configured to input the first customer information feature weighted graph into the first graph attention network, perform linear transformation, attention mechanism operation, normalization and feature aggregation on the first customer information feature weighted graph, and obtain a first attention feature;

[0161] The attention unit is further used to input the first customer information feature weighted graph into the first graph attention network, perform linear transformation, attention mechanism operation, normalization and feature aggregation on the first customer information feature weighted graph, and obtain a first attention feature;

[0162] The first prediction unit is used to input the second attention feature into a normalized inactivation activation block, perform batch normalization, random inactivation, and nonlinear transformation on the second attention feature to obtain the first prediction result.

[0163] In a possible implementation, the credit risk prediction device provided in the embodiment of the present application further includes:

[0164] A fine-tuning module, used to fine-tune the credit risk prediction model using the first customer information feature vector to obtain a fine-tuned credit risk prediction model;

[0165] The input module 401 is specifically used to input the first customer information feature vector into the fine-tuned credit risk prediction model.

[0166] In a possible implementation, in the credit risk prediction device provided in the embodiment of the present application, there are multiple second customer information feature vectors;

[0167] The input module 401 is further used to input a plurality of the second customer information feature vectors into the training model;

[0168] The calculation module 402 is further used to perform similarity calculation on a plurality of the second customer information feature vectors to obtain a second customer information feature graph;

[0169] The calculation module 402 is further used to obtain a second customer information feature weighted graph based on the second customer information feature graph and the weight parameter matrix;

[0170] The prediction module 403 is further configured to obtain a second prediction result based on the second customer information feature weighted graph;

[0171] The calculation module 402 is further used to obtain a loss value based on the second prediction result and the credit risk label corresponding to the historical credit customer;

[0172] The device also includes:

[0173] A training module is used to iteratively train the training model based on the loss value to obtain the credit risk prediction model.

[0174] In a possible implementation, the credit information of the customer to be predicted in the credit risk prediction device provided in the embodiment of the present application includes: first credit information of floating point type, second credit information of integer type, and third credit information of discrete type, and the device also includes:

[0175] A preprocessing module, used for processing the first credit information using a maximum-minimum normalization method to obtain a first sub-feature vector;

[0176] The preprocessing module is further used to process the second credit information using an equal frequency binning method to obtain a second sub-feature vector;

[0177] The preprocessing module is further used to perform numerical encoding on the third credit information to obtain a third sub-feature vector;

[0178] The preprocessing module is further used to obtain a first customer information feature vector based on the first sub-feature vector, the second sub-feature vector, and the third sub-feature vector.

[0179] Furthermore, the present application also provides a credit risk prediction device, comprising:

[0180] At least one processor, the processor is used to call the computer instructions in the memory so that the credit risk prediction device executes any one of the implementation methods of the above-mentioned credit risk prediction method.

[0181] Furthermore, an embodiment of the present application also provides a computer program product, including instructions, which, when executed on a computer, enable the computer to execute any one of the implementation methods of the above-mentioned credit risk prediction method.

[0182] Furthermore, an embodiment of the present application also provides a computer-readable storage medium for storing a computer program, which, when executed on a computer, enables the computer to execute any one of the implementation methods of the above-mentioned credit risk prediction method.

[0183] It can be known from the description of the above implementation mode that those skilled in the art can clearly understand that all or part of the steps in the above-mentioned embodiment method can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product can be stored in a storage medium such as ROM / RAM, a disk, an optical disk, etc., including several instructions for enabling a computer device (which can be a personal computer, a server, or a network communication device such as a media gateway, etc.) to execute the methods described in the various embodiments of the present application or certain parts of the embodiments.

[0184] It should be noted that the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same or similar parts between the various embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part description.

[0185] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0186] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0187] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A credit risk prediction method, characterized in that: The method comprises: Inputting a first customer information feature vector of a customer to be predicted into a credit risk prediction model; the credit risk prediction model is obtained by training a second customer information feature vector of a historical credit customer; Calculating similarity between the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph; Based on the first customer information feature graph and the weight parameter matrix, obtaining a first customer information feature weighted graph; Based on the first customer information feature weighted graph, a first prediction result is obtained.

2. The method according to claim 1, characterized in that The performing similarity calculation on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph includes: Based on a similarity calculation formula, similarity calculation is performed on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph; the similarity calculation formula includes at least two of the following: a cosine similarity calculation formula, a Euclidean distance calculation formula, and a Pearson correlation coefficient calculation formula.

3. The method according to claim 1, characterized in that There are multiple historical credit customers, there are multiple second customer information feature vectors, and similarity calculation is performed on the first customer information feature vector and the second customer information feature vector to obtain a first customer information feature graph, including: Calculating similarities between the first customer information feature vector and the plurality of second customer information feature vectors to obtain a plurality of first similarities; Determine the first similarity greater than the similarity threshold as the second similarity; Sorting the second similarities to obtain a sorting result; Based on the sorting result, a first customer information feature graph is obtained.

4. The method according to claim 1, characterized in that The credit risk prediction model includes a first graph attention network, a second graph attention network and a normalized inactivation activation block, and the first prediction result is obtained based on the first customer information feature weighted graph, including: Inputting the first customer information feature weighted graph into the first graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first customer information feature weighted graph to obtain a first attention feature; Inputting the first attention feature into the second graph attention network, performing linear transformation, attention mechanism operation, normalization and feature aggregation on the first attention feature to obtain a second attention feature; The second attention feature is input into the normalized inactivation activation block, and batch normalization, random inactivation, and nonlinear transformation are performed on the second attention feature to obtain the first prediction result.

5. The method according to claim 1, characterized in that The method further comprises: Fine-tuning the credit risk prediction model using the first customer information feature vector to obtain a fine-tuned credit risk prediction model; The step of inputting the first customer information feature vector of the customer to be predicted into the credit risk prediction model comprises: The first customer information feature vector is input into the fine-tuned credit risk prediction model.

6. The method according to claim 1, characterized in that There are multiple second customer information feature vectors, and the method further includes: Inputting a plurality of the second customer information feature vectors into a training model; Performing similarity calculation on a plurality of the second customer information feature vectors to obtain a second customer information feature graph; Based on the second customer information feature graph and the weight parameter matrix, obtaining a second customer information feature weighted graph; Obtaining a second prediction result based on the second customer information feature weighted graph; Obtaining a loss value based on the second prediction result and the credit risk label corresponding to the historical credit customer; The training model is iteratively trained based on the loss value to obtain the credit risk prediction model.

7. The method according to claim 1, characterized in that The credit information of the customer to be predicted includes: first credit information of floating point type, second credit information of integer type, and third credit information of discrete type. The method further includes: Processing the first credit information using a maximum-minimum normalization method to obtain a first sub-feature vector; Processing the second credit information using an equal frequency binning method to obtain a second sub-feature vector; Numerically encoding the third credit information to obtain a third sub-feature vector; A first customer information feature vector is obtained based on the first sub-feature vector, the second sub-feature vector, and the third sub-feature vector.

8. A credit risk prediction device, characterized in that: The system comprises at least one processor, wherein the processor is used to call computer instructions in a memory so that the credit risk prediction device executes the credit risk prediction method according to any one of claims 1 to 7.

9. A computer program product, characterized in that The method comprises instructions which, when executed on a computer, enable the computer to execute the credit risk prediction method according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that: Used to store a computer program, when the computer program is run on a computer, the computer executes the credit risk prediction method according to any one of claims 1 to 7.