Multi-model scoring fusion method based on dynamic programming

Abstract

The invention provides a multi-model score fusion method based on dynamic programming, and relates to the technical field of application of a computer system in financial credit risk control. The method comprises the following steps: in a model correction stage, carrying out standardization processing on scores of each scoring model; in the constraint condition analysis stage, an optimal score mapping value is obtained by constructing and solving a target optimization function; in a dynamic planning optimization stage, constructing an optimal division strategy of scores; in the grading and dividing rule screening stage, an optimal grading and dividing rule is selected by adopting a stability screening method based on matrix logarithm transformation; making a score fusion scheme based on the optimal score division rule; in the index evaluation stage, the stability of the score fusion scheme is evaluated based on the optimal score mapping value. The problems that an existing score fusion method usually adopts a pairwise cross fusion mode to carry out score calculation, score constraint analysis depends on a fixed rule, score division is usually based on an empirical rule and the like are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of application of computer systems in financial credit risk control, and in particular to a multi-model scoring fusion method based on dynamic programming. Background Art

[0002] In the financial lending industry, scoring models are widely used to assess customer credit risk, assisting financial institutions in developing lending strategies, risk management plans, and customer credit decisions. Modeling teams construct multiple risk models for various business scenarios, using the scores predicted by the models to differentiate the risk profiles of relevant users, effectively identifying high- and low-performing customers. In more refined business scenarios, strategy analysts typically select several strong and effective models for integrated decision-making to enhance the model's overall performance and robustness.

[0003] The current common method for fusing model scores in the industry is to cross-fuse model scores two by two to produce an intermediate rating, which is then fused with the remaining model scores one by one until all selected model scores are exhausted, producing the final fused rating. However, with the significant increase in the number of models related to business scenarios, this method has gradually exposed pain points such as long solution time, high reliance on expert experience, and complex processes, which seriously affect the output efficiency of the strategy.

[0004] Furthermore, existing scoring fusion methods suffer from the following technical issues: scoring constraint resolution relies on fixed rules, and scoring partitioning relies on empirical rules. To address these issues, a multi-model scoring fusion method based on dynamic programming is urgently needed. Summary of the Invention

[0005] The present invention provides a multi-model scoring fusion method based on dynamic programming to solve the problems that existing scoring fusion methods usually adopt a pairwise cross-fusion approach to perform scoring calculations, resulting in excessively high computational complexity; scoring constraint parsing relies on fixed rules, making it difficult to dynamically adapt to different business scenarios, which may cause score mapping mutations or discontinuities; scoring division is usually based on empirical rules and lacks a global optimization strategy, resulting in unreasonable scoring interval division; and when the model scoring order changes, it will have a significant impact on the final result, resulting in a decrease in the stability of the scoring fusion, thereby affecting the robustness of the risk control strategy.

[0006] A multi-model scoring fusion method based on dynamic programming of the present invention comprises the following steps: S1. A scoring fusion method based on dynamic programming is proposed, which includes the model correction stage, the constraint analysis stage, the dynamic programming optimization stage, the scoring division rule screening stage, and the indicator evaluation stage. In the model correction stage, a nonlinear topological transformation correction model is used to standardize the scores of each scoring model. In the constraint analysis stage, a high-order Lagrangian constraint analysis method is introduced to obtain the optimal scoring mapping value by constructing and solving the target optimization function. S2. In the dynamic programming optimization stage, a segmented optimization method based on dynamic programming is used to construct the optimal scoring partitioning strategy; in the scoring partitioning rule screening stage, a stability screening method based on matrix logarithmic transformation is used to select the optimal scoring partitioning rule; based on the optimal scoring partitioning rule, a scoring fusion scheme is formulated; in the indicator evaluation stage, the stability of the scoring fusion scheme is evaluated based on the optimal scoring mapping value.

[0007] Preferably, the S1 specifically includes: In the implementation process of the nonlinear topological transformation correction model, a score set for each scoring model is defined, and a normalized score is calculated based on the median and standard deviation of each scoring model.

[0008] Preferably, the S1 specifically includes: The normalized scores are adjusted to a standardized probability scale to obtain the mapping scores.

[0009] Preferably, the S1 specifically includes: In the implementation of the high-order Lagrangian constraint analysis method, the target optimization function is constructed based on the mapping score.

[0010] Preferably, the S1 specifically includes: In the process of constructing the target optimization function, a target scoring function is designed to generate a target score.

[0011] Preferably, the S2 specifically includes: In the implementation process of the segmented optimization method based on dynamic programming, the scoring intervals are divided and the scoring state transition equation is defined to minimize the uncertainty of the scoring division.

[0012] Preferably, the S2 specifically includes: In the process of implementing the stability screening method based on matrix logarithmic transformation, a Markov transition matrix of the scoring interval is constructed to measure the stability of the scoring division rule in the time dimension.

[0013] Preferably, the S2 specifically includes: The stability of the rating fusion scheme is calculated based on the Markov transition matrix of the optimal rating mapping value and the rating interval.

[0014] The beneficial effects of the technical solution of the present invention are:

[0015] 1. The present invention provides a scoring fusion method based on dynamic programming. By constructing multiple optimization levels, it achieves efficient coordination of steps such as scoring standardization, constraint analysis, scoring partition optimization, scoring partition rule screening, and stability assessment, thereby improving the scientificity and stability of scoring fusion and enhancing computational efficiency.

[0016] 2. Through the nonlinear topological transformation correction model, the distribution of different scoring models is adjusted to a unified scale to ensure the comparability of the scores and enhance the anti-interference ability of abnormal data; the nonlinear mapping function is used to convert the normalized scores to the standardized probability scale, enhance the resolution of the scores in different intervals, and improve the stability of subsequent score division and optimization calculations.

[0017] 3. During the constraint analysis phase, a high-order Lagrangian constraint analysis method is introduced to ensure that the score mapping function maintains smoothness and continuity while meeting business requirements, avoiding drastic changes or unreasonable jumps in the score mapping process. A target score calculation method based on weighted expected distribution is adopted to ensure that the target score can dynamically adapt to the data influence of different time windows, thereby improving the robustness of score optimization.

[0018] 4. During the dynamic programming optimization phase, a segmented optimization method based on dynamic programming is used to achieve the optimal global division of the scoring intervals while ensuring the stability and rationality of the scoring. During the scoring division rule screening phase, a stability screening method based on matrix logarithmic transformation is proposed. This method constructs a Markov transition matrix for the scoring intervals, measures the stability of the scoring scheme over time, and ensures the consistency of the scoring division rules over different time periods. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a multi-model scoring fusion method based on dynamic programming described in the present invention. DETAILED DESCRIPTION

[0020] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0021] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0022] The following describes in detail a multi-model scoring fusion method based on dynamic programming provided by the present invention with reference to the accompanying drawings.

[0023] Refer to the attached Figure 1 , which shows a flow chart of a multi-model scoring fusion method based on dynamic programming provided by an embodiment of the present invention, the method comprising the following steps:

[0024] S1. A scoring fusion method based on dynamic programming is proposed, which includes the model correction stage, the constraint analysis stage, the dynamic programming optimization stage, the scoring division rule screening stage, and the indicator evaluation stage. In the model correction stage, a nonlinear topological transformation correction model is used to standardize the scores of each scoring model. In the constraint analysis stage, a high-order Lagrangian constraint analysis method is introduced to obtain the optimal scoring mapping value by constructing and solving the target optimization function.

[0025] Based on the business scenario of financial credit risk control, a scoring fusion method based on dynamic programming is proposed. It consists of five stages: model correction, constraint analysis, dynamic programming optimization, scoring partitioning rule screening, and indicator evaluation. By constructing multiple optimization hierarchies, this scoring fusion method organically combines scoring standardization, business constraint analysis, scoring partitioning optimization, rule screening, and indicator evaluation, ensuring the scientific and stable scoring results while improving computational efficiency.

[0026] During the model correction phase, the scores of multiple scoring models are standardized to eliminate scale differences between different scoring models and ensure the comparability of the scores. In actual business scenarios, different scoring models may use different data distributions and scoring rules. Therefore, before fusion, the outputs of each scoring model must be adjusted to the same scale range through mathematical transformation. A nonlinear topological transformation correction model is used to adjust the distribution of different scoring models to a consistent scale range through methods such as logarithmic stretching, skewness correction, and local smoothing. Specifically, set N scoring models, and the score set of each scoring model is expressed as:

[0027] in, It is A scoring set for a scoring model, including the scores of all samples. A sample refers to an individual or data point that needs to be scored, that is, a customer or user in a financial credit risk control scenario. A current customer will receive different risk scores under different scoring models to assess their credit risk level. For the The sample in The ratings under the rating model, , It is The number of samples under each scoring model. In order to eliminate the scale differences between the scores, normalization is required. By calculating the median and standard deviation of each scoring model, the normalized score is defined:

[0028] in, It is The sample in Normalized score under each scoring model; It is The median of the scoring models; It is The number of samples under each scoring model; It is The skewness of each scoring model is used as an index to adjust the shape of the score distribution by enhancing or weakening the effect of skewness on the normalized score, so as to better handle the differences between scoring models, especially when the score data has a skewed distribution; It is The standard deviation of each scoring model; is the stretching factor used to adjust the contrast between different scoring models; A measure that reflects the relative distribution differences of each sample in the scoring model combined with the volatility of the score. It can weight outliers or irregularities, thereby better adjusting the scale differences between the outputs of each scoring model and ensuring that the fused score has good stability and comparability.

[0029] Since the output values ​​of many scoring models may contain extreme outliers, the logarithmic function is used to effectively reduce the range of the score and compress the maximum value into a smaller range, thereby enhancing the robustness of the scoring model. In addition, the logarithmic function can also be used to smooth some nonlinear growth or change relationships, especially when the distribution of the scoring data is more complex. In the financial risk control scenario, the scoring data often involves nonlinear features. The logarithmic transformation can make the changes of these data more linear, which is convenient for subsequent fusion. and Addition enhances the ability to adjust to data distribution, especially the handling of outliers or noise in the scoring model; For the The sample in The ratings under the rating model, ,and ; is an exponentially weighted smoothing parameter used to control the similarity effect between ratings. It is obtained through experiments and has a value range of ; It represents the similarity between the rating values. The form of the exponential function shows that the similarity between the ratings has a decaying nature. The farther the distance, the lower the similarity. It is The kurtosis of a scoring model describes the shape of the data distribution, especially the sharpness of the data distribution. It is obtained by calculating the fourth moment of the scoring model, which aims to measure the "peak" degree of the scoring model data distribution, that is, the degree of data concentration; Used as an index, this means that the differences between scores will be affected by Control, in When the value is larger, the change of the score will be more significant; specifically, The calculation formula for the skewness and kurtosis of a scoring model is:

[0030] Normalization ensures that the output of the scoring model has the same scale and is resistant to outliers.

[0031] In order to ensure the uniformity of the scoring model output and make the scores from different sources comparable when fused, the normalized scores need to be further converted to conform to the standardized probability distribution; a nonlinear mapping function familiar to those skilled in the art is used to adjust the normalized scores to a standardized probability scale, making them more suitable for subsequent scoring division and optimization calculations; the nonlinear mapping function limits the normalized scores to between (0, 1), so that the scores of all scoring models are converted to the same scale range and enhance the resolution of scores in different intervals. As an embodiment, the nonlinear mapping function can also be designed as follows:

[0032] in, is the normalized The scoring mapping function of a scoring model is used to obtain the mapping score; It is The normalized comprehensive score of the scoring model is based on all samples in the The normalized score under each scoring model is obtained; It is The nonlinear mapping function converts the scores of all scoring models into a standard probability distribution, making the subsequent scoring fusion more robust.

[0033] After obtaining the mapping score, it is necessary to analyze the constraints in the business scenario to ensure that the scoring division complies with industry standards and business needs. In the constraint analysis stage, a high-order Lagrangian constraint analysis method is introduced, and mathematical optimization methods are used to analyze and execute the scoring constraints. A target optimization function is constructed so that the final scoring mapping function can meet business needs while maintaining a certain degree of smoothness and continuity, minimizing the difference between the scoring mapping function and the target scoring function set by the business, and applying a smoothness regularization term to avoid drastic changes or unreasonable jumps in the scoring mapping function. Define the target optimization function:

[0034] in, is the target optimization function, which represents the objective function in the scoring model fusion process; is the Lagrange multiplier used to ensure that the mapping score approaches the target score during the target optimization process. It can be set by cross-validation, grid search or expert experience rules and has a value range of ; It is a target scoring function used to generate target scores. It can be specified based on historical experience, business logic, or data trends. It can use existing piecewise linear objective functions, logistic objective functions, exponential decay functions, etc. It is a Lagrange multiplier used to control the smoothness of the score mapping function to prevent drastic nonlinear fluctuations in the mapping score. It can be determined by empirical tuning, Bayesian optimization, etc. The value range is ; and are the boundaries of the scoring interval, representing the The lowest and highest scores of each scoring model; It is used to constrain the deviation between the scoring mapping function and the target scoring function, ensuring that the scoring fusion process complies with the preset business rules and target scoring trends. It is equivalent to controlling the global constraints of the scoring division to prevent the fusion score from deviating too much from business requirements. is a smoothness regularization term, which is used to constrain the smoothness of the score mapping function, ensuring that there will be no drastic changes in the score division process and avoiding mutations that affect the stability of the mapping score. and Added together, they synergistically control the precision (accuracy) and smoothness (stability) of the score mapping function.

[0035] When constructing the target scoring function, a stable target score is extracted from the data distribution of multiple historical time windows based on the database to ensure that the target score reflects the business logic and improves the robustness of the scoring optimization process. To this end, an existing weighting method is used to obtain the final target score. As a specific embodiment, the following method can also be used to calculate the final target score: a target score calculation method based on weighted expected distribution is used, which combines the statistical characteristics of historical time window data and introduces a weight adjustment mechanism to dynamically adapt to the data influence of different time windows.

[0036] Specifically, a period of time in the past is selected and divided into multiple time windows. Each time window contains multiple sample data, and each sample data corresponds to a score. In each time window, the weighted expected value of all sample scores in the current time period is calculated, that is, all sample scores are weighted and summed according to the weights, and then divided by the sum of all weights to obtain the representative score of the current time window. The representative scores of all time windows are combined to obtain the final target score.

[0037] The target optimization function is solved using the gradient descent method known to those skilled in the art to obtain the optimal scoring mapping function , which is the optimal score mapping value.

[0038] S2. In the dynamic programming optimization stage, a segmented optimization method based on dynamic programming is used to construct the optimal scoring partitioning strategy; in the scoring partitioning rule screening stage, a stability screening method based on matrix logarithmic transformation is used to select the optimal scoring partitioning rule; based on the optimal scoring partitioning rule, a scoring fusion scheme is formulated; in the indicator evaluation stage, the stability of the scoring fusion scheme is evaluated based on the optimal scoring mapping value.

[0039] During the dynamic programming optimization phase, the scores need to be reasonably divided to ensure that different scoring levels can effectively distinguish risk levels while ensuring the stability and rationality of the scores. A segmented optimization method based on dynamic programming is used to construct an optimal scoring division strategy, so that the division of the scoring intervals can be both optimal globally and meet business needs. A scoring state transition equation is defined based on the distribution information of the scoring data to minimize the uncertainty of the scoring division while ensuring that the score distribution of each interval after division is as balanced as possible. To this end, the scoring state transition equation is defined as follows:

[0040] in, Indicates that the The scoring data of samples are divided into The optimal partitioning cost for each rating level (interval), where each rating level corresponds to a rating level; is the search variable, which represents the sample division point, that is, the boundary sample of the scoring level; Is a recursive state, indicating that the previous The samples are divided into The optimal partitioning cost when the scoring level is 1; It is The optimal score mapping value within the score level is obtained by optimizing the target function. The solution is obtained; is the mean of the global optimal score mapping, which is obtained by adding the optimal score mapping values ​​of all score levels and dividing it by the total number of score levels; is the standard deviation of the globally optimal score map. For the comprehensive cost function term within each rating level, in the process of dividing the rating interval, the chaos (entropy) of the rating distribution is minimized at the same time. and the global consistency deviation of the optimal score mapping value in each score interval , achieving optimal stability and discrimination of score partitioning.

[0041] During the scoring division rule screening phase, since there may be multiple candidate solutions for the scoring division scheme, all scoring division rules need to be screened to select the optimal scoring division rule. In order to ensure that the final selected scoring division scheme has strong stability and business applicability, a stability screening method based on matrix logarithmic transformation is adopted. The stability of the scoring division scheme in the time dimension is measured by constructing the Markov transition matrix of the scoring interval. The stability of the scoring division scheme is reflected in the following aspects: the distribution of users in the same scoring interval in different time periods should not change drastically, and at the same time, it should avoid frequent changes in customer ratings due to unreasonable scoring division, thereby affecting the reliability of the risk control strategy. Define the Markov transition matrix of the scoring interval:

[0042] in, It is the Markov transfer matrix, which represents the transition probability matrix after the score division, and is used to measure the similarity and stability between different scores. Elements in Indicates from arrive The transition probability of 、 Represents the scoring intervals and rating intervals The central value of is the score similarity scaling factor, which is used to control the scaling ratio of score similarity calculation and is obtained through experiments. The above Markov transfer matrix is ​​derived from the softmax function variant, and the numerator is represents the transfer similarity metric, the denominator represents the normalization factor.

[0043] Furthermore, based on the optimal scoring division rule, that is, the final selected scoring division scheme, a scoring fusion scheme is formulated to calculate the final score of the scoring model. In order to comprehensively take into account the following two goals:

[0044] High score differentiation: makes the score division meaningful and can identify different risk levels;

[0045] Stable scoring system: prevents scores from fluctuating significantly over time and enhances the continuity of risk control strategies;

[0046] To find the optimal balance between the two objectives, the scoring fusion solution must meet the following requirements:

[0047] in, It is the weight parameter in the score division optimization objective, which is used to control the influence of the score division. It is determined by experimental tuning and has a value range of ; is the weight parameter in the scoring stability optimization objective, which is used to control the importance of scoring stability. It is obtained through experiments and has a value range of ; is a measure of the stability of the scoring fusion scheme, represents the Markov transition matrix The trace operation, i.e., the sum of the matrix diagonal elements, is used to ensure the stability and temporal consistency of the scoring partitioning rules.

[0048] After the scoring fusion scheme is determined, the indicator evaluation phase begins. By evaluating the stability of the scoring fusion scheme, it is ensured that the final score remains consistent in different time periods and meets business needs. The stability calculation is based on the final fusion score value and the Markov transition matrix in the scoring division process. By calculating the changing trend of the scoring time series and the entropy stability of the scoring division rule, the robustness of the score is measured. The final calculated stability index can be used to adjust the scoring division rule to ensure the reliability of the scoring model in long-term operation and prevent the performance of the scoring model from degrading due to data drift.

[0049]

[0050] in, is a measure of the temporal stability of the scoring fusion scheme; is the length of the overall time window, determined by business needs; is the time index; is The optimal score mapping value obtained at the moment is the final fusion score value; is The optimal score mapping value obtained at the moment; is the mean of the global optimal score mapping; is the Markov entropy regularization parameter, which is used to control the impact of the stability of the scoring interval division on the final stability evaluation. It is obtained through experiments and has a value range of ; Indicates from arrive The transition probability of 、 Represents the scoring intervals and rating intervals The center value of . express The measure of the change in the moment-to-moment rating stability is used to measure the degree of change in the optimal rating mapping value in two adjacent time periods 𝑡 and 𝑡−1, and a normalization mechanism is introduced to suppress the impact of abnormal fluctuations on the overall rating stability evaluation. The entropy regularization term representing the rating interval division is used to measure the uncertainty of the rating division in the Markov rating transition matrix, that is, the rating stability.

[0051] In summary, a multi-model scoring fusion method based on dynamic programming was completed.

[0052] The order in which the embodiments of the invention are presented is for illustrative purposes only and does not necessarily represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0053] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments.

[0054] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A multi-model scoring fusion method based on dynamic programming, characterized in that: The following steps are involved: S1. A scoring fusion method based on dynamic programming is proposed, which includes the model correction stage, the constraint analysis stage, the dynamic programming optimization stage, the scoring division rule screening stage, and the indicator evaluation stage. In the model correction stage, a nonlinear topological transformation correction model is used to standardize the scores of each scoring model. In the constraint analysis stage, a high-order Lagrangian constraint analysis method is introduced to obtain the optimal scoring mapping value by constructing and solving the target optimization function. S2. In the dynamic programming optimization phase, a segmented optimization method based on dynamic programming is used to construct the optimal scoring partitioning strategy. In the scoring partitioning rule screening phase, a stability screening method based on matrix logarithmic transformation is used to select the optimal scoring partitioning rule. Based on the optimal scoring partitioning rule, a scoring fusion plan is formulated. In the indicator evaluation stage, the stability of the scoring fusion scheme is evaluated based on the optimal scoring mapping value.

2. The multi-model scoring fusion method based on dynamic programming according to claim 1, characterized in that: Said S1 specifically includes: In the implementation process of the nonlinear topological transformation correction model, a score set for each scoring model is defined, and a normalized score is calculated based on the median and standard deviation of each scoring model.

3. The multi-model scoring fusion method based on dynamic programming according to claim 2, characterized in that: Said S1 specifically includes: The normalized scores are adjusted to a standardized probability scale to obtain the mapping scores.

4. The multi-model scoring fusion method based on dynamic programming according to claim 3 is characterized in that: Said S1 specifically includes: In the implementation of the high-order Lagrangian constraint analysis method, the target optimization function is constructed based on the mapping score.

5. The multi-model scoring fusion method based on dynamic programming according to claim 4 is characterized in that: Said S1 specifically includes: In the process of constructing the target optimization function, a target scoring function is designed to generate a target score.

6. The multi-model scoring fusion method based on dynamic programming according to claim 1, characterized in that: Said S2 specifically includes: In the implementation process of the segmented optimization method based on dynamic programming, the scoring intervals are divided and the scoring state transition equation is defined to minimize the uncertainty of the scoring division.

7. The multi-model scoring fusion method based on dynamic programming according to claim 1, characterized in that: Said S2 specifically includes: In the process of implementing the stability screening method based on matrix logarithmic transformation, a Markov transition matrix of the scoring interval is constructed to measure the stability of the scoring division rule in the time dimension.

8. The multi-model scoring fusion method based on dynamic programming according to claim 7, characterized in that: Said S2 specifically includes: The stability of the rating fusion scheme is calculated based on the Markov transition matrix of the optimal rating mapping value and the rating interval.

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