Federal learning-based cross-regional examinee ability benchmark modeling system and method

Abstract

The invention discloses a federated learning-based cross-regional examinee ability benchmark modeling system and method, and relates to the technical field of education evaluation, and the method comprises the following steps: executing Z standardization operation on all examinee ability scores of a small sample region, obtaining a standardization sequence of zero mean value unit variance, and recording an original mean value and a standard deviation; and constructing a probability density curve based on the standardized sequence, calculating the quartile spacing, skewness, kurtosis and the tail density ratio of the upper and lower 5% tail sections of the sequence, and forming a multi-dimensional abnormal feature vector by using the statistics. Through Z standardization, multi-dimensional abnormal feature extraction, impact value construction and dynamic weight regulation and control, interference of a small sample extreme region on a federated model is effectively identified and inhibited, the stability and generalization ability of the model under heterogeneous data are improved, the fairness and credibility of cross-region ability evaluation are enhanced, and the method is suitable for large-scale popularization and application. And educational fair analysis and personalized teaching strategy making are facilitated.

Description

Technical Field

[0001] This invention relates to the field of educational assessment technology, specifically to a cross-regional candidate competency benchmark modeling system and method based on federated learning. Background Technology

[0002] The cross-regional student competency benchmark modeling system based on federated learning is an intelligent analysis system designed for educational assessment scenarios. Its core objective is to construct a unified and comparable competency assessment benchmark while protecting the privacy and data sovereignty of students in each region. The system deploys model training nodes locally in each region to perform local modeling and analysis of characteristics such as students' answering behavior, knowledge mastery, and answering time. It then uses a federated learning framework to periodically aggregate the parameters or gradients of models from each region, rather than using raw data, to achieve joint optimization of the global model. This system can automatically identify differences in competency distribution between regions, eliminate systematic biases caused by differences in regional educational resources, and establish objective and unified competency evaluation standards. This supports multi-regional performance benchmarking, educational equity analysis, and the development of personalized teaching strategies. It boasts significant advantages such as high data security, strong model generalization ability, and high reliability of assessment results.

[0003] The existing technology has the following shortcomings:

[0004] In existing federated learning-based cross-regional competency modeling processes, there is a significant difference in sample size across regions. Some small-sample regions, due to their extreme competency distributions, are assigned the same model update weights as large-sample regions during the federated model aggregation phase. This causes the global model to be frequently affected by these extreme samples during iterations, exhibiting significant parameter oscillations. This oscillation effect not only makes the model prone to getting trapped in local optima but also causes unstable fluctuations in the global competency assessment standards over multiple training cycles, severely reducing the interpretability and reference value of the assessment results. Consequently, it becomes difficult to support cross-regional comparisons of educational equity and the development of personalized teaching strategies.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a cross-regional candidate ability benchmark modeling system and method based on federated learning. By adaptively adjusting the model update weights of each region according to the extreme index of the ability distribution during the federated learning model aggregation stage, the aggregation strategy can dynamically suppress the interference of abnormal regions on the global model training, effectively improving the robustness and generalization ability of the federated model in heterogeneous data environments. At the same time, it enhances the stability, interpretability, and fairness of cross-regional ability assessment results, providing more reliable technical support for educational equity analysis and the formulation of personalized teaching strategies, thereby solving the problems in the background technology mentioned above.

[0007] To achieve the above objectives, this invention provides the following technical solution: a cross-regional candidate competency benchmark modeling method based on federated learning, comprising the following steps:

[0008] Perform Z-standardization on all candidates' ability scores in a small sample area to obtain a standardized series with zero mean and unit variance, and record the original mean and standard deviation.

[0009] Based on the standardized sequence, a probability density curve is constructed, and the interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals of the sequence are calculated. The above statistics (interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals) are combined into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution.

[0010] A sample sparsity penalty function is introduced, which multiplies the Euclidean norm of the anomalous feature vector by the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity.

[0011] The Softmax function is applied to fuse the components of the impact value to generate an extreme index of capability distribution ranging from 0 to 1. A dynamic threshold is set, and the small sample region is determined to be an extreme region of capability distribution based on the extreme index of capability distribution, and the corresponding label information is output.

[0012] During the model aggregation phase of federated learning, the model update weights for the small sample region are adaptively adjusted based on the extreme index of the ability distribution of that small sample region, so that they are intelligently matched with the extreme degree of its ability distribution.

[0013] Preferably, the specific steps for performing Z-standardization on candidates' ability scores are as follows:

[0014] First, for each candidate's raw ability score in a small sample region, the mean and standard deviation of all candidates' ability scores in that region are calculated to ensure that the selected sample set meets the minimum sample size requirement and basic statistical stability conditions. Second, based on the mean and standard deviation, Z-standardization is performed on each raw ability score, specifically by subtracting the mean from each score and then dividing by the standard deviation to obtain the corresponding standardized ability score. Finally, the resulting set of standardized ability score sequences is constructed into a zero-mean, unit-variance standardized ability score sequence, and the original mean and standard deviation are stored for subsequent measurement and labeling of outlier distributions.

[0015] Preferably, the construction steps for the multidimensional anomaly feature vector are as follows:

[0016] First, based on the standardized ability score sequence, a smooth probability density function curve is constructed using kernel density estimation to replace the discrete estimation error generated by the histogram. Second, statistical indicators describing the distribution pattern are extracted from this probability density function curve, including interquartile range (IQR) to measure the dispersion of the central tendency of the data, skewness to measure the symmetry of the distribution, and kurtosis to reflect the thickness of the tail and the degree of concentration of extreme values. Finally, the upper and lower 5% tail intervals are intercepted from the probability density function curve, and the sum of the probability densities within these tail intervals is calculated as the tail density percentage. The interquartile range, skewness, kurtosis, and tail density percentage are combined to form a multidimensional anomaly feature vector to reflect the degree of anomaly and structural deviation of the ability distribution in small sample areas.

[0017] Preferably, the calculation steps for the tail density percentage include the following:

[0018] First, based on the probability density function curve constructed from the standardized ability score sequence, a corresponding cumulative distribution function (CDF) is generated. This determines the lower 5% and upper 95% quantiles of the distribution, and delineates the left and right tail intervals accordingly. Second, the kernel density function within the lower 5% and upper 5% intervals is integrated to obtain the tail density proportions of the left and right tail regions. If necessary, the tail density proportions of these two tails can be recorded separately to further analyze the asymmetry of tail distribution. Finally, the tail density proportions of the upper and lower tails are fused in a weighted manner to generate a tail density proportion used to measure the degree of clustering of extreme samples.

[0019] Preferably, the specific steps for calculating the impact value are as follows:

[0020] First, based on the constructed multidimensional anomaly feature vector, its norm in Euclidean space is calculated, which is obtained by summing the squares of each statistical component and taking the square root to obtain a scalar value that comprehensively characterizes the degree of distribution anomaly. Second, the total number of samples in the current small sample region is counted, and the reciprocal of this sample size is calculated and squared to construct a scaling factor used to penalize sample sparsity. Finally, the Euclidean norm of the anomaly vector is multiplied by the square root of the reciprocal of the sample size to obtain the shock value after coupling capability distribution anomaly with sample scarcity. This accurately reflects the potential perturbation intensity of the small sample region on the global model in the subsequent model aggregation process, and enhances the sensitivity and control capability for extreme regions.

[0021] Preferably, the steps for generating the extreme index of capability distribution are as follows:

[0022] First, the multidimensional components constituting the impact value are normalized using minimum-maximum scaling or Z-normalization to align the scale of each component. This ensures relative numerical comparability before inputting to the Softmax function and avoids output offset due to excessively large individual component values. Second, the Softmax function is applied to the normalized impact value components. An exponential function enhances the high-value response capability while compressing all outputs to between 0 and 1, ensuring that the output corresponding to each component has a "probabilistic" characteristic, representing its relative importance in the overall anomaly composition. Finally, the Softmax output value of each component is used as a corresponding weighting coefficient to perform weighted fusion processing on the original impact value components, resulting in a unique capability distribution extreme index. This index comprehensively measures the overall intensity of capability distribution anomalies in the small sample region, providing an interpretable and measurable indicator basis for subsequent "extreme region" labeling and dynamic adjustment of model aggregation weights.

[0023] Preferably, the extreme label determination steps for small sample regions are as follows: First, a dynamic threshold range for the extreme index of capability distribution is set. This dynamic threshold range is automatically updated based on the distribution characteristics of the shock values ​​of all small sample regions during the federated training process. Specifically, the upper and lower bounds are dynamically adjusted by setting a statistical quantile value (such as the 85th percentile) or by adding or subtracting a certain number of standard deviations from the mean, in order to adapt to changes in the global distribution at different times. Second, the extreme index of capability distribution calculated for each small sample region is compared and analyzed with the currently updated dynamic threshold range to determine the relative position of the abnormality of the small sample region in the global context. Finally, if the extreme index of capability distribution exceeds the upper limit of the dynamic threshold range, the small sample region is automatically marked as an extreme region; otherwise, it is marked as a "normal" region, and the corresponding label information is output to guide the subsequent adjustment decisions of model update weights and intervention for regional stability.

[0024] Preferably, during the model aggregation phase of federated learning, the model update weights for the small sample region are adaptively adjusted based on the extreme index of the capability distribution of that small sample region. The specific steps are as follows:

[0025] First, the extreme index of the capability distribution in a small sample region is compared with the dynamic threshold range to determine its degree of anomaly. A regional regulation factor is defined to adjust the model contribution weight of this small sample region in the federated aggregation process. The calculation expression of the regional regulation factor is as follows: ,in: This is the extreme index of the ability distribution in a small sample region i. The larger the value, the more abnormal the distribution. The dynamic upper limit threshold for the extreme index of ability distribution is usually set to the 85th percentile. To regulate the intensity factor, the degree of compression after the extreme index of the capability distribution exceeds its limit is controlled. ; This is a factor controlling the slope of the compression curve; the larger the factor, the steeper the compression. ; The model updates the control factor to penalize extreme regions; its value range is [range missing]. ;

[0026] During the model aggregation phase, the final normalized aggregation weight is calculated based on the original sample size and model update control factor of each small sample region. The calculation expression is as follows: ,in: Let i be the number of samples in the small sample region i. This is a sample weight index adjustment factor that controls the degree to which the number of samples affects the weights. ; The final model aggregation weights for the small sample region i are normalized and used for global model updates; the denominator term... The normalization constant ensures that the sum of all weights is 1. j represents any small sample region among all small sample regions. Its function is to traverse all small sample regions in the normalization calculation to ensure that the model update weights of each small sample region are reasonably allocated based on "global comparison".

[0027] A cross-regional candidate competency benchmark modeling system based on federated learning includes a data standardization module, a distribution feature extraction module, an impact value construction module, an extreme region identification module, and a model weight adjustment module.

[0028] The data standardization module performs Z-standardization on the ability scores of all candidates in a small sample area to obtain a standardized sequence with zero mean and unit variance, and records the original mean and standard deviation.

[0029] The distribution feature extraction module constructs a probability density curve based on the standardized sequence, calculates the interquartile range, skewness, kurtosis, and tail density percentage of the upper and lower 5% tail intervals of the sequence, and combines the above statistics (interquartile range, skewness, kurtosis, and tail density percentage of the upper and lower 5% tail intervals) into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution.

[0030] The shock value construction module introduces a sample sparsity penalty function, which multiplies the Euclidean norm of the abnormal feature vector with the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity.

[0031] The extreme region identification module applies the Softmax function to fuse the components of the impact value, generates an extreme index of capability distribution ranging from 0 to 1, sets a dynamic threshold, determines whether the small sample region belongs to the extreme region of capability distribution based on the extreme index of capability distribution, and outputs the corresponding label information.

[0032] The model weight adjustment module adaptively adjusts the model update weights of the small sample region based on the extreme index of the ability distribution of the small sample region during the model aggregation stage of federated learning, so as to intelligently match the extreme degree of its ability distribution.

[0033] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0034] This invention Z-standardizes the ability scores of small sample regions to ensure comparability of data from different regions under the same scale. Subsequently, it extracts higher-order statistical features to construct a multi-dimensional anomaly feature vector, comprehensively characterizing the skewness, tail thickness, and central tendency of the ability distribution, thereby achieving precise identification of distribution anomalies. Combined with a sample sparsity penalty mechanism, anomaly features are coupled with sample quantity to generate a quantifiable impact value, used to measure the potential perturbation effect of a region on the global model. Based on this, a Softmax function is introduced to fuse the impact value components, constructing a normalized ability distribution extreme index, and a dynamic threshold mechanism is used to achieve intelligent identification and label classification of extreme regions. Finally, in the federated learning model aggregation stage, the model update weights of each region are adaptively adjusted according to this ability distribution extreme index, enabling the aggregation strategy to dynamically suppress the interference of anomaly regions on the global model training. This effectively improves the robustness and generalization ability of the federated model in heterogeneous data environments, while enhancing the stability, interpretability, and fairness of cross-regional ability assessment results. It provides more reliable technical support for educational equity analysis and the formulation of personalized teaching strategies, possessing good practical value and promising prospects for promotion. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0036] Figure 1 This is a flowchart of the cross-regional candidate competency benchmark modeling method based on federated learning, as described in this invention.

[0037] Figure 2 This is a schematic diagram of the modules of the cross-regional candidate competency benchmark modeling system based on federated learning of the present invention. Detailed Implementation

[0038] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art.

[0039] This invention provides, for example Figure 1 The federated learning-based cross-regional candidate competency benchmark modeling method shown includes the following steps:

[0040] Z-standardization was performed on the ability scores of all candidates in the small sample area to obtain a standardized sequence with zero mean and unit variance. The original mean and standard deviation were recorded for subsequent anomaly measurement calculation.

[0041] The specific steps for performing Z-standardization on candidates' ability scores are as follows:

[0042] First, for each candidate's raw ability score in a small sample region, the mean and standard deviation of all candidates' ability scores in that region are calculated to ensure that the selected sample set meets the minimum sample size requirement and basic statistical stability conditions. Second, based on the mean and standard deviation, Z-standardization is performed on each raw ability score, specifically by subtracting the mean from each score and then dividing by the standard deviation to obtain the corresponding standardized ability score. Finally, the resulting set of standardized ability score sequences is constructed into a zero-mean, unit-variance standardized ability score sequence, and the original mean and standard deviation are stored for subsequent measurement and labeling of outlier distributions.

[0043] Z-standardization is performed on the ability scores of all candidates in a small sample region. Its purpose is to provide a unified and comparable dimensional basis for subsequent anomaly detection and extreme region identification. In cross-regional ability modeling, due to significant differences in sample size, candidate ability distribution patterns, and assessment dimensions across regions, directly comparing raw scores can lead to misjudgments due to scale inconsistencies. This is especially true when processing data from small sample regions, where local skewness can easily cause bias. Z-standardization transforms the raw ability scores into a standard normal form with a mean of zero and a standard deviation of one, eliminating the absolute dimensions and scale interference of the raw data and giving the data from each region uniform statistical properties. Furthermore, recording the raw mean and standard deviation for each small sample region not only facilitates the restoration of the standardized results to their true values ​​in the original space but also provides a basic statistical basis for constructing anomaly detection indicators (such as skewness, kurtosis, and tail density). Therefore, this step not only improves the stability and comparability of data analysis, but also provides a unified metric for anomaly detection, shock value construction, and quantification of extreme indexes of capability distribution. It is a key pre-processing step for achieving fairness and robustness in cross-regional capability evaluation.

[0044] Based on the standardized sequence, a probability density curve is constructed, and the interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals of the sequence are calculated. The above statistics (interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals) are combined into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution.

[0045] The specific steps for constructing multidimensional anomaly feature vectors are as follows:

[0046] First, based on the standardized ability score sequence, a smooth probability density function curve is constructed using kernel density estimation to replace the discrete estimation error generated by the histogram. Second, statistical indicators describing the distribution pattern are extracted from this probability density function curve, including interquartile range (IQR) to measure the dispersion of the central tendency of the data, skewness to measure the symmetry of the distribution, and kurtosis to reflect the thickness of the tail and the degree of concentration of extreme values. Finally, the upper and lower 5% tail intervals are intercepted from the probability density function curve, and the sum of the probability densities within these tail intervals is calculated as the tail density percentage. The interquartile range, skewness, kurtosis, and tail density percentage are combined to form a multidimensional anomaly feature vector to reflect the degree of anomaly and structural deviation of the ability distribution in small sample areas.

[0047] The calculation steps for the tail density ratio include the following:

[0048] First, based on the probability density function curve constructed from the standardized ability score sequence, a corresponding cumulative distribution function (CDF) is generated. This determines the lower 5% and upper 95% quantiles of the distribution, and delineates the left and right tail intervals accordingly. Second, the kernel density function within the lower 5% and upper 5% intervals is integrated to obtain the tail density proportions of the left and right tail regions. If necessary, the tail density proportions of these two tails can be recorded separately to further analyze the asymmetry of tail distribution. Finally, the tail density proportions of the upper and lower tails are fused in a weighted manner to generate a tail density proportion used to measure the degree of clustering of extreme samples.

[0049] The core function of this step is to conduct a comprehensive and quantifiable anomaly analysis of the ability distribution characteristics in small sample regions, supporting the subsequent automatic identification of "extreme regions" and model weight adjustment. Specifically, traditional first- and second-order statistics such as mean and variance have significant limitations in measuring the anomalies of sample distributions, especially when facing complex situations such as skewness, asymmetry, and heavy tails in the ability distribution of small sample regions, lacking sufficient sensitivity and characterization ability. Therefore, this step constructs probability density curves (such as kernel density estimation) on the standardized ability score sequence, avoiding the discrete errors caused by interval settings in the histogram method, and making the distribution estimation more continuous and smooth, facilitating the subsequent accurate extraction of statistical morphological features.

[0050] Based on this, interquartile range, skewness, kurtosis, and tail density percentage were selected as anomaly measures to cover three core dimensions of distribution patterns: the dispersion of central tendency, the degree of symmetry shift, and the degree of clustering of extreme values. Specifically, the interquartile range reflects the dispersion of ability distribution in the central region, revealing the volatility of the overall ability level; skewness is used to detect whether the distribution is left- or right-skewed, reflecting the tilt direction of the ability structure; kurtosis describes the steepness or flatness of the score distribution curve, and is key to identifying high-frequency concentrated areas or sparsely distributed areas; while the tail density percentage in the upper and lower 5% tail intervals directly reflects whether there are a large number of clustered samples in the extremely high or low score segments of the ability distribution, possessing significant value in identifying "extreme distribution areas."

[0051] By combining the four types of statistical indicators mentioned above into a multidimensional anomaly feature vector, the "abnormal structure" of capability distribution in small sample areas can be characterized in a high-dimensional and three-dimensional way. This allows subsequent impact value calculation and extreme index assessment to no longer rely on a single scale or indicator, but rather on multi-feature fusion judgment. This process not only enhances the accuracy of identifying regions with abnormal capability distribution, but also provides a scientific and data-driven basis for weight adjustment in the aggregation stage of the federated model, significantly improving the robustness of the global capability model to extreme regional disturbances, and ultimately promoting the consistency, fairness, and interpretability of cross-regional assessment standards. Therefore, this step is a key intermediate link in achieving intelligent identification, effective intervention, and stable modeling.

[0052] A sample sparsity penalty function is introduced, which multiplies the Euclidean norm of the anomalous feature vector by the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity.

[0053] The specific steps for calculating the impact value are as follows:

[0054] First, based on the constructed multidimensional anomaly feature vector, its norm in Euclidean space is calculated, which is obtained by summing the squares of each statistical component and taking the square root to obtain a scalar value that comprehensively characterizes the degree of distribution anomaly. Second, the total number of samples in the current small sample region is counted, and the reciprocal of this sample size is calculated and squared to construct a scaling factor used to penalize sample sparsity. Finally, the Euclidean norm of the anomaly vector is multiplied by the square root of the reciprocal of the sample size to obtain the shock value after coupling capability distribution anomaly with sample scarcity. This accurately reflects the potential perturbation intensity of the small sample region on the global model in the subsequent model aggregation process, and enhances the sensitivity and control capability for extreme regions.

[0055] The main purpose of this step is to organically couple the anomaly of the capability distribution in small sample regions with the scarcity of their samples by introducing a sample sparsity penalty function. This generates a dimensionless shock value that simultaneously reflects both "distribution extremism" and "sample representativeness," used to assess the potential perturbation impact of this region on the stability of the global model. In cross-regional modeling scenarios of federated learning, some regions with extremely small sample sizes often exhibit statistically unstable structures, extremely high skewness, or tail bulging in their capability distribution due to insufficient data points, making them easily misjudged as important signals. If left uncontrolled, these "low representativeness + high anomaly" regions may cause strong interference during the model aggregation stage, leading to oscillations in global model parameters or even deviations from the main distribution. Therefore, relying solely on the anomaly features themselves (such as skewness and kurtosis) cannot accurately measure the perturbation capability of a region; a structural correction factor related to the sample size must be introduced.

[0056] Calculating the Euclidean norm of the anomalous feature vectors yields a scalar measure of overall anomaly, but this only reflects the severity of the distribution deviation, not the reliability and representativeness of the distribution. Therefore, this step introduces a sample sparsity penalty function, calculated as the square root of the reciprocal of the sample size in the small sample region, as a scaling factor based on sample size. The underlying logic is that the smaller the sample size, the more susceptible the statistical results are to random factors, thus their influence in the global evaluation should be appropriately suppressed. Multiplying this scaling factor by the Euclidean norm of the anomalous features yields a shock value corrected for "sparseness." This shock value is dimensionless, uniformly measuring the potential perturbation intensity of each region, and serves as an important basis for subsequent aggregation weight adjustment and extreme region labeling. This step, by designing a quantitative index coupling anomaly degree and sample reliability, introduces a stronger robustness control mechanism during modeling, preventing excessive interference from statistical randomness in small sample extreme regions to the federated model. This is a key step in improving modeling stability and enhancing evaluation explanatory power.

[0057] The Softmax function is applied to fuse the components of the impact value to generate an extreme index of capability distribution ranging from 0 to 1. A dynamic threshold is set, and the small sample region is determined to be an extreme region of capability distribution based on the extreme index of capability distribution, and the corresponding label information is output.

[0058] The specific steps for generating the extreme index of capability distribution are as follows:

[0059] First, the multidimensional components constituting the impact value are normalized using minimum-maximum scaling or Z-normalization to align the scale of each component. This ensures relative numerical comparability before inputting to the Softmax function and avoids output offset due to excessively large individual component values. Second, the Softmax function is applied to the normalized impact value components. An exponential function enhances the high-value response capability while compressing all outputs to between 0 and 1, ensuring that the output corresponding to each component has a "probabilistic" characteristic, representing its relative importance in the overall anomaly composition. Finally, the Softmax output value of each component is used as a corresponding weighting coefficient to perform weighted fusion processing on the original impact value components, resulting in a unique capability distribution extreme index. This index comprehensively measures the overall intensity of capability distribution anomalies in the small sample region, providing an interpretable and measurable indicator basis for subsequent "extreme region" labeling and dynamic adjustment of model aggregation weights.

[0060] The steps for determining extreme labels in small sample regions are as follows: First, a dynamic threshold range for the extreme index of capability distribution is set. This dynamic threshold range is automatically updated based on the distribution characteristics of shock values ​​in all small sample regions during federated training. Specifically, the upper and lower bounds are adjusted dynamically by setting statistical quantile values ​​(such as the 85th percentile) or by adding or subtracting a certain number of standard deviations from the mean, to adapt to changes in the global distribution at different times. Second, the extreme index of capability distribution calculated for each small sample region is compared and analyzed with the currently updated dynamic threshold range to determine the relative position of the abnormality of the small sample region in the global context. Finally, if the extreme index of capability distribution exceeds the upper limit of the dynamic threshold range, the small sample region is automatically marked as an extreme region; otherwise, it is marked as a "normal" region, and the corresponding label information is output to guide subsequent decisions on weight adjustment and regional stability intervention in model updates.

[0061] The core function of this step is to fuse and calculate the anomalous features of ability distribution across multiple dimensions, generating a measurable and interpretable extreme ability distribution index. A dynamic threshold mechanism is then used to intelligently identify and classify whether small sample regions belong to extreme ability distribution states, thus providing decision support for the subsequent aggregation process of the federated model. In real-world cross-regional education modeling scenarios, multiple small sample regions often exhibit varying degrees of ability distribution anomalies, which may include severe skewness, tail regrouping, excessive clustering, or dispersion. Since these anomalous factors are distributed across multiple statistical dimensions, such as skewness, kurtosis, tail density, and distribution span, a single indicator cannot accurately characterize their overall impact. Therefore, this step introduces the Softmax function to weight and fuse these shock value components to construct a unified, continuous, and normalized extreme ability distribution index.

[0062] The introduction of the Softmax function is significant: on the one hand, it enhances the expression weights of components with significant outliers across all dimensions, improving sensitivity to truly anomalous regions; on the other hand, its output is naturally compressed between 0 and 1, providing good comparability and visual interpretability. The generated capability distribution extreme index represents the relative degree of capability distribution anomaly in the entire federated system for that small sample region.

[0063] Subsequently, a dynamic threshold judgment mechanism allows for a flexible interpretation of the extreme index of the ability distribution. Unlike fixed thresholds, dynamic thresholds consider the real-time changes in the global impact value distribution, typically set based on quantiles (e.g., the 85th percentile) or mean ± standard deviation. This effectively adapts to system shifts caused by factors such as the introduction of new data and the evolution of sample distribution during training. The extreme index of the ability distribution in each small sample region is compared with this dynamic threshold interval. If it exceeds the upper limit of the dynamic threshold interval, the small sample region is determined to belong to an extreme region of ability distribution, and a corresponding label is output; otherwise, it is considered a "normal" region. This label not only provides data-driven basis for model weight adjustment but can also be used in subsequent analysis reports, educational intervention strategy formulation, and other scenarios, possessing strong practical application value.

[0064] Therefore, this step technically achieves dimensionality reduction and fusion from "multi-dimensional anomaly features" to "single-value index evaluation", and introduces dynamic thresholds to enhance robustness in the algorithm mechanism, ultimately providing key support for anomaly region control and intelligent governance in large-scale federated learning systems.

[0065] In the model aggregation phase of federated learning, the model update weights of the small sample region are adaptively adjusted based on the extreme index of the ability distribution of the small sample region, so as to intelligently match the extreme degree of its ability distribution, thereby reducing the interference on the global model training process and improving the stability and generalization ability of the aggregated model.

[0066] During the model aggregation phase of federated learning, the model update weights for the small sample region are adaptively adjusted based on the extreme exponent of the capability distribution of that small sample region. The specific steps are as follows:

[0067] First, the extreme index of the capability distribution in a small sample region is compared with the dynamic threshold range to determine its degree of anomaly. A regional regulation factor is defined to adjust the model contribution weight of this small sample region in the federated aggregation process. The calculation expression of the regional regulation factor is as follows: ,in: This is the extreme index of the ability distribution in a small sample region i. The larger the value, the more abnormal the distribution. The dynamic upper limit threshold for the extreme index of ability distribution is usually set to the 85th percentile. To regulate the intensity factor, the degree of compression after the extreme index of the capability distribution exceeds its limit is controlled. ; This is a factor controlling the slope of the compression curve; the larger the factor, the steeper the compression. ; The model updates the control factor to penalize extreme regions; its value range is [range missing]. ;

[0068] This step utilizes the degree of deviation of the extreme index of the capability distribution from the dynamic upper limit threshold, and uses an exponential function to perform nonlinear suppression, thereby achieving a stronger penalty for the "more extreme distribution area" while keeping the weight of the normally distributed area unchanged, thus enhancing the system's ability to suppress disturbances in abnormal areas.

[0069] During the model aggregation phase, the final normalized aggregation weight is calculated based on the original sample size and model update control factor of each small sample region. The calculation expression is as follows: ,in: Let i be the number of samples in the small sample region i. This is a sample weight index adjustment factor that controls the degree to which the number of samples affects the weights. ; The final model aggregation weights for the small sample region i are normalized and used for global model updates; the denominator term... The normalization constant ensures that the sum of all weights is 1. j represents any small sample region among all small sample regions. Its function is to traverse all small sample regions in the normalization calculation to ensure that the model update weights of each small sample region are reasonably allocated based on "global comparison".

[0070] This optimized aggregation weight design integrates two core dimensions: the representativeness of the regional sample size and the penalty for anomalies in the ability distribution. Used for flexible control over the relative dominance of a large number of sample regions. The ability to constrain perturbations in extreme regions enables the final model aggregation strategy to achieve the best balance between fairness, stability, and generalization, significantly improving the adaptability and interpretability of the federated model to complex real-world educational data.

[0071] In the model aggregation phase of federated learning, the model update weights are adaptively adjusted based on the extreme index of ability distribution in small sample regions. This is crucial for addressing the problem of excessive perturbation of the global model caused by abnormal distribution in small sample regions, thereby improving the overall stability and generalization ability of the aggregated model. In practical educational assessment or intelligent evaluation applications, there are significant differences in the number of samples and ability distribution patterns across different regions. Especially in some marginal regions with small sample sizes, ability scores exhibit skewed, heavy-tailed, and outlier characteristics, which can easily have a disproportionate impact on the update direction of the federated model. Traditional federated learning aggregation strategies, such as FedAvg, typically aggregate models from different regions based on sample size or equal weights, failing to fully consider differences in data quality and distribution patterns. This results in the update gradient of a model in a small sample region, which has distributional bias, still being indiscriminately added to the global model update, leading to model oscillations, convergence failures, and even a decline in global performance.

[0072] Therefore, this step introduces the capability distribution extreme index as a quantitative indicator to systematically evaluate the degree of anomaly in the capability score distribution of each small sample region. It then uses a dynamic threshold mechanism to determine whether a region is an "extreme region" and adaptively adjusts its model update weights accordingly. This capability distribution extreme index is constructed by fusing multiple anomaly features (such as skewness, kurtosis, and tail density), accurately capturing the degree of deviation in the distribution pattern and effectively mapping high-dimensional anomaly structures to usable control signals. Based on this, the system designs a weight scaling mechanism that assigns smaller weights to regions with higher capability distribution extreme indices and stronger anomalies, while retaining higher weights for regions with low capability distribution extreme indices and stable distributions. This ensures that model training is more focused on representative and stable data regions.

[0073] This mechanism not only effectively suppresses the impact of anomalous regions on the global model and improves the robustness of the model aggregation process, but also accelerates the convergence speed of the global model and enhances its generalization ability in unseen regions. Furthermore, this adjustment mechanism is dynamic and interpretable, updating in real time during training to adapt to the evolution of capability distribution patterns, demonstrating highly intelligent federated collaborative optimization capabilities. Therefore, this step is a key technical step in achieving reliable, sustainable, and high-performance federated modeling.

[0074] The aforementioned federated learning-based cross-regional student ability benchmark modeling method effectively addresses the interference caused by the extreme distribution of ability in small sample regions on the global model training process, significantly improving the stability of model aggregation and the interpretability of evaluation results. Specifically, this method ensures comparability of data from different regions through Z-standardization, then utilizes higher-order statistical features to construct multi-dimensional anomaly vectors, comprehensively characterizing the skewness and tail risk of ability distribution. Furthermore, a sample sparsity penalty mechanism couples distribution anomalies with sample representativeness into shock values, accurately reflecting the potential for regional disturbances. Softmax fusion and dynamic threshold judgment are further employed to automatically identify and label extreme regions. Finally, during the federated model aggregation stage, the model update weights for each region are adaptively adjusted based on the ability distribution extreme index, enabling the system to dynamically suppress the adverse effects of anomalies on global parameters. This approach not only enhances the robustness of the global model to heterogeneous data but also improves the objectivity and fairness of cross-regional ability assessment, providing a more reliable data foundation and modeling tools for educational equity analysis and personalized teaching strategies, demonstrating significant application value and promising prospects for wider adoption.

[0075] This invention provides, for example Figure 2 The federated learning-based cross-regional candidate competency benchmark modeling system shown includes a data standardization module, a distribution feature extraction module, an impact value construction module, an extreme region identification module, and a model weight adjustment module.

[0076] The data standardization module performs Z-standardization on the ability scores of all candidates in a small sample area to obtain a standardized sequence with zero mean and unit variance, and records the original mean and standard deviation.

[0077] The distribution feature extraction module constructs a probability density curve based on the standardized sequence, calculates the interquartile range, skewness, kurtosis, and tail density percentage of the upper and lower 5% tail intervals of the sequence, and combines the above statistics (interquartile range, skewness, kurtosis, and tail density percentage of the upper and lower 5% tail intervals) into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution.

[0078] The shock value construction module introduces a sample sparsity penalty function, which multiplies the Euclidean norm of the abnormal feature vector with the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity.

[0079] The extreme region identification module applies the Softmax function to fuse the components of the impact value, generates an extreme index of capability distribution ranging from 0 to 1, sets a dynamic threshold, determines whether the small sample region belongs to the extreme region of capability distribution based on the extreme index of capability distribution, and outputs the corresponding label information.

[0080] The model weight adjustment module adaptively adjusts the model update weights of the small sample region based on the extreme index of the ability distribution of the small sample region during the model aggregation stage of federated learning, so as to intelligently match the extreme degree of its ability distribution.

[0081] The cross-regional candidate competency benchmark modeling method based on federated learning provided in this embodiment of the invention is implemented through the aforementioned cross-regional candidate competency benchmark modeling system based on federated learning. For details of the specific methods and processes of the cross-regional candidate competency benchmark modeling system based on federated learning, please refer to the embodiments of the aforementioned cross-regional candidate competency benchmark modeling method based on federated learning, which will not be repeated here.

[0082] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0083] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0084] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A cross-regional candidate competency benchmark modeling method based on federated learning, characterized in that, Includes the following steps: Perform Z-standardization on all candidates' ability scores in a small sample area to obtain a standardized series with zero mean and unit variance, and record the original mean and standard deviation. Based on the standardized sequence, a probability density curve is constructed, and the interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals of the sequence are calculated. The statistics are then combined into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution. A sample sparsity penalty function is introduced, which multiplies the Euclidean norm of the anomalous feature vector by the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity. The Softmax function is applied to fuse the components of the impact value to generate an extreme index of capability distribution ranging from 0 to 1. A dynamic threshold is set, and the small sample region is determined to be an extreme region of capability distribution based on the extreme index of capability distribution, and the corresponding label information is output. During the model aggregation phase of federated learning, the model update weights for the small sample region are adaptively adjusted based on the extreme index of the ability distribution of that small sample region, so that they are intelligently matched with the extreme degree of its ability distribution.

2. The cross-regional candidate competency benchmark modeling method based on federated learning according to claim 1, characterized in that, The specific steps for performing Z-standardization on candidates' ability scores are as follows: For each candidate's raw ability score in a small sample area, the mean and standard deviation of the ability scores of all candidates in that small sample area are statistically analyzed and calculated. Based on the mean and standard deviation, Z-standardization is performed on each raw ability score. Specifically, the mean is subtracted from each score and then divided by the standard deviation to obtain the corresponding standardized ability score. The obtained set of standardized ability score sequences is constructed into a standardized ability score sequence with zero mean and unit variance.

3. The cross-regional candidate ability benchmark modeling method based on federated learning according to claim 1, characterized in that, The specific steps for constructing multidimensional anomaly feature vectors are as follows: Based on the standardized ability score sequence, a smooth probability density function curve is constructed using the kernel density estimation method to replace the discrete estimation error generated by the histogram; Statistical indicators describing the distribution shape are extracted from the probability density function curve, including interquartile range - used to measure the dispersion of the central tendency of the data, skewness - used to measure the symmetry of the distribution, and kurtosis - used to reflect the thickness of the tail and the degree of concentration of extreme values. The probability density function curve is intercepted at the top and bottom 5%, and the sum of the probability densities within the tail interval is calculated as the tail density proportion. The interquartile range, skewness, kurtosis and tail density proportion are combined together to form a multidimensional anomaly feature vector, which is used to reflect the degree of anomaly and structural deviation of the ability distribution in small sample areas.

4. The cross-regional candidate ability benchmark modeling method based on federated learning according to claim 1, characterized in that, The calculation steps for the tail density ratio include the following: Based on the probability density function curve constructed from the standardized ability score sequence, the corresponding cumulative distribution function is generated, and the lower 5% and upper 95% quantiles of the distribution are determined accordingly, and the left and right tail intervals are delineated accordingly. Integrate the kernel density function in the lower 5% and upper 5% intervals respectively to obtain the tail density ratio values ​​of the left and right tail regions; The tail density proportions of the upper and lower tails are fused in a weighted manner to generate a tail density proportion used to measure the degree of clustering of extreme samples.

5. The cross-regional candidate competency benchmark modeling method based on federated learning according to claim 1, characterized in that, The specific steps for calculating the impact value are as follows: Based on the constructed multidimensional anomaly feature vector, its norm in Euclidean space is calculated, which is the square root of the sum of the squares of each statistical component to obtain a scalar value that comprehensively characterizes the degree of distribution anomaly. Count the total number of samples in the current small sample region, calculate the reciprocal of the sample size and take the square root, and construct a scaling factor to penalize sample sparsity; Multiplying the Euclidean norm of the anomaly vector by the square root of the inverse of the sample size yields the shock value that couples the anomaly of the capability distribution with the scarcity of samples. This shock value accurately reflects the potential perturbation intensity of small sample regions on the global model during subsequent model aggregation.

6. The cross-regional candidate competency benchmark modeling method based on federated learning according to claim 1, characterized in that, The specific steps for generating the extreme index of capability distribution are as follows: The multidimensional components constituting the impact value are normalized, and the components are scaled using minimum-maximum scaling. The normalized impulse components are processed using the Softmax function, which improves the high-value response capability through the exponential function, while compressing all outputs to between 0 and 1. Using the Softmax output value of each component as the corresponding weighting coefficient, the original impact value components are weighted and fused to obtain a unique extreme index of capability distribution, which is used to comprehensively measure the overall intensity of capability distribution anomalies in this small sample area.

7. The cross-regional candidate competency benchmark modeling method based on federated learning according to claim 1, characterized in that, The steps for determining extreme labels in small sample regions are as follows: Set a dynamic threshold range for the extreme index of capability distribution. The dynamic threshold range is automatically updated based on the distribution characteristics of the impact values ​​of all small sample regions during the federated training process. The extreme index of the capability distribution calculated for each small sample region is compared and analyzed with the currently updated dynamic threshold range to determine the relative position of the abnormality of the small sample region in the global context. If the extreme index of the capability distribution exceeds the upper limit of the dynamic threshold range, the small sample region is automatically marked as an extreme region; otherwise, it is marked as a "normal" region, and the corresponding label information is output.

8. The cross-regional candidate competency benchmark modeling method based on federated learning according to claim 7, characterized in that, During the model aggregation phase of federated learning, the model update weights for the small sample region are adaptively adjusted based on the extreme exponent of the capability distribution of that small sample region. The specific steps are as follows: The extreme index of the capability distribution in a small sample region is compared with the dynamic threshold range to determine its degree of anomaly. A regional regulation factor is defined to adjust the model contribution weight of this small sample region in the federated aggregation process. The calculation expression of the regional regulation factor is as follows: ,in: The extreme index of the capability distribution in a small sample region i; This is the dynamic upper limit threshold for the extreme index of capability distribution; To regulate the intensity factor, the degree of compression after the extreme index of the capability distribution exceeds its limit is controlled. ; This is the slope control factor for the compression curve. ; The model updates the control factor to penalize extreme regions; its value range is [range missing]. ; During the model aggregation phase, the final normalized aggregation weight is calculated based on the original sample size and model update control factor of each small sample region. The calculation expression is as follows: ,in: Let i be the number of samples in the small sample region i. This is a sample weight index adjustment factor that controls the degree to which the number of samples affects the weights. ; The final model aggregation weights for the small sample region i are normalized and used for global model updates; the denominator term... This is a normalization constant to ensure that the sum of all weights is 1. j represents any one of the small sample regions, and its function is to traverse all small sample regions in the normalization calculation.

9. A cross-regional candidate competency benchmark modeling system based on federated learning, used to implement the cross-regional candidate competency benchmark modeling method based on federated learning as described in any one of claims 1-8, characterized in that, It includes a data standardization module, a distribution feature extraction module, an impact value construction module, an extreme region identification module, and a model weight adjustment module; The data standardization module performs Z-standardization on the ability scores of all candidates in a small sample area to obtain a standardized sequence with zero mean and unit variance, and records the original mean and standard deviation. The distribution feature extraction module constructs a probability density curve based on the standardized sequence, calculates the interquartile range, skewness, kurtosis, and tail density ratio of the upper and lower 5% tail intervals of the sequence, and combines the statistics into a multidimensional anomaly feature vector to describe the central tendency, tail thickness, and symmetry of the ability distribution. The shock value construction module introduces a sample sparsity penalty function, which multiplies the Euclidean norm of the abnormal feature vector with the inverse square root of the number of samples in the small sample region to obtain the shock value that couples the distribution anomaly with the sample scarcity. The extreme region identification module applies the Softmax function to fuse the components of the impact value, generates an extreme index of capability distribution ranging from 0 to 1, sets a dynamic threshold, determines whether the small sample region belongs to the extreme region of capability distribution based on the extreme index of capability distribution, and outputs the corresponding label information. The model weight adjustment module adaptively adjusts the model update weights of the small sample region based on the extreme index of the ability distribution of the small sample region during the model aggregation stage of federated learning, so as to intelligently match the extreme degree of its ability distribution.

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