Vertical Federated Softmax Regression Method and System Supporting Multiple Participants

Abstract

The present invention belongs to the technical field related to federated learning, and particularly relates to a vertical federated Softmax regression method and system supporting multiple participants. According to the vertical distribution law of the data set, participants and a coordinator for assisting the participants in modeling as a third party are set. Among them, the participants include: an active party with labeled samples and passive parties with the remaining unlabeled samples; the coordinator and the active party create a public-private key pair through homomorphic encryption and send the public keys to each other respectively; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties; the Softmax model is jointly trained by the active party with labeled samples and the passive parties with unlabeled samples, and the coordinator is used to complete the secure transmission of the intermediate calculation results between the active party and the passive parties during the joint training. Each passive party can only obtain the finally trained model parameters from the coordinator and cannot obtain the gradient values during the iteration process. The present invention can realize the joint Softmax multi-classification modeling of multiple participants on the premise of protecting the privacy of the original data of the participants, improve the model training efficiency, and facilitate the application in actual scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field related to federated learning, and particularly relates to a vertical federated Softmax regression method and system supporting multiple participants. Background Technique

[0002] With the advent of the big data era, machine learning has witnessed a booming development in the field of artificial intelligence applications. Data is the guarantee for these machine learning algorithms to achieve good results in various tasks, but at the same time, it has also become a bottleneck. In practical applications, large-scale data is scattered in different companies or departments. Due to issues such as commercial competition and privacy policies, data cannot be shared or integrated with each other and exists in the form of "data silos". Under this background, machine learning models trained solely based on the data owned by each party cannot achieve satisfactory results, while the centralized learning method of first aggregating the data of multiple parties and then training the model has the risk of privacy data leakage. How to enable multiple parties to collaboratively train a machine learning model with good performance using the data they possess while ensuring the non-disclosure of private data is a hot issue in the current academic community.

[0003] Federated learning can enable multiple data participants to collaboratively conduct machine learning training on the premise of protecting data privacy and meeting the requirements of relevant privacy laws and regulations. According to different data partitioning methods, federated learning can be further divided into horizontal federated learning, vertical federated learning, and federated transfer learning. Among them, vertical federated learning is applicable to scenarios where the data sets owned by different parties share the same sample space but have different feature spaces, and the training data is data with the same samples for multiple parties but the corresponding features are not completely the same. Compared with traditional machine learning methods, vertical federated learning can break down data barriers, expand the feature system, and achieve joint modeling between different enterprises while ensuring data security, thereby improving the model performance.

[0004] Most of the existing vertical federated logistic regression methods currently only support collaborative modeling between two participants and cannot be directly applied or simply extended to the case of multiple participants; most of the existing methods are limited to binary classification tasks and cannot meet the widespread multi-classification requirements in the real world. Summary of the Invention

[0005] Therefore, the present invention provides a vertical federated Softmax regression method and system supporting multiple participants, which can realize joint Softmax multi-classification modeling of multiple participants on the premise of protecting the privacy of the original data of the participants, improve the model training efficiency, and facilitate practical scenario applications.

[0006] According to the design scheme provided by the present invention, a vertical federated Softmax regression method supporting multiple participants is provided, including the following content:

[0007] Set up participants and a coordinator that assists the participants in modeling as a third party according to the vertical distribution law of the dataset. Among them, the participants include: an active party with labeled samples and a passive party with the remaining unlabeled samples.

[0008] The coordinator and the active party create a public-private key pair through homomorphic encryption and send the public keys to each other respectively; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties.

[0009] Use the active party with labeled samples and the passive party with unlabeled samples to jointly train the Softmax model, and use the coordinator in the joint training to complete the secure transfer of the intermediate calculation results between the active party and the passive party. Each passive party can only obtain the finally trained model parameters from the coordinator and cannot obtain the gradient values during the iteration process.

[0010] As the vertical federated Softmax regression method supporting multiple participants in the present invention, further, during the joint training of the Softmax model, the coordinator homomorphically encrypts the initialized Softmax model parameters of the passive parties using the public key of the active party and sends the encrypted model parameters to the corresponding passive parties; each passive party operates on the local data and the received model parameters to obtain the encrypted local calculation results and feeds them back to the active party; the active party decrypts the local calculation results fed back by the passive parties using its own private key, obtains the residual matrix by using the operation results of the fed-back local calculation results of the passive parties, its own model parameters, and local data, and encrypts the residual matrix using the public key of the coordinator and sends the encrypted result to each passive party; the passive party combines its local data and the encrypted result of the residual matrix sent by the active party to obtain the encrypted gradient value and sends it to the coordinator; the coordinator decrypts the gradient value using its own private key to obtain the gradient plaintext and updates the Softmax model parameters of the passive parties, repeating the iteration multiple times until the maximum iteration number is reached or the loss value does not decrease continuously for multiple iterations.

[0011] As the vertical federated Softmax regression method supporting multiple participants in the present invention, further, during the joint training, it is set that there are n participants, denoted as p1, p2, …, p n ; the data in the dataset is vertically distributed among the participants, and the Softmax model parameters are also correspondingly distributed among the participants. Select participant p1 as the active party and the remaining participants as the passive parties.

[0012] As the vertical federated Softmax regression method supporting multiple participants in the present invention, further, during the joint training, it is set that the corresponding Softmax model parameter dimensions of all participants are d×k, where d is the number of features owned by the participants and k is the total number of categories.

[0013] As the vertical federated Softmax regression method of the present invention supporting multiple participating parties, further, in the joint training, by constructing the objective loss function When the loss value does not decrease or reaches the preset iteration threshold, stop the joint training, and the coordinator sends the trained model parameters to the passive parties respectively, where Sum(·) represents the sum of all elements of the matrix, represents the element-wise multiplication between matrices, Y represents the label matrix, P represents the predicted probability matrix, and θ represents the training parameters.

[0014] As the vertical federated Softmax regression method of the present invention supporting multiple participating parties, further, for the encrypted local calculation results fed back by all passive parties, the active party decrypts to obtain the plaintext and obtains the residual matrix by executing the preset local iteration algorithm.

[0015] As the vertical federated Softmax regression method of the present invention supporting multiple participating parties, further, in the preset local iteration algorithm, the active party first operates its own model parameters with its local data to obtain its local calculation result; then, aggregates its local calculation result with the local calculation results fed back by all passive parties to obtain the model predicted probability matrix, and combines the label data to obtain the predicted residual matrix; then combines the residual matrix with its local data to obtain the gradient value and updates the local parameters; repeats the above steps, and terminates the local iteration process by judging whether the preset iteration termination condition is reached to output all the residual matrices obtained during the iteration process.

[0016] As the vertical federated Softmax regression method of the present invention supporting multiple participating parties, further, the iteration termination condition is the set maximum number of iterations.

[0017] Further, the present invention also provides a vertical federated Softmax regression system supporting multiple participating parties, including: a setting module, an initialization module, and a joint training module, where,

[0018] The setting module is used to set the participating parties and the coordinator that acts as a third party to assist the participating parties in modeling according to the vertical distribution law of the data set, where the participating parties include: the active party with labeled samples and the passive parties with the remaining unlabeled samples;

[0019] The initialization module is used for the coordinator and the active party to create public and private key pairs through homomorphic encryption and send the public keys to each other respectively; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties;

[0020] A joint training module is used to jointly train a Softmax model using an active party with labeled samples and a passive party with unlabeled samples, and in the joint training, a coordinator is used to complete the secure transfer of model parameter data between the active party and the passive party. Each passive party only obtains its own model parameter data through the coordinator.

[0021] Advantages of the present invention:

[0022] In the Softmax regression in vertical federated learning, the present invention uses multiple passive parties and an active party as participants for joint training, and a coordinator is used to assist in updating the model parameters of the passive parties. The passive parties only obtain their own model parameters after the final training, and do not obtain the gradient values in each joint training, which can ensure the privacy of their data when both the participants and the coordinator are semi-honest, and meet the multi-class joint modeling of multiple participants; moreover, only through one communication, multiple model parameter updates can be performed locally by the active party, improving the model training efficiency and facilitating practical scenario applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the vertical federated Softmax regression process supporting multiple participants in the embodiment;

[0024] Figure 2 It is a schematic diagram of the vertical federated Softmax regression algorithm process in the embodiment;

[0025] Figure 3 It is a schematic diagram of the local iteration process of the active party in the embodiment;

[0026] Figure 4 It is a schematic diagram of the model accuracy obtained by the algorithm in this case with different numbers of participants on the Digits and Create-dataset data sets in the embodiment;

[0027] Figure 5 It is a schematic diagram of the comparison of the change of the loss value when the local iteration times s takes different values on the Satimage data set in the embodiment;

[0028] Figure 6 It is a schematic diagram of the comparison of the change of the loss value when the local iteration times s takes different values on the Movement-libras data set in the embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the drawings and technical solutions.

[0030] In the embodiment of the present invention, refer to Figure 1 As shown, a vertical federated Softmax regression method supporting multiple participants is provided, including:

[0031] S001. Set up participants and a coordinator that acts as a third party to assist the participants in modeling according to the vertical distribution law of the data set. Among them, the participants include: an active party with labeled samples and a passive party with the remaining unlabeled samples.

[0032] S002. The coordinator and the active party create a public-private key pair through homomorphic encryption and send the public key to each other. The active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties.

[0033] S003. Use the active party with labeled samples and the passive party with unlabeled samples to jointly train the Softmax model, and use the coordinator in the joint training to complete the secure transfer of the local calculation results between the active party and the passive party. Each passive party can only obtain the finally trained model parameters from the coordinator and cannot obtain the gradient values during the iteration process.

[0034] In the Softmax regression in vertical federated learning, use multiple passive parties and an active party as participants for joint training, and use a coordinator to assist in updating the model parameters of the passive parties. The passive parties only get their own finally trained model parameters and do not obtain the gradient values in each joint training, which can ensure the privacy of their data when both the participants and the coordinator are semi-honest, and meet the multi-class joint modeling of multiple participants.

[0035] Furthermore, in the joint training of the Softmax model in the embodiments of this case, the coordinator homomorphically encrypts the initialized Softmax model parameters of the passive parties using the public key of the active party and sends the encrypted model parameters to the corresponding passive parties. Each passive party operates on the local data and the received model parameters to obtain the encrypted local calculation results and feeds them back to the active party. The active party decrypts the local calculation results fed back by the passive parties using its own private key, obtains the residual matrix by using the fed-back local calculation results of the passive parties and the operation results of its own model parameters and local data, encrypts the residual matrix using the public key of the coordinator, and sends the encrypted result to each passive party. The passive party combines its local data and the encrypted result of the residual matrix sent by the active party to obtain the encrypted gradient value and sends it to the coordinator. The coordinator decrypts the gradient value using its own private key to obtain the gradient plaintext and updates the Softmax model parameters of the passive parties, repeating the iteration multiple times until the maximum iteration number is reached or the loss value does not decrease continuously for multiple iterations.

[0036] The coordinator and the active party create a key pair and send the public key to each other. The active party initializes its own model parameters, and the coordinator initializes the model parameters of all passive parties. Among them, the coordinator is a third party assisting in modeling, the active party is the labeled participating party, and there is only one. The passive parties are the unlabeled participating parties, and there can be multiple. The coordinator encrypts the model parameters of the passive parties with the public key of the active party and sends them to the corresponding passive parties. Each passive party calculates the encrypted local calculation result in combination with the local data and sends the result to the active party. The active party decrypts to obtain the local calculation results of the passive parties, performs multiple local iterations, encrypts all the obtained residuals with the public key of the coordinator, and sends them to each passive party. Each passive party calculates the encrypted gradient value in combination with its local data and the encrypted residuals and sends it to the coordinator. The coordinator decrypts and updates the corresponding parameters. Iterative training is performed until a preset stop condition is met to complete the training. The coordinator sends the trained parameters to the corresponding passive parties, and each passive party can only obtain its own model parameters.

[0037] In the embodiments of this case, further, for the local calculation results fed back by all passive parties, the active party obtains the residual matrix by executing a preset local iteration algorithm. In the preset local iteration algorithm, the active party can first operate its own model parameters with its local data to obtain its local calculation result; then, aggregate its local calculation result with the local calculation results fed back by all passive parties to obtain the model prediction probability matrix, and combine the label data to obtain the prediction residual matrix; then combine the residual matrix with its local data to obtain the gradient value and update the local parameters; repeat the above steps, and terminate the local iteration process by judging whether the preset iteration cut-off condition is reached to output all the residual matrices obtained during the iteration process.

[0038] There is a data set one-hot label matrix In the column vectors of Y, only one element takes the value of 1, and the other elements take the value of 0. Assume that the data is vertically distributed among n participating parties p1, p2,..., p n where the corresponding data is Softmax model parameters are also distributed among n participating parties. The label matrix Y belongs to the first participating party p1. The p1 is called the active party, and the remaining participating parties are called passive parties. The coordinator is denoted as C. Refer to Figure 2 The process of the joint training algorithm shown can be specifically designed as follows:

[0039] S101. The coordinator C and the active party p1 create public keys and private keys through homomorphic encryption, and respectively obtain pk C and sk C , and Send the created public key to the other party; the initiator p1 initializes θ 1 , and the coordinator C initializes all the passive party parameters θ 2 , θ 3 ,…, θ n .

[0040] S102. The coordinator C transposes the passive party parameter and encrypts it with the public key of the initiator p1 to obtain where represents the result after homomorphic encryption with the public key of p1. The coordinator C sends to the corresponding passive party, and the corresponding passive party p i (i ∈ [2, n]) can only obtain its own encrypted model parameter . Since there is no private key for decryption, no passive party can decrypt the plaintext.

[0041] S103. Each passive party p i (i ∈ [2, n]) multiplies the received encrypted parameter by the local data X i to obtain . Due to the property of homomorphic encryption, the calculated result is still the encrypted matrix after homomorphic encryption with the public key of p1. Each passive party p i (i ∈ [2, n]) sends the obtained to the initiator p1.

[0042] S104. The initiator p1 decrypts to obtain the local calculation result of the passive party, combines it with its local result, and iterates locally s times to obtain s residual matrices (Y - P) T , and encrypts the obtained s residual matrices (Y - P) T with the public key pk C of the coordinator C and sends them to each passive party, where P is the calculated predicted probability matrix, which has the same dimension as Y.

[0043] S105. Each passive party p i (i ∈ [2, n]) combines its local data X i with the s encrypted residual matrices received to obtain s encrypted gradients, and then sends the obtained encrypted gradients to the coordinator C; the coordinator decrypts them to obtain the plaintext matrix and updates the corresponding model parameters.

[0044] Each passive party p i (i ∈ [2, n]) multiplies its local data X i with the s encrypted residual matrices received to obtain s encrypted gradients Due to the property of homomorphic encryption, the calculated result is still encrypted with the public key pk of the coordinator C C The encrypted matrix after homomorphic encryption. Each passive party p i (i ∈ [2, n]) will obtain s encrypted gradients and send them to the coordinator C.

[0045] For any passive party p i (i ∈ [2, n]), the coordinator C decrypts the s encrypted gradients sent by it and locally performs s updates In this way, the parameters of the active party p1 and all passive parties have been updated s times.

[0046] S106. Repeat steps S102 - S105 until the preset number of iterations is reached or the calculated loss value L(θ) does not decrease for several consecutive iterations, and then stop training. The coordinator C sends the trained parameters θ 2 , θ 3 , …, θ n to the passive parties p2, p3, …, p n respectively. Each passive party can only obtain its own model parameters.

[0047] Among them, as shown in Figure 3 , the specific process of the local iteration of the active party p1 in S104 can be designed as follows:

[0048] Step 1: The active party p1 uses its private key to decrypt and obtains The active party p1 starts s local iterations;

[0049] Step 2: The active party p1 multiplies the transpose of the model parameter θ 1 by the data to obtain the local calculation result (θ 1 ) T X 1 . Combining with the local calculation results of the passive parties, it aggregates to obtain and further obtains the predicted probability matrix P = Pro(θ T X) and the residual matrix (Y - P) T . Among them, the dimensions of the probability matrix and the residual matrix can be set to k × m, where m is the total number of training samples,

[0050] θ T X = (w1, w2, …, w m ), Pro(θ T X) = [Softmax(w1), Softmax(w2), …, Softmax(w m )]

[0051] The upcoming θ with dimension k×m T Each column in X is input into the Softmax function. In the obtained probability matrix P, each column corresponds to the probability that a sample is predicted to be of k classes. The elements in any column vector range from [0,1], and the sum of all elements in the same column is 1.

[0052] Step 3: The active party p1 calculates the gradient values corresponding to the local parameters Update the gradient

[0053] Step 4: The active party p1 determines whether it enters the local iteration for the first time. If so, it calculates the loss value where Sum(·) represents the sum of all elements in the matrix, represents the element-by-element multiplication of two matrices;

[0054] Step 5: If the preset number of iterations s is reached, the active party p1 encrypts the s residual matrices (Y - P) calculated during the iteration process T using the public key pk of the coordinator C C to obtain and sends it to each passive party. If the preset number of iterations s is not reached, it jumps to Step 2. Among them, since the passive party does not have the private key sk C , it cannot decrypt the plaintext residual matrix.

[0055] Furthermore, based on the above method, an embodiment of the present invention also provides a vertical federated Softmax regression system supporting multiple participating parties, including: a setting module, an initialization module, and a joint training module, where,

[0056] The setting module is used to set the participating parties and the coordinator that acts as a third party to assist the participating parties in modeling according to the vertical distribution law of the data set. Among them, the participating parties include: the active party with labeled samples and the passive parties with the remaining unlabeled samples;

[0057] The initialization module is used for the coordinator and the active party to create public-private key pairs through homomorphic encryption and send the public keys to each other; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties;

[0058] The joint training module is used to jointly train the Softmax model using the active party with labeled samples and the passive parties with unlabeled samples, and use the coordinator to complete the secure transfer of model parameter data between the active party and the passive parties during the joint training. Each passive party only obtains its own model parameter data through the coordinator.

[0059] To verify the effectiveness of the solution in this case, the following further explains with experimental data:

[0060] Figure 4 The model accuracies obtained by the algorithm of this case for different numbers of participating parties on the Digits and Create-dataset data sets. As the number of passive parties participating increases, the prediction accuracy of the model is continuously improving, indicating that vertical federated learning can expand the feature system and improve the model accuracy.

[0061] Figure 5 and Figure 6 are the graphs of the loss value changes of the corresponding solutions for different local iteration times on the Satimage and Movement-libras data sets. As the local iteration times increase, the model can converge faster and train a model with better performance under the same number of iterations.

[0062] Unless otherwise specifically stated, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.

[0063] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0064] The units and method steps of each example described in combination with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation is not considered to exceed the scope of the present invention.

[0065] Those of ordinary skill in the art can understand that all or part of the steps in the above methods can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disc, etc. Optionally, all or part of the steps of the above embodiments can also be implemented using one or more integrated circuits. Correspondingly, each module / unit in the above embodiments can be implemented in the form of hardware or in the form of a software functional module. The present invention is not limited to any specific form of the combination of hardware and software.

[0066] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the technical field can still modify the technical solutions recorded in the foregoing embodiments or easily conceive of changes, or perform equivalent replacements on some of the technical features; and these modifications, changes or replacements 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, and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A vertical federated Softmax regression method supporting multiple participants, characterized in that, It includes the following content: Set the participating parties and the coordinator that acts as a third party to assist the participating parties in modeling according to the vertical distribution law of the dataset. Among them, the participating parties include: the active party with labeled samples and the passive party with the remaining unlabeled samples; The coordinator and the active party create a public-private key pair through homomorphic encryption and send the public key to each other; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties; Use the active party with labeled samples and the passive party with unlabeled samples to jointly train the Softmax model, and use the coordinator in the joint training to complete the secure transmission of the intermediate calculation results between the active party and the passive party. And each passive party obtains the finally trained model parameters from the coordinator. Among them, in the joint training of the Softmax model, the coordinator homomorphically encrypts the initialized Softmax model parameters of the passive party using the public key of the active party and sends the encrypted model parameters to the corresponding passive party; each passive party operates on the local data and the received model parameters to obtain the encrypted local calculation result and feeds it back to the active party; the active party decrypts the local calculation result fed back by the passive party using its own private key, combines the fed-back local calculation result of the passive party with the operation results of its own model parameters and local data to obtain the residual matrix, and encrypts the residual matrix using the public key of the coordinator and sends the encrypted result to each passive party; the passive party combines its local data and the encrypted result of the residual matrix sent by the active party to obtain the encrypted gradient value and sends it to the coordinator; the coordinator decrypts the gradient value using its own private key to obtain the gradient plaintext and updates the Softmax model parameters of the passive party, repeating the iteration multiple times until the maximum iteration number is reached or the loss value does not decrease continuously for multiple iterations.

2. The vertical federated Softmax regression method for supporting multiple participants according to claim 1, characterized in that In the joint training, there are n participating parties, denoted as p1, p2, …, p n ; the data in the dataset is vertically distributed among the participating parties, and the Softmax model parameters are also correspondingly distributed among the participating parties. The participating party p1 is selected as the active party, and the remaining participating parties are passive parties.

3. The vertical federated Softmax regression method supporting multiple participants according to claim 2, characterized in that In the joint training, set the dimension of the corresponding Softmax model parameters of all participating parties to d×k, where d is the number of features owned by the participating party and k is the total number of categories.

4. The vertical federated Softmax regression method supporting multiple participants according to claim 1, characterized in that, In joint training, by constructing a target loss function When the loss value does not decrease or reaches a preset iteration threshold, stop the joint training, and the coordinator sends the trained model parameters to the passive party respectively. Among them, Sum(·) represents the sum of all elements of the matrix represents the element-by-element multiplication between matrices, Y represents the label matrix, P represents the predicted probability matrix, and θ represents the training parameters 5. The vertical federated Softmax regression method supporting multiple participants according to claim 1, wherein For the encrypted local calculation results fed back by all passive parties, the active party decrypts to obtain the plaintext and obtains the residual matrix by executing a preset local iteration algorithm.

6. The vertical federated Softmax regression method supporting multiple participants according to claim 4, wherein In the preset local iteration algorithm, the active party first operates on its own model parameters and its local data to obtain its local calculation result; then, aggregates its local calculation result with the local calculation results fed back by all passive parties to obtain the model prediction probability matrix, and combines the label data to obtain the prediction residual matrix; then combines the residual matrix with its local data to obtain the gradient value and updates the local parameters; Repeat the above steps and terminate the local iteration process by judging whether the preset iteration cut-off condition is reached to output all the residual matrices obtained during the iteration.

7. The vertical federated Softmax regression method supporting multiple participants according to claim 4 or 5, characterized in that The iteration termination condition is the set maximum iteration number.

8. A vertical federated Softmax regression system supporting multiple participants, characterized in that, It includes: a setting module, an initialization module, and a joint training module, where The setting module is used to set the participating parties and the coordinator that acts as a third party to assist the participating parties in modeling according to the vertical distribution law of the dataset. Among them, the participating parties include: the active party with labeled samples and the passive party with the remaining unlabeled samples; An initialization module, which is used for the coordinator and the active party to create a public-private key pair through homomorphic encryption and send the public key to the other party respectively; the active party initializes its own Softmax model parameters, and the coordinator initializes the Softmax model parameters of all passive parties; A joint training module, which is used for jointly training the Softmax model by using the active party with labeled samples and the passive parties with unlabeled samples, and using the coordinator to complete the secure transmission of intermediate calculation results between the active party and the passive parties during the joint training. Each passive party obtains the finally trained model parameters from the coordinator. Among them, during the joint training of the Softmax model, the coordinator uses the public key of the active party to homomorphically encrypt the initialized Softmax model parameters of the passive parties and sends the encrypted model parameters to the corresponding passive parties; each passive party operates on the local data and the received model parameters to obtain the encrypted local calculation results and feeds them back to the active party; the active party decrypts the local calculation results fed back by the passive parties by using its own private key, obtains the residual matrix by using the operation results of the fed-back local calculation results of the passive parties, its own model parameters and local data, and encrypts the residual matrix by using the public key of the coordinator and sends the encrypted result to each passive party; the passive party combines its local data and the encrypted result of the residual matrix sent by the active party to obtain the encrypted gradient value and sends it to the coordinator; the coordinator decrypts the gradient value by using its own private key to obtain the plaintext gradient and updates the Softmax model parameters of the passive parties, and repeats the iteration multiple times until the maximum iteration number is reached or the loss value does not decrease continuously for multiple iterations.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method steps described in any one of claims 1 to 7 are implemented.

Images