A method and system for selecting longitudinal federated causal features under distribution offset
By training low-dimensional representations using a client-side encoder and combining weighted logistic regression and weighted path analysis, the cross-distribution invariance and privacy protection issues of causal feature selection in vertical federated learning are resolved, achieving stable feature selection and improved interpretability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF POSTS & TELECOMM
- Filing Date
- 2026-04-23
- Publication Date
- 2026-07-03
AI Technical Summary
In longitudinal federated learning, existing feature selection methods struggle to guarantee cross-distribution invariance, leading to decreased out-of-distribution generalization performance. Furthermore, they lack causal interpretability and interpretability, making it difficult to map the feature space under privacy constraints.
The low-dimensional representation is trained by the client encoder, the server concatenates and balances the loss, and combines weighted logistic regression to estimate causal importance. Finally, weighted path analysis is used to map back to the original features to achieve causal feature selection.
It achieves cross-distribution stable feature selection, improves interpretability and privacy protection, reduces computational cost, and performs more stably on out-of-distribution tasks.
Smart Images
Figure CN122065918B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of federated learning technology, specifically to a method and system for selecting longitudinal federated causal features under distribution offset. Background Technology
[0002] In vertical federated learning, different participants hold different feature subsets of the same batch of samples, and usually only the active party holds the labels. This makes it difficult to directly implement the traditional "label-feature correlation" driven feature selection, and it is easily affected by the difference in training / test distribution.
[0003] Existing technologies mostly rely on local representation or embedding followed by server-side aggregation and importance pruning, or achieve vertical federated training through encryption or privacy protocols, then contribute features by approximating them with model weights or gradients. However, existing technologies have the following shortcomings:
[0004] 1. In longitudinal federated learning, existing feature selection methods mostly rely on relevance or model weight pruning. When faced with distribution drift such as sample selection bias, it is difficult to guarantee the cross-distribution invariance of the selected features, resulting in a decrease in out-of-distribution generalization performance.
[0005] 2. Under privacy constraints that do not share original features, existing methods struggle to provide causal explanations for why a feature is important, resulting in insufficient interpretability;
[0006] 3. Under the condition of vertical segmentation of multi-party feature space, how to reliably map the "abstract representation / embedding layer importance" obtained by the server back to the original feature space of each client and maintain the causal relationship with the label is a weak link of the existing technology. Summary of the Invention
[0007] This invention proposes a method and system for selecting longitudinal federated causal features under distribution offset, in order to solve the problems mentioned above in the background.
[0008] To achieve the above objectives, the present invention employs the following technical solution: A method for selecting longitudinal federated causal features under distribution offset, comprising the following steps:
[0009] S1. Initialization and Role Configuration: Initialize the participant set to obtain the local feature matrix;
[0010] S2. Client-side local encoder training: The client trains the encoder to obtain a low-dimensional representation, and then uploads the low-dimensional representation to the server.
[0011] S3. Server-side concatenation of global representation: Concatenate the low-dimensional representations of each client to obtain the concatenated representation;
[0012] S4. Global Sample Distribution Balancing: Construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective to output global sample weights;
[0013] S5. The active party performs weighted causal effect estimation: For the classification task, regularized weighted logistic regression is used to obtain regression coefficients and low-dimensional causal importance is calculated based on the regression coefficients;
[0014] S6. Low-dimensional causal representation filtering: A set of low-dimensional causal indexes is obtained by threshold filtering based on the importance of low-dimensional causality;
[0015] S7. Weight path analysis for each client and back-transfer of the importance of the original features: Through weight path analysis, the low-dimensional causal importance is back-transferred to the original features, and the causal importance score of each original feature is calculated.
[0016] S8. Server-side global feature selection output: Construct a global importance vector based on the causal importance score of each original feature and sort them. Select the top few features to obtain and output the feature subset.
[0017] Preferably, step S1 includes the following steps:
[0018] S11, Input the set of participating client clients The set of participating client clients includes the active client. hold Passive client hold ;
[0019] in, For client-side local feature matrix, For local tag matrix, The total number of participating client groups. For the client;
[0020] S12. Let the total characteristic number be... in For the client The local original feature dimensions held.
[0021] Preferably, step S2 includes the following steps:
[0022] S21. Input the local feature matrix of each client;
[0023] S22. Train the encoder for each client based on the local feature matrix of each client. and decoder Optimization target
[0024]
[0025] in, For row Regular expression The regularization coefficient is... Represents the weight matrix row index, Represents the weight matrix The first in row vectors For the client The autoencoder reconstruction loss function, This represents the total number of samples. For the client Self-encoder The weight matrix of the layer, For the client The total number of layers in a local autoencoder network model. For the layer index of the autoencoder network layer, and ;
[0026] Output low-dimensional representation ;
[0027] S23. Each client sends a low-dimensional representation to the server.
[0028] Preferably, the splicing is represented as .
[0029] Preferably, step S4 includes the following steps:
[0030] S41. Construct a balanced loss for each original feature in the global original feature set based on the concatenated representation:
[0031]
[0032] in, For the first The balance loss of each original feature, For the sample The square of the weights, The original features have an indicator factor, and the global original feature set is composed of the local feature matrices of each client. The features in each column are logically pieced together;
[0033] S42. Jointly optimize the global objective based on the balance loss:
[0034]
[0035] in, The overall objective function is to achieve global sample distribution balance. For global sample weights, The regularization coefficient is... For Hadamard product, The global total feature dimension;
[0036] S43. Optimize G iteratively using the gradient method. When the preset iteration number T is reached, or... Stop when convergence occurs and output the global sample weights.
[0037] Preferably, step S5 includes the following steps:
[0038] S51. A classification task that predicts the label matrix Y held locally by the active party based on the global sample weights, using regularized weighted logistic regression:
[0039]
[0040] in, The loss function for weighted causal effect estimation. For category The corresponding weighted causal effect coefficient, c represents the total number of target categories for the classification task. For the summation index, Indicates the first The true class label of each sample , As an indicator function, when the sample The real label equals When the condition is met, the value of this item is 1; otherwise, it is 0. For the first The transpose of the concatenated low-dimensional representation vector of each sample is the global feature vector formed by concatenating the low-dimensional features extracted by each client. for Regularization hyperparameters are used to adjust the regression coefficient matrix of the model. The degree of sparsity;
[0041] S52. Calculate low-dimensional causal importance based on the loss function estimated by weighted causal effects:
[0042]
[0043] in, For the first Causal importance scores of low-dimensional encoded features Indicates belonging to a category regression coefficient vector The first in The element corresponding to the component element, Causal weights of low-dimensional features; similarly, For the first in this vector Each component element;
[0044] S53. Output the causal importance score to the server.
[0045] Preferably, S6 includes:
[0046] A set of low-dimensional causal indexes is obtained by threshold filtering based on low-dimensional causal importance:
[0047]
[0048] in, This is the causal threshold.
[0049] Preferably, step S7 includes the following steps:
[0050] S71. Use encoder layer weights to approximate the linearization transformation from input to low-dimensional representation of output:
[0051] ;
[0052] S72. Based on the causal low-dimensional index set and the linearization transformation, calculate the causal importance score for each original feature:
[0053]
[0054] in, To map back to the client through weighted path analysis Local No. The final importance score of each original feature, This is a set of causal low-dimensional indexes after client-side segmentation. Indicates the client After the weight matrices of each layer are multiplied consecutively, the product matrix containing the weights at the th layer is obtained. line, number The elements of the column, in physical terms, represent the input layer's first... The first original feature affects the output layer. The linearization of low-dimensional features affects the weights;
[0055] S73, Each client uploads data to the server. Mapping relationship with feature global index, where, Indicates the client For its local inclusion The set of importance score sequences is calculated from the original features.
[0056] Preferably, step S8 includes the following steps:
[0057] S81, All clients return a set of causal importance scores;
[0058] S82. Construct a global importance vector based on the causal importance score of each original feature and sort them, then select the top... One characteristic:
[0059]
[0060] in, For the selected feature subset, The retention ratio for features selected by the user. ; This represents the total number of original global features after multi-party splicing; This represents the floor function, which filters out the most important values from the global scope. Features;
[0061] S83, Output feature subset.
[0062] A longitudinal federated causal feature selection system under distribution offset includes:
[0063] The client-side local encoder training module is used to train the encoder on the client side, obtain a low-dimensional representation, and upload the low-dimensional representation to the server.
[0064] The splicing and communication orchestration module is used to splice the low-dimensional representations of each client to obtain a spliced representation;
[0065] The global sample distribution balancing module is used to construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective, outputting global sample weights.
[0066] The weighted causal effect estimation module is used to apply regularized weighted logistic regression to classification tasks, obtain regression coefficients, and calculate low-dimensional causal importance based on the regression coefficients.
[0067] The spatial mapping and weighted path analysis module is used to obtain a set of low-dimensional causal indexes by thresholding based on low-dimensional causal importance; the low-dimensional causal importance is then fed back to the original features through weighted path analysis to calculate the causal importance score of each original feature.
[0068] The global feature selection and output module is used to construct a global importance vector based on the causal importance score of each original feature and sort it, select the top few features, and obtain and output the feature subset.
[0069] As can be seen from the above technical solution, the present invention provides a method for selecting longitudinal federated causal features under distribution offset. Compared with the prior art, the present invention has the following advantages:
[0070] 1. This invention achieves privacy protection by sharing only the low-dimensional representation of the client encoder without sharing the client's local feature matrix, and by utilizing the irreversibility caused by compression; at the same time, dimensionality reduction reduces the computational cost of subsequent causal learning.
[0071] 2. The present invention is crucial for eliminating spurious correlations caused by selection bias through sample reweighting or distribution balancing; the performance tends to decline when this module is ablated and removed.
[0072] 3. Compared with various VFL feature selection baseline methods, this invention demonstrates greater stability and less fluctuation in out-of-distribution tasks in both synthetic and real-world cross-domain tasks.
[0073] 4. This invention uses weighted path analysis to trace causal relationships back from the encoded representation to the original features, and finally outputs a subset of the original features of each party, thereby improving interpretability and deployability. Attached Figure Description
[0074] Figure 1 This is a flowchart illustrating a vertical federated causal feature selection method under distribution offset according to the present invention.
[0075] Figure 2 This is a schematic diagram of the functional module structure of a feature selection system based on a causal graph model in federated learning according to the present invention.
[0076] Figure 3 The figure shows the experimental results calculated using a logistic regression classifier on a real dataset according to this invention.
[0077] Figure 4 The figure shows the experimental results calculated using a multilayer perceptron classifier on a real dataset according to this invention. Detailed Implementation
[0078] 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.
[0079] like Figure 1 As shown in this embodiment, a method for selecting longitudinal federated causal features under distribution offset includes the following steps:
[0080] S1. Initialization and Role Configuration: Initialize the participant set to obtain the local feature matrix;
[0081] S2. Client-side local encoder training: The client trains the encoder to obtain a low-dimensional representation, and then uploads the low-dimensional representation to the server.
[0082] S3. Server-side concatenation of global representation: Concatenate the low-dimensional representations of each client to obtain the concatenated representation;
[0083] S4. Global Sample Distribution Balancing: Construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective to output global sample weights;
[0084] S5. The active party performs weighted causal effect estimation: For the classification task, regularized weighted logistic regression is used to obtain regression coefficients and low-dimensional causal importance is calculated based on the regression coefficients;
[0085] S6. Low-dimensional causal representation filtering: A set of low-dimensional causal indexes is obtained by threshold filtering based on the importance of low-dimensional causality;
[0086] S7. Weight path analysis for each client and back-transfer of the importance of the original features: Through weight path analysis, the low-dimensional causal importance is back-transferred to the original features, and the causal importance score of each original feature is calculated.
[0087] S8. Server-side global feature selection output: Construct a global importance vector based on the causal importance score of each original feature and sort them. Select the top few features to obtain and output the feature subset.
[0088] Furthermore, S1 includes the following steps:
[0089] S11, Input the set of participating client clients The set of participating clients includes the initiating client. hold Passive client hold ;
[0090] in, For client-side local feature matrix, For local tag matrix, The total number of participating client groups. For the client;
[0091] S12. Let the total characteristic number be... in For the client The local original feature dimensions held.
[0092] Furthermore, S2 includes the following steps:
[0093] S21. Input the local feature matrix of each client;
[0094] S22. Train the encoder for each client based on the local feature matrix of each client. and decoder Optimization target
[0095]
[0096] in, For row Regular expression The regularization coefficient is... Represents the weight matrix row index, Represents the weight matrix The first in row vectors For the client The autoencoder reconstruction loss function, This represents the total number of samples. For the client Self-encoder The weight matrix of the layer, For the client The total number of layers in a local autoencoder network model. For the layer index of the autoencoder network layer, and ;
[0097] Output low-dimensional representation ;
[0098] S23. Each client sends a low-dimensional representation to the server.
[0099] Furthermore, splicing is represented as .
[0100] Furthermore, S4 includes the following steps:
[0101] S41. Construct a balanced loss for each original feature in the global original feature set based on the concatenated representation:
[0102]
[0103] in, For the first The balance loss of each original feature, For the sample The square of the weights, The original features have an indicator factor, and the global original feature set is composed of the local feature matrices of each client. The features in each column are logically pieced together;
[0104] S42. Jointly optimize the global objective based on the balance loss:
[0105]
[0106] in, The overall objective function is to achieve global sample distribution balance. For global sample weights, The regularization coefficient is... For Hadamard product, The global total feature dimension;
[0107] S43. Optimize G iteratively using the gradient method. When the preset iteration number T is reached, or... Stop when convergence occurs and output the global sample weights.
[0108] Furthermore, S5 includes the following steps:
[0109] S51. A classification task that predicts the label matrix Y held locally by the active party based on the global sample weights, using regularized weighted logistic regression:
[0110]
[0111] in, The loss function for weighted causal effect estimation. For category The corresponding weighted causal effect coefficient, c represents the total number of target categories for the classification task. For the summation index, Indicates the first The true class label of each sample , As an indicator function, when the sample The real label equals When the condition is met, the value of this item is 1; otherwise, it is 0. For the first The transpose of the concatenated low-dimensional representation vector of each sample is the global feature vector formed by concatenating the low-dimensional features extracted by each client. for Regularization hyperparameters are used to adjust the regression coefficient matrix of the model. The degree of sparsity;
[0112] S52. Calculate low-dimensional causal importance based on the loss function estimated by weighted causal effects:
[0113]
[0114] in, For the first Causal importance scores of low-dimensional encoded features Indicates belonging to a category regression coefficient vector The first in The element corresponding to the component element, Causal weights of low-dimensional features; similarly, For the first in this vector Each component element;
[0115] S53. Output the causal importance score to the server.
[0116] Furthermore, S6 includes:
[0117] A set of low-dimensional causal indexes is obtained by threshold filtering based on low-dimensional causal importance:
[0118]
[0119] in, This is the causal threshold.
[0120] Furthermore, S7 includes the following steps:
[0121] S71. Use encoder layer weights to approximate the linearization transformation from input to low-dimensional representation of output:
[0122] ;
[0123] S72. Based on the causal low-dimensional index set and combined with linearization transformation, calculate the causal importance score for each original feature:
[0124]
[0125] in, To map back to the client through weighted path analysis Local No. The final importance score of each original feature, This is a set of causal low-dimensional indexes after client-side segmentation. Indicates the client After the weight matrices of each layer are multiplied consecutively, the product matrix containing the weights at the th layer is obtained. line, number The elements of the column, in physical terms, represent the input layer's first... The first original feature affects the output layer. The linearization of low-dimensional features affects the weights;
[0126] S73, Each client uploads data to the server. Mapping relationship with feature global index, where, Indicates the client For its local inclusion The set of importance score sequences is calculated from the original features.
[0127] Furthermore, S8 includes the following steps:
[0128] S81, All clients return a set of causal importance scores;
[0129] S82. Construct a global importance vector based on the causal importance score of each original feature and sort them, then select the top... One characteristic:
[0130]
[0131] in, For the selected feature subset, The retention ratio for features selected by the user. ; This represents the total number of original global features after multi-party splicing; This represents the floor function, which filters out the most important values from the global scope. Features;
[0132] S83, Output feature subset.
[0133] like Figure 2 As shown, a longitudinal federated causal feature selection system under distribution offset includes:
[0134] The client-side local encoder training module is used to train the encoder on the client side, obtain a low-dimensional representation, and upload the low-dimensional representation to the server.
[0135] The splicing and communication orchestration module is used to splice the low-dimensional representations of each client to obtain a spliced representation;
[0136] The global sample distribution balancing module is used to construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective, outputting global sample weights.
[0137] The weighted causal effect estimation module is used to apply regularized weighted logistic regression to classification tasks, obtain regression coefficients, and calculate low-dimensional causal importance based on the regression coefficients.
[0138] The spatial mapping and weighted path analysis module is used to obtain a set of low-dimensional causal indexes by thresholding based on low-dimensional causal importance; the low-dimensional causal importance is then fed back to the original features through weighted path analysis to calculate the causal importance score of each original feature.
[0139] The global feature selection and output module is used to construct a global importance vector based on the causal importance score of each original feature and sort it, select the top few features, and obtain and output the feature subset.
[0140] To verify the effectiveness of this invention in real-world scenarios, a cross-domain sentiment classification experiment was conducted using the Amazon product review dataset. This dataset contains reviews from four product domains: books (B), DVDs (D), electronics (E), and kitchenware (K), with approximately 2,000 reviews (half positive and half negative) in each domain. The experiment constructed 12 cross-domain tasks (e.g., B→D indicates training in domain B and testing in domain D). The features of each training set were also vertically partitioned across three clients. The core hyperparameters of the simulation experiment are shown in Table 1 below.
[0141] Table 1. Core Hyperparameter Configuration of the CDFS-VFL Method
[0142] Hyperparameters Setting value illustrate Self-encoder compression rate 0.5 The encoding dimension is 50% of the original dimension. L2,1 regularization coefficient λl21 0.0001 Controlling row sparsity of the weight matrix Globally balanced learning rate 0.005 RMSprop optimizer, 2000 iterations The equilibrium regularization coefficient λreg 0.0001 Preventing weight extremism Weighted Logistic Regression Learning Rate 0.005 RMSprop optimizer, 3000 iterations L1 regularization coefficient λl1 0.001 Promoting the sparsity of causal effects Causal threshold α 0.01 Importance threshold for screening causal representations Feature selection ratio ρ 0.4 Select 40% of the features as the final subset Number of clients K 3 Features are vertically divided into 3 clients Sample size n 3,000 Number of training samples in each experiment
[0143] On 12 cross-domain classification tasks of the Amazon product review dataset, CDFS-VFL achieved state-of-the-art performance across all three metrics in 11 / 12 tasks, respectively, when using LR and MLP classifiers. This result further validates the effectiveness of the causal feature selection method of this invention in real-world OOD scenarios: through autoencoder representation learning and causal effect estimation, CDFS-VFL can identify domain-invariant causal features across domains, avoiding cross-domain generalization failures caused by baseline methods capturing domain-specific statistical correlations.
[0144] like Figure 3 and Figure 4 As shown, the longitudinal federated causal feature selection method under distribution offset (CDFS-VFL) proposed in this invention demonstrates significantly better overall performance than the five existing state-of-the-art baseline methods on both synthetic and real OOD datasets; the experimental results fully verify the effectiveness of the following innovations:
[0145] (1) Privacy-preserving low-dimensional representation learning based on autoencoder L2,1 regularization preserves sufficient causal information while protecting the original data of all parties;
[0146] (2) The global sample equalization mechanism effectively eliminates the spurious correlations introduced by sample selection bias through sample reweighting, providing a reliable basis for subsequent causal effect estimation;
[0147] (3) The weighted path analysis based on spatial mapping accurately transmits the causal representation to the original feature space. The selected feature subset maintains causal invariance under different data distributions and has excellent OOD generalization ability.
[0148] 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.
[0149] 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.
[0150] 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.
[0151] 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 method for selecting longitudinal federated causal features under distribution offset, characterized in that, Includes the following steps: S1. Initialize the participant set to obtain the local feature matrix; S2. The client trains the encoder to obtain a low-dimensional representation and uploads the low-dimensional representation to the server. S3. Concatenate the low-dimensional representations of each client to obtain the concatenated representation; S4. Construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective to output the global sample weights; S5. Apply regularized weighted logistic regression to the classification task to obtain regression coefficients and calculate low-dimensional causal importance based on the regression coefficients; S6. Obtain a set of low-dimensional causal indexes by threshold filtering based on low-dimensional causal importance; S7. Use weighted path analysis to backpropagate the low-dimensional causal importance to the original features and calculate the causal importance score for each original feature; S8. Construct a global importance vector based on the causal importance score of each original feature and sort them. Select the top few features to obtain and output the feature subset. S1 includes the following steps: S11, Input the set of participating client clients The set of participating client clients includes the active client. hold Passive client hold ; in, For client-side local feature matrix, For local tag matrix, The total number of participating client groups. For the client; S12. Let the total characteristic number be... in For the client The local original feature dimension held; S2 includes the following steps: S21. Input the local feature matrix of each client; S22. Train the encoder for each client based on the local feature matrix of each client. and decoder Optimization target in, For row Regular expression The regularization coefficient is... Represents the weight matrix row index, Represents the weight matrix The first in row vectors For the client The autoencoder reconstruction loss function, This represents the total number of samples. For the client Self-encoder The weight matrix of the layer, For the client The total number of layers in a local autoencoder network model. For the layer index of the autoencoder network layer, and ; Output low-dimensional representation ; S23. Each client sends a low-dimensional representation to the server.
2. The method for selecting longitudinal federated causal features under distribution offset according to claim 1, characterized in that: The splicing is represented as .
3. The method for selecting longitudinal federated causal features under distribution offset according to claim 2, characterized in that: S4 includes the following steps: S41. Construct a balanced loss for each original feature in the global original feature set based on the concatenated representation: in, For the first The balance loss of each original feature, For the sample The square of the weights, The original features have an indicator factor, and the global original feature set is composed of the local feature matrices of each client. The features in each column are logically pieced together; S42. Jointly optimize the global objective based on the balance loss: in, The overall objective function is to achieve global sample distribution balance. For global sample weights, The regularization coefficient is... For Hadamard product, The global total feature dimension; S43. Optimize G iteratively using the gradient method. When the preset iteration number T is reached, or... Stop when convergence occurs and output the global sample weights.
4. The method for selecting longitudinal federated causal features under distribution offset according to claim 3, characterized in that: S5 includes the following steps: S51. A classification task that predicts the label matrix Y held locally by the active party based on the global sample weights, using regularized weighted logistic regression: in, The loss function for weighted causal effect estimation. For category The corresponding weighted causal effect coefficient, c represents the total number of target categories for the classification task. For the summation index, Indicates the first The true class label of each sample , As an indicator function, when the sample The real label equals When the condition is met, the value of this item is 1; otherwise, it is 0. For the first The transpose of the concatenated low-dimensional representation vector of each sample is the global feature vector formed by concatenating the low-dimensional features extracted by each client. for Regularization hyperparameters are used to adjust the regression coefficient matrix of the model. The degree of sparsity; S52. Calculate low-dimensional causal importance based on the loss function estimated by weighted causal effects: in, For the first Causal importance scores of low-dimensional encoded features Indicates belonging to a category regression coefficient vector The first in The element corresponding to the component element, Causal weights of low-dimensional features; similarly, For the first in this vector Each component element; S53. Output the causal importance score to the server.
5. The method for selecting longitudinal federated causal features under distribution offset according to claim 4, characterized in that: S6 includes: A set of low-dimensional causal indexes is obtained by threshold filtering based on low-dimensional causal importance: in, This is the causal threshold.
6. The method for selecting longitudinal federated causal features under distribution offset according to claim 5, characterized in that: S7 includes the following steps: S71. Use encoder layer weights to approximate the linearization transformation from input to low-dimensional representation of output: ； S72. Based on the causal low-dimensional index set and the linearization transformation, calculate the causal importance score for each original feature: in, To map back to the client through weighted path analysis Local No. The final importance score of each original feature, This is a set of causal low-dimensional indexes after client-side segmentation. Indicates the client After the weight matrices of each layer are multiplied consecutively, the product matrix containing the weights at the th layer is obtained. line, number The elements of the column, in physical terms, represent the input layer's first... The first original feature affects the output layer. The linearization of low-dimensional features affects the weights; S73, Each client uploads data to the server. Mapping relationship with feature global index, where, Indicates client For its local inclusion The set of importance score sequences is calculated from the original features.
7. The method for selecting longitudinal federated causal features under distribution offset according to claim 6, characterized in that: S8 includes the following steps: S81, All clients return a set of causal importance scores; S82. Construct a global importance vector based on the causal importance score of each original feature and sort them, then select the top... One characteristic: in, For the selected feature subset, The retention ratio for features selected by the user. ; This represents the total number of original global features after multi-party splicing; This represents the floor function, which filters out the most important values from the global scope. Features; S83, Output feature subset.
8. A longitudinal federated causal feature selection system under distribution offset, employing the longitudinal federated causal feature selection method under distribution offset according to any one of claims 1-7, characterized in that, include: The client-side local encoder training module is used to train the encoder on the client side, obtain a low-dimensional representation, and upload the low-dimensional representation to the server. The splicing and communication orchestration module is used to splice the low-dimensional representations of each client to obtain a spliced representation; The global sample distribution balancing module is used to construct a balanced loss for each original feature based on the concatenated representation and jointly optimize the global objective, outputting global sample weights. The weighted causal effect estimation module is used to apply regularized weighted logistic regression to classification tasks, obtain regression coefficients, and calculate low-dimensional causal importance based on the regression coefficients. The spatial mapping and weighted path analysis module is used to obtain a set of low-dimensional causal indexes by threshold filtering based on low-dimensional causal importance. The low-dimensional causal importance is backpropagated to the original features through weighted path analysis, and the causal importance score of each original feature is calculated. The global feature selection and output module is used to construct a global importance vector based on the causal importance score of each original feature and sort it, select the top few features, and obtain and output the feature subset.