A method and system for feature selection based on causal graph model in federated learning

Abstract

The application discloses a feature selection method and system based on a causal graph model in federated learning, and the method comprises the following steps: S1, initializing a candidate set and a default weight; S2, estimating and updating the weight through local bootstrap stability; S3, calculating a growth statistic and a mask and aggregating the optimal features to join the candidate set; S4, performing pruning statistic evaluation on the features in the candidate set and aggregating the false positive features; and S5, cyclically executing S3 and S4 until there is no feature meeting the gating condition, and outputting a final Markov boundary candidate set, so that only the candidate features which are positive across clients enter a competitive set through the consistency gating of the symbolic mask, thereby reducing the influence of pseudo correlation under heterogeneous distribution, and improving the cross-client consistency and interpretability of the selected features.

Description

Technical Field

[0001] This invention relates to the field of federated learning technology, specifically to a feature selection method and system based on a causal graph model in federated learning. Background Technology

[0002] In horizontal federated learning, multiple clients collaboratively train or select features while sharing the same feature space. Existing federated feature selection methods often employ relevance or importance metrics for aggregation, typically requiring pre-setting the number of features or thresholds. However, they face challenges when dealing with heterogeneous data distributions and varying sample sizes, including unstable aggregation results, weak interpretability, insufficient cross-distribution generalization, and suboptimal results due to the inability to determine sample size, leading to equal-weighted aggregation. Meanwhile, Markov boundary discovery techniques in non-federated scenarios can provide the minimum optimal feature set related to the label variable, but traditional implementations are mostly centralized and difficult to directly transfer to federated environments.

[0003] The existing technologies mainly suffer from the following technical bottlenecks:

[0004] 1. In a federated environment, feature selection based solely on relevance metrics is insufficient to provide a clear causal explanation between the feature selection and the label variable, and it lacks generalization ability under conditions of data distribution migration and heterogeneity. It is also difficult to achieve consistent aggregation under heterogeneous distribution: when the client distribution is heterogeneous, the target feature sets learned by each client may be significantly different, and the server may have difficulty aggregating them into a correct and consistent result, resulting in misselection and omission.

[0005] 2. Most federated feature selection methods require pre-setting the number of features or a fixed screening scale, making it difficult to automatically obtain the smallest and optimal feature subset in real-world business scenarios where the optimal feature scale is unknown.

[0006] 3. When the data distribution of each client is heterogeneous, the feature subsets learned by each client are very different, making it difficult for the server to aggregate a consistent and correct feature set, which can easily introduce spurious features or miss key features.

[0007] 4. In scenarios where sample sizes differ significantly and are considered private, the server cannot know the sample size of each client and can only aggregate with equal weights, resulting in insufficient reliability of aggregated statistics and suboptimal feature selection results. Summary of the Invention

[0008] This invention proposes a feature selection method and system based on a causal graph model in federated learning to solve the problems mentioned in the background.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: A feature selection method based on a causal graph model in federated learning according to the present invention includes the following steps:

[0010] S1. Initialize the candidate set and default weights;

[0011] S2. Stability estimation and weight update are performed through local bootstrapping;

[0012] S3. Calculate the growth statistics and mask, and aggregate them to select the optimal features to add to the candidate set;

[0013] S4. Evaluate the pruning statistics of the features in the candidate set and aggregate and remove false positive features;

[0014] S5. Repeat steps S3 and S4 until no features satisfy the gating condition are found, and output the final Markov boundary candidate set.

[0015] Preferably, step S1 includes the following steps:

[0016] S11. Initialize the candidate set: ;

[0017] S12. Assign initial weights to each client: .

[0018] Preferably, step S2 includes the following steps:

[0019] S21. Calculate the mean of bootstrap mutual information;

[0020] S22. Calculate the stability measure based on the mean of bootstrap mutual information;

[0021] S23. Calculate the weights based on the stability metric.

[0022] Preferably, step S3 includes the following steps:

[0023] S31. Distribute the current candidate set to each client. ;

[0024] S32. Calculate the conditional mutual information of each candidate feature locally during the growth phase;

[0025] S33. Generate a mask value based on the preset threshold of the conditional mutual information of the growth stage;

[0026] S34. Perform weighted aggregation of the mask values ​​based on the client weight;

[0027] S35. Select the optimal feature that satisfies the condition and add it to the candidate set, then update the candidate set.

[0028] Preferably, step S4 includes the following steps:

[0029] S41. Issue the updated candidate set and enter the pruning phase. Calculate the mutual information of the pruning phase conditions and generate the mask value.

[0030] S42. Identify and remove false positive features generated after addition based on the mask value;

[0031] S43. Weighted aggregation of pruning mask values ​​and removal of false positives.

[0032] Preferably, the formula for calculating the mean of the bootstrap mutual information is as follows:

[0033]

[0034] in, This indicates the total number of rounds of bootstrapping sampling. For the first The round index corresponding to the round of bootstrapping sampling. For the client The average mutual information estimate obtained on the h-th bootstrap sample;

[0035]

[0036] in, This represents the features estimated on this bootstrap sample. With label variables Mutual information between them The total number of features in the feature space;

[0037] The formula for calculating the stability metric is as follows:

[0038]

[0039] The formula for calculating the weight is as follows:

[0040]

[0041] in, Representing the One client participating in the computation, It is a loop variable. This represents the total number of clients participating in this round of federated computing.

[0042] Preferably, the formula for calculating the conditional mutual information is as follows:

[0043]

[0044] in, Represents the first in the feature space One characteristic, For feature index, For label variables;

[0045] The mask value is as follows:

[0046]

[0047] in, For the threshold, The mask value;

[0048] The weighted aggregation of the mask values ​​is as follows:

[0049]

[0050] in, The mask value is the weighted aggregated value, and is... As a gating condition that satisfies the conditional characteristics;

[0051] The updated candidate set:

[0052]

[0053] in, The index for the optimal feature. This refers to the specific features corresponding to the index.

[0054] Preferably, the calculation formula for the conditional mutual information during the pruning stage is as follows:

[0055]

[0056] in, Represents the current candidate Markov boundary set The first in One characteristic, For the index of this feature, and ;

[0057] The mask value is as follows:

[0058]

[0059] The weighted aggregation of pruned mask values:

[0060]

[0061] And remove those that satisfy the criteria from the candidate set. Features:

[0062] .

[0063] A feature selection system based on a causal graph model in federated learning includes:

[0064] The server-side modules include a candidate Markov boundary set maintenance module, a federated growth-pruning control module, a mask weighted aggregation module, a client weight calculation module, and a communication management module.

[0065] The candidate Markov boundary set maintenance module is used to take initialization parameters and the current candidate set as input; maintain the candidate Markov boundaries and broadcast them to the client module; and output the updated candidate Markov boundaries.

[0066] The mask weighted aggregation module is used to take as input the conditional mutual information and its symbol mask results uploaded by each client module; it performs weighted aggregation according to weights and outputs the aggregated vector and the judgment result used for selection or elimination.

[0067] The federated growth-pruning control module takes the aggregation result and stopping conditions as input; it performs alternating iterations from the growth phase to the pruning phase, outputs the feature index and the elimination set selected in this round, and drives the candidate set update.

[0068] The client-side weight calculation module takes as input the stability metric uploaded by each client and outputs the weights for the mask weighted aggregation module to call.

[0069] Preferably, the system further includes:

[0070] The client module includes a local conditional mutual information calculation module, a local information mask module, a local resampling stability evaluation module, an upload module, and a receive module;

[0071] The local conditional mutual information calculation module is used to take local datasets and candidate sets issued by the server as inputs; and outputs conditional mutual information during the growth or pruning phase.

[0072] The local information mask module is used to input conditional mutual information and threshold, and output a symbol mask;

[0073] The local resampling stability evaluation module is used to input the local dataset and bootstrap mutual information; output the stability metric and upload it to the server module.

[0074] The upload module and the receiving module are used to receive weight requests broadcast by the server module and to perform traditional metering.

[0075] As can be seen from the above technical solution, this invention provides a feature selection method based on a causal graph model in federated learning. Compared with the prior art, this invention has the following advantages:

[0076] 1. This invention uses symbol mask consistency gating to ensure that only candidate features that are consistently positive across clients enter the competition set, thereby reducing the impact of spurious correlations under heterogeneous distributions and improving the cross-client consistency and interpretability of selected features.

[0077] 2. This invention can remove false features immediately after including candidate features through alternating growth-pruning iteration, suppress candidate set expansion, and promote faster and more stable convergence of the Markov boundary discovery process.

[0078] 3. This invention uses a stability metric as a privacy proxy for the sample size to perform weighted aggregation, which can improve the reliability of the aggregated statistics without disclosing the sample size and reduce the impact of small sample client noise on global selection. Attached Figure Description

[0079] Figure 1 This is a flowchart illustrating a feature selection method based on a causal graph model in federated learning according to the present invention.

[0080] Figure 2 This is a system block diagram of a feature selection system based on a causal graph model in federated learning according to the present invention.

[0081] Figure 3 This is a schematic diagram illustrating the interaction sequence and process between the server and multiple clients in this invention.

[0082] Figure 4 This is a comparison of the accuracy of the various federal feature selection methods of the present invention on real datasets. Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0084] like Figure 1 As shown in this embodiment, a feature selection method based on a causal graph model in federated learning includes the following steps:

[0085] S1. Initialize the candidate set and default weights;

[0086] S2. Stability estimation and weight update are performed through local bootstrapping;

[0087] S3. Calculate the growth statistics and mask, and aggregate them to select the optimal features to add to the candidate set;

[0088] S4. Evaluate the pruning statistics of the features in the candidate set and aggregate and remove false positive features;

[0089] S5. Repeat steps S3 and S4 until no features satisfy the gating condition are found, and output the final Markov boundary candidate set.

[0090] Furthermore, S1 includes the following steps:

[0091] S11. Initialize the candidate set: ;

[0092] S12. Assign initial weights to each client: .

[0093] Furthermore, S2 includes the following steps:

[0094] S21. Calculate the mean of bootstrap mutual information;

[0095] S22. Calculate the stability measure based on the mean of bootstrap mutual information;

[0096] S23. Calculate the weights based on the stability metric.

[0097] Furthermore, S3 includes the following steps:

[0098] S31. Distribute the current candidate set to each client. ;

[0099] S32. For each candidate feature, calculate the conditional mutual information (CMI) during the growth phase locally;

[0100] S33. Generate a mask value based on the preset threshold of the conditional mutual information of the growth stage;

[0101] S34. Perform weighted aggregation of the mask values ​​based on the client weight;

[0102] S35. Select the optimal feature that satisfies the condition and add it to the candidate set, then update the candidate set.

[0103] Furthermore, S4 includes the following steps:

[0104] S41. Issue the updated candidate set and enter the pruning phase. Calculate the conditional mutual information (CMI) for the pruning phase and generate the mask value.

[0105] S42. Identify and remove false positive features generated after addition based on the mask value;

[0106] S43. Weighted aggregation of pruning mask values ​​and removal of false positives.

[0107] Furthermore, the formula for calculating the mean of bootstrap mutual information is as follows:

[0108]

[0109] in, This indicates the total number of rounds of bootstrapping sampling. For the first The round index corresponding to the round of bootstrapping sampling. For the client The average mutual information estimate obtained on the h-th bootstrap sample;

[0110]

[0111] in, This represents the features estimated on this bootstrap sample. With label variables Mutual information between them The total number of features in the feature space;

[0112] The formula for calculating the stability metric is as follows:

[0113]

[0114] The formula for calculating the weight is as follows:

[0115]

[0116] in, Representing the One client participating in the computation, It is a loop variable. This represents the total number of clients participating in this round of federated computing.

[0117] Furthermore, the formula for calculating conditional mutual information is as follows:

[0118]

[0119] in, Represents the first in the feature space One characteristic, For feature index, For label variables;

[0120] The mask values ​​are as follows:

[0121]

[0122] in, For the threshold, The mask value;

[0123] Perform weighted aggregation on the mask values:

[0124]

[0125] in, The mask value is the weighted aggregated value, and is... As a gating condition that satisfies the conditional characteristics;

[0126] Update candidate sets:

[0127]

[0128] in, The index for the optimal feature. This refers to the specific features corresponding to the index.

[0129] Furthermore, the formula for calculating the conditional mutual information during the pruning stage is as follows:

[0130]

[0131] in, Represents the current candidate Markov boundary set The first in One characteristic, For the index of this feature, and ;

[0132] The mask values ​​are as follows:

[0133]

[0134] Weighted aggregation of pruned mask values:

[0135]

[0136] And remove those that satisfy the criteria from the candidate set. Features:

[0137] .

[0138] like Figure 2 As shown, a feature selection system based on a causal graph model in federated learning includes:

[0139] The server-side modules include a candidate Markov boundary set maintenance module, a federated growth-pruning control module, a mask weighted aggregation module, a client weight calculation module, and a communication management module.

[0140] The candidate Markov boundary set maintenance module takes initialization parameters and the current candidate set as input, maintains the candidate Markov boundaries, broadcasts them to the client module, and outputs the updated candidate Markov boundaries.

[0141] The mask weighted aggregation module is used to take as input the conditional mutual information and its symbol mask results uploaded by each client module; it performs weighted aggregation according to weights and outputs the aggregated vector and the judgment result used for selection or elimination.

[0142] The federated growth-pruning control module takes the aggregation result and stopping conditions as input; it performs alternating iterations from the growth phase to the pruning phase, outputs the feature index and the elimination set selected in this round, and drives the candidate set update.

[0143] The client-side weight calculation module takes as input the stability metric uploaded by each client and outputs the weights for the mask weighted aggregation module to call.

[0144] Furthermore, the system also includes:

[0145] The client module includes a local conditional mutual information calculation module, a local information mask module, a local resampling stability evaluation module, an upload module, and a receive module;

[0146] The local conditional mutual information calculation module is used to take local datasets and candidate sets issued by the server as inputs; and outputs conditional mutual information during the growth or pruning phase.

[0147] The local information mask module is used to input conditional mutual information and threshold, and output a symbol mask;

[0148] The local resampling stability evaluation module is used to input the local dataset and bootstrap mutual information; it outputs the stability metric and uploads it to the server module.

[0149] The upload module and the receive module are used to receive weight requests broadcast by the server module and then apply them to traditional metering.

[0150] like Figure 3 As shown, the present invention performs iterative calculations under server-side control. The method consists of two alternating iterative phases: a federated growth phase and a federated pruning phase, to address the heterogeneity of data distribution; at the same time, a client-side weighting strategy is introduced to address differences in sample size.

[0151] To verify the feature selection and classification performance of FedCFS in real-world scenarios, experiments were conducted using six real-world datasets from the UCI machine learning library. The core parameter configurations are shown in Table 1, and the basic information of the datasets is shown in Table 2.

[0152] Table 1

[0153]

[0154] Table 2

[0155]

[0156] For real datasets, 10-fold cross-validation is used to split the training and test sets. Feature selection is performed only on the training set. The selected feature subset is used to train logistic regression (LR) and multilayer perceptron (MLP) classifiers. Finally, the feature quality is evaluated by the accuracy and F1 score on the test set.

[0157] The results are as follows Figure 4 As shown:

[0158] (1) FedCFS achieved the highest classification accuracy on almost all datasets and all client configurations, demonstrating the comprehensive performance advantages of this invention. In particular, FedCFS’s advantages are most prominent on high-dimensional complex datasets (bankruptcy and semeion): on the bankruptcy dataset, the baseline method showed a significant performance degradation with the increase of the number of clients, while FedCFS remained robust; on the semeion dataset (256 dimensions), FedCFS’s accuracy consistently outperformed all the comparison methods.

[0159] (2) Correlation methods (MS-GINI, FPSO-FS, Fed-MOFS, Fed-mRMR) are competitive on simple datasets (optdigits, krvskp), but lag significantly behind in imbalanced classes or high-dimensional scenarios. This is because of the inherent limitations of correlation feature selection—when there is distribution shift or strong data heterogeneity, the generalization ability of feature subsets selected solely based on statistical correlation is limited.

[0160] (3) Variant methods based on causal voting (CFS-MI-V3, CFS-MI-V5, LaCFS-V3, LaCFS-V5) outperform pure correlation methods, but due to their simple aggregation mechanism, they are unstable when the client data is highly heterogeneous. FedCFS, through alternating growth-pruning mechanism and adaptive client weighting, can more effectively handle data distribution heterogeneity and achieve more robust MB discovery.

[0161] (4) As the number of clients increases (from 3 to 20), the accuracy of FedCFS remains stable or even slightly improves, demonstrating the good adaptability of the invention in terms of scale expansion.

[0162] In summary, the experimental results of this invention on real-world IID datasets fully demonstrate that:

[0163] (1) Comprehensive performance advantages: In all experiments with 6 real-world datasets, 5 client number configurations (K ∈ {3, 5, 10, 15, 20}), and MLP and LR classifiers, FedCFS outperformed 8 baseline methods in almost all configurations, verifying the comprehensive competitiveness of the present invention.

[0164] (2) Handling data distribution heterogeneity: FedCFS can accurately discover the true Markov boundary of the label even when there are differences in the data distribution of each client through the alternating growth-pruning mechanism. The selected causal feature subset has stronger distribution invariance and generalization ability, overcoming the shortcomings of existing correlation methods in generalization in the case of data heterogeneity.

[0165] (3) Imbalanced sample size handling: The privacy-preserving client weighting strategy designed in this invention estimates the relative sample size through local resampling stability. It can assign reasonable weights to clients of different sizes without exposing the real sample size, thereby improving the reliability of feature selection. The effect is particularly outstanding in highly imbalanced sample allocation scenarios (the ratio of the largest to the smallest client sample size exceeds 3:1).

[0166] (4) No need to preset the number of features: Unlike existing correlation methods that require manual preset of the selected feature ratio (such as top 10%), FedCFS automatically determines the optimal minimum feature subset based on Markov boundary theory, avoiding performance loss caused by improper preset of the number of features, and is more practical.

[0167] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk), etc.

[0168] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0169] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0170] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A feature selection method based on a causal graph model in federated learning, characterized in that, Applied to a federated learning system comprising a server and multiple clients, the method includes: S1. Initialize the candidate set and default weights on the server side; S2. Each client performs stability estimation through local bootstrapping and uploads the stability metrics to the server. The server updates the weights based on the stability metrics of each client. S3. The server distributes the current candidate set to each client; each client calculates the conditional mutual information of the growth stage locally and generates a mask, and uploads the mask to the server; the server receives the mask uploaded by each client, performs weighted aggregation on the mask according to the weight, and selects the optimal feature that meets the gating condition to add to the candidate set. S4. The server distributes the updated candidate set to each client; each client performs conditional mutual information evaluation on the features in the candidate set during the pruning stage and generates a pruning mask, which is then uploaded to the server; the server performs weighted aggregation on the pruning mask and removes false positive features from the candidate set based on the aggregation result. S5. Repeat S3 and S4 until no feature satisfies the gating condition, and output the final Markov boundary candidate set; S1 includes the following steps: S11. Initialize the candidate set: ; S12. Assign initial weights to each client: ,in This indicates the total number of clients participating in this round of federated computing; S2 includes the following steps: S21. Calculate the mean of bootstrap mutual information; S22. Calculate the stability measure based on the mean of bootstrap mutual information; S23. Calculate the weights based on the stability metric; The formula for calculating the mean of the bootstrap mutual information is as follows: in, This indicates the total number of rounds of bootstrapping sampling. For the first The round index corresponding to the round of bootstrapping sampling. For the client The average mutual information estimate obtained on the h-th bootstrap sample; in, This represents the features estimated on this bootstrap sample. With label variables Mutual information between them The total number of features in the feature space; The formula for calculating the stability metric is as follows: The formula for calculating the weight is as follows: in, Representing the One client participating in the computation, It is a loop variable. This indicates the total number of clients participating in this round of federated computing. Indicates the first Client The corresponding stability metric value; The formula for calculating the conditional mutual information is as follows: in, Represents the first in the feature space One characteristic, For feature index, For label variables, Indicates client-side Conditional mutual information calculated from the local dataset; The mask value is as follows: in, For the threshold, The mask value; The weighted aggregation of the mask values ​​is as follows: in, The mask value is the weighted aggregated value, and is... As a gating condition that satisfies the conditional characteristics; The updated candidate set: in, The index for the optimal feature. For the specific features corresponding to the index; The formula for calculating the conditional mutual information during the pruning stage is as follows: in, Represents the current candidate Markov boundary set The first in One characteristic, For the index of this feature, and , Indicates a given set of conditional features Calculate conditional mutual information under the given conditions; The mask value is as follows: The weighted aggregation of pruned mask values: And remove those that satisfy the criteria from the candidate set. Features: 。 2. The feature selection method based on a causal graph model in federated learning according to claim 1, characterized in that: S3 includes the following steps: S31. Distribute the current candidate set to each client. ; S32. Calculate the conditional mutual information of each candidate feature locally during the growth phase; S33. Generate a mask value based on the preset threshold of the conditional mutual information of the growth stage; S34. Perform weighted aggregation of the mask values ​​based on the client weight; S35. Select the optimal feature that satisfies the condition and add it to the candidate set, then update the candidate set.

3. The feature selection method based on a causal graph model in federated learning according to claim 2, characterized in that: S4 includes the following steps: S41. Issue the updated candidate set and enter the pruning phase. Calculate the mutual information of the pruning phase conditions and generate the mask value. S42. Identify and remove false positive features generated after addition based on the mask value; S43. Weighted aggregation of pruning mask values ​​and removal of false positives.

4. A feature selection system based on a causal graph model in federated learning, comprising a server and multiple clients, wherein the server is communicatively connected to the multiple clients, for executing the feature selection method based on a causal graph model in federated learning as described in any one of claims 1-3, characterized in that, A server-side module is deployed on the server, and a client-side module is deployed on the client. The server-side module includes a candidate Markov boundary set maintenance module, a federated growth-pruning control module, a mask weighted aggregation module, a client weight calculation module, and a communication management module. The candidate Markov boundary set maintenance module is used to take initialization parameters and the current candidate set as input; maintain the candidate Markov boundaries and broadcast them to the client module; and output the updated candidate Markov boundaries. The mask weighted aggregation module is used to take as input the conditional mutual information and its symbol mask results uploaded by each client module; it performs weighted aggregation according to weights and outputs the aggregated vector and the judgment result used for selection or elimination. The federated growth-pruning control module takes the aggregation result and stopping conditions as input; it performs alternating iterations from the growth phase to the pruning phase, outputs the feature index and the elimination set selected in this round, and drives the candidate set update. The client-side weight calculation module takes as input the stability metric uploaded by each client and outputs the weights for the mask weighted aggregation module to call. The client module includes a local conditional mutual information calculation module, a local information mask module, a local resampling stability evaluation module, an upload module, and a receive module.

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