A causal inference matrix factorization recommendation method based on differential privacy

Abstract

This invention relates to a causal inference matrix factorization recommendation method based on differential privacy, belonging to the fields of computer recommendation systems and information security. The method specifically includes: transforming the user's implicit feedback data into an implicit feedback matrix with values ​​of 0 or 1; constructing an objective function L; and applying a recommendation algorithm based on causal inference to matrix P. int P con Sum matrix Q int Q con Solve and store the user latent factor matrix P. int and P con The obtained user latent factor matrix Q int Q con Re-initialize randomly and substitute the results back into the objective function L, rewriting the objective function as L(Q). int |D) and L(Q) con |D), to obtain the latent factor matrix Q of the project. int Q con The objective function is to use gradient descent on the latent factor matrix Q. int Q con To solve this, consider the latent factor gradient for each project and perturb the gradient using a small amount of Laplace noise based on different privacy budgets; for the objective function L(Q int |D) and L(Q) con |D) Gradient descent is performed to obtain the matrix. This invention has good privacy protection and model accuracy.

Description

Technical Field

[0001] This invention belongs to the fields of computer recommendation systems and information security, and relates to a causal inference matrix factorization recommendation method based on differential privacy. Background Technology

[0002] Using causal matrix factorization (CFB) in recommender systems is a common and effective technique for recommending to target users. By modeling implicit user feedback data, it can better personalize recommendations and improve the user experience. Implicit feedback data includes various types of user behavior, such as purchase history, browsing history, and webpage click-through rates. However, from the perspective of protecting user privacy, causal matrix factorization relies on learning from a large amount of implicit user feedback data. Releasing these filtering recommendation models learned from large amounts of user privacy data inevitably poses a risk of leaking user privacy. Furthermore, causal inference-based CFB decomposes the implicit user feedback matrix into multiple user matrices and item matrices based on different reasons. Different item matrices have different impacts on user privacy; therefore, to avoid compromising model performance, item matrices generated for different reasons should receive different levels of protection.

[0003] Differential privacy is a privacy protection framework capable of quantifying the level of privacy protection. Under this framework, changes to individual data points have a minimal impact on the processing results of the dataset, and attackers cannot infer the privacy information of a particular data sample from publicly available datasets. Furthermore, differential privacy assumes that attackers possess maximum background knowledge—that is, they control all data except the target data. Under this maximum background knowledge assumption, differential privacy does not need to consider any information that attackers might possess and can still protect the privacy of individual data points. In addition, differential privacy, based on mathematical and statistical knowledge, provides a rigorous definition of privacy protection and proposes a quantitative evaluation method for the level of privacy protection, making the privacy protection levels of datasets comparable under different parameter processing conditions. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a causal inference matrix factorization recommendation method based on differential privacy, so as to achieve a good balance between security and usability in collaborative filtering recommendation models.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A causal inference matrix factorization recommendation method based on differential privacy includes the following steps:

[0007] S1: Implicit feedback data of users to the project is represented by an implicit feedback matrix with values ​​of 0 or 1. 0 indicates non-positive feedback from users to the project, and 1 indicates positive feedback from users to the project.

[0008] S2: Randomly initialize matrix P int P con Q int Q con ;P int It is a latent factor matrix of user interests. Representation matrix P int The u-th row represents the latent interest factor vector of the u-th user; P int It is a user-following latent factor matrix. Representation matrix P con The u-th row represents the latent conformity factor vector of the u-th user; Q int It is a latent factor matrix of project interests. Representation matrix Q int The i-th row represents the latent interest factor vector of the i-th item; Q con It is the project's hidden factor matrix. Representation matrix Q con The i-th row represents the latent factor vector of the i-th item; It is a noisy latent factor matrix of project interests. Representation matrix The i-th row represents the latent factor vector of the interest addition noise for the i-th project; d represents the dimension of the latent factor vector; It is a noisy latent factor matrix of project interests. Representation matrix The i-th row represents the latent factor vector of the i-th item with added noise; d represents the dimension of the latent factor vector.

[0009] S3: Divide user clicks into two cases. Case 1: The user clicked on a less popular item. In this case, it can be inferred that the user has a high interest in the item, and loss functions can be constructed separately for user interest and conformity reasons. and Use Bayesian personalized ranking to maximize the score difference between the two. Scenario 2: The user clicked on a highly popular item. In this case, it's impossible to infer the user's true interest, so a loss function can only be constructed based on herd mentality. Bayesian feasibility ranking is used to maximize the score difference between the two. Finally, a click loss function is constructed based on the actual click situation. Therefore, it can be based on as well as The loss function L of the model is solved by P. int P conQ int and Q con , will P int and P con The user matrix P and Q are obtained by concatenation. int and Q con The project matrix Q is obtained by concatenating the components.

[0010] S4: Convert the matrices P and P obtained in S3. int and P con Fixed, randomly initialized matrix Q int and Q con Substitute into the loss function L and recalculate matrix Q int and Q con The loss function L is used to obtain information about matrix Q. int and Q con gradient and And calculate the sensitivity of datasets D and D', and calculate the sensitivity assigned to Q. int and Q con The privacy budget is used to sample noise from the Laplace distribution and apply it to the gradient. and By perturbing the gradient, we obtain a noisy gradient. and

[0011] S5: Using the gradient obtained after perturbation, perform gradient descent on the loss function L to obtain the final matrix. and Will and By splicing together, a differential privacy-preserving project matrix is ​​obtained.

[0012] S6: According to the formula Make predictions, sort the prediction results of non-positive feedback items in the implicit feedback matrix described in S1, and recommend the TOP-N items to the user.

[0013] Random initialization matrix P int P con Q int Q con ;P int It is a latent factor matrix of user interests. Representation matrix P int The u-th row represents the latent interest factor vector of the u-th user; P int It is a user-following latent factor matrix. Representation matrix P con The u-th row represents the latent conformity factor vector of the u-th user; Q int It is a latent factor matrix of project interests. Representation matrix Q int The i-th row represents the latent interest factor vector of the i-th item; Q con It is the project's hidden factor matrix. Representation matrix Q con The i-th row represents the latent factor vector of the i-th item; It is a noisy latent factor matrix of project interests. Representation matrix The i-th row represents the latent factor vector of the interest addition noise for the i-th project; d represents the dimension of the latent factor vector; It is a noisy latent factor matrix of project interests. Representation matrix The i-th row represents the latent factor vector of the i-th item with added noise; d represents the dimension of the latent factor vector.

[0014] Furthermore, in step S3, an objective function L is constructed, and a recommendation algorithm based on Bayesian personalized ranking is used to solve for matrix P. int P con Q int and Q con And save matrix P int P con Specifically, it includes the following steps:

[0015] S31: Decompose the implicit feedback matrix into four low-dimensional matrices P int P con Q int and Q con For case 1, construct a matrix P. int With Q int Objective function:

[0016]

[0017] Construct about matrix P con With Q con Objective function:

[0018]

[0019] Where u represents the u-th user and i represents the i-th project. It is a loss function. Represents the regularization coefficient of the user vector. This represents the regularization coefficient of the positive feedback project vector. Let ||·||² represent the regularization coefficient of the non-positive feedback item vector, and ||·||² represent the l² norm of the matrix. For case 2, construct the regularization coefficient for matrix P. int With Q int Objective function:

[0020]

[0021] Construct an objective function for matrices P and Q, based on actual project clicks by end users:

[0022]

[0023] Where, p u Depend on and Composition, q i Depend on and Composition, q j Depend on and Composition. The final loss function is obtained from all the loss functions:

[0024]

[0025] S32: Perform gradient descent on the loss function L. For each user, calculate the user interest and conformity latent factor vector; for each item, calculate the item interest and conformity latent factor vector. Based on all user latent factor vectors and all item latent factor vectors, calculate the gradient with respect to the objective function and update matrix P. int P con Q int and Q con The vector of user interest and conformity latent factors for the u-th user. and The gradient and the i-th interest and the latent factor vector of the crowd. and The calculation formula is as follows:

[0026]

[0027] Where η1 represents the learning rate, and

[0028]

[0029] in, and This represents the gradient of user u with respect to positive feedback item i. and This represents the gradient of user u with respect to non-positive feedback item j, based on the calculated gradient. Update.

[0030] Repeat step S32 for P int P con Q int and Q con Perform iterations, P intP con Q int and Q con The iteration ends and matrix P is saved when the stopping condition is met. int P con .

[0031] Furthermore, in step S4, the Q obtained in S3 is... int and Q con Perform random initialization and save the matrix P int P con By fixing L and substituting it into the equation, we obtain information about Q. int and Q con The loss function L is used, and the sensitivity is calculated for neighboring datasets D and D', and for Q. int and Q con Allocate a privacy budget, sample noise from the Laplace distribution according to the privacy budget, and apply Q... int and Q con By perturbing the gradient, we obtain a noisy gradient. and Specifically, the following steps are included:

[0032] S41: Substitute the P obtained in S3 into L to obtain a new loss function for Q, and then rewrite the objective function L to obtain a new objective function L(Q). int |D) and L(Q) con |D):

[0033]

[0034] in, Let represent the set of positive feedback items i for user u. Let represent the set of non-positive feedback items j for user u. This represents the regularization coefficient of the positive feedback project vector. Let ||·||2 represent the regularization coefficient of the non-positive feedback project vector, and let ||·||2 represent the l2 norm of the vector.

[0035] S42: The formula for calculating the gradient of the objective function L(H|D) is as follows:

[0036]

[0037] in, This represents the gradient of user u with respect to positive feedback item i. This represents the gradient of user u with respect to non-positive feedback item j, based on the calculated gradient. and Update.

[0038] S43: Calculate the sensitivity Δ of datasets D and D' in the objective function L(H|D) respectively. + ,Δ - Δ; the calculation formula is as follows:

[0039]

[0040]

[0041] in, and This represents the upper bound of the l1 norm of the user vector and the item vector. This represents the regularization coefficient of the positive feedback project vector. This represents the regularization coefficient of the non-positive feedback item vector.

[0042] S44: Calculate the similarity between the latent factor vector of project interest and the latent factor vector of project conformity to determine the size of the privacy budget allocated to the project interest matrix and the project conformity matrix. The calculation method is as follows:

[0043]

[0044] After determining the privacy budget, distribute it from Laplace. and Sampling noise Gradient of project interest matrix and project conformity matrix and The perturbation is applied, where ∈ represents the overall privacy budget. The gradient after the Laplace noise perturbation. and as follows:

[0045]

[0046] Based on all the noisy gradient vectors and Update matrix and Where η2 is the learning rate, and then the updated value will be used to... and The final project matrix is ​​obtained by splicing.

[0047] Furthermore, in step S6, the prediction vector for the u-th user is calculated. The prediction results of non-positive feedback items in the implicit feedback matrix R are sorted, and the top-N items are recommended to the u-th user.

[0048] The beneficial effects of this invention are as follows: Addressing the privacy leakage problem in matrix factorization based on causal inference, this invention proposes a causal inference matrix factorization recommendation method based on differential privacy. This method decomposes the implicit feedback data matrix of users to items into two low-dimensional matrices, representing the user latent factor matrix and the item latent factor matrix, respectively. Directly perturbing the objective function with Laplace noise introduces excessive noise, severely impacting the usability of the recommendation model. Therefore, gradient descent is used to solve the objective function, reducing its sensitivity to noise and minimizing its impact, thus preserving the model's accuracy to the greatest extent possible. This algorithm ensures the usability of the recommendation model while guaranteeing the security of user privacy data.

[0049] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0050] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0051] Figure 1 This is a schematic diagram illustrating how a recommendation algorithm based on Bayesian personalized ranking solves for matrices W and H.

[0052] Figure 2 A schematic diagram of solving H using the gradient descent (SGD) method to add noise to the gradient;

[0053] Figure 3 This is an illustration of recommending projects to user u.

[0054] Figure 4 The results of comparing this invention with other methods on HR metrics under different privacy budgets;

[0055] Figure 5 The results show the comparison of this invention with other methods on the NDCG metric under different privacy budgets. Detailed Implementation

[0056] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0057] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0058] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0059] Please see Figures 1-3 Specifically, it includes the following steps:

[0060] Step 1: The recommendation system transforms the collected implicit user feedback data into an implicit feedback matrix with values ​​of 0 or 1. A value of 0 indicates a user's negative feedback to the item, and a value of 1 indicates a user's positive feedback to the item. U is a set containing all users, and I is a set containing all items. |U| represents the number of users in U, and |I| represents the number of items in I.

[0061] Step 2: The recommendation system uses the implicit feedback matrix. The dimension d of the latent factor vector generates the matrix P. int P con Q int Q con And initialize.

[0062] Step 3: Construct the loss function L:

[0063]

[0064] Where u represents the u-th user, i represents the i-th item, and λ P Represents the regularization coefficient of the user vector. and This represents the regularization coefficient of the positive feedback project vector. and Let ||·||2 represent the regularization coefficient of the non-positive feedback project vector, and let ||·||2 represent the l2 norm of the matrix.

[0065] Step 4: Perform gradient descent on the objective function. Calculate the user latent factor vector for each user and the item latent factor vector for each item. Based on all user and item latent factor vectors, calculate the gradient with respect to the objective function and update matrices P and Q. The u-th user latent factor vector w... u The gradient and the i-th latent factor vector item h i The calculation formula is as follows:

[0066]

[0067]

[0068] Where η1 represents the learning rate, and

[0069]

[0070] in, and This represents the gradient of user u with respect to positive feedback item i. and This represents the gradient of user u with respect to non-positive feedback item j, based on the calculated gradient. Update.

[0071] Repeat step S32 for P int P con Q int and Q con Perform iterations, Q int P con Q int and Q con The iteration ends and matrix P is saved when the stopping condition is met. int p con .

[0072] Step 5: Substitute the P calculated in Step 4 into L to obtain a new loss function for Q. This allows us to rewrite the objective function L to obtain the new objective function L(Q). int |D) and L(Q) con|D):

[0073]

[0074] in, Let represent the set of positive feedback items i for user u. Let represent the set of non-positive feedback items j for user u. This represents the regularization coefficient of the positive feedback project vector. Let ||·||2 represent the regularization coefficient of the non-positive feedback project vector, and let ||·||2 represent the l2 norm of the vector.

[0075] The formula for calculating the gradient of the objective function L(H|D) is as follows:

[0076] The formula for calculating the gradient of the objective function L(H|D) is as follows:

[0077]

[0078] in, This represents the gradient of user u with respect to positive feedback item i. This represents the gradient of user u with respect to non-positive feedback item j, based on the calculated gradient. and Update.

[0079] Step 6: Calculate the sensitivity Δ of datasets D and D' in the objective function L(H|D) respectively. + ,Δ - Δ; the calculation formula is as follows:

[0080]

[0081]

[0082]

[0083] in, and This represents the upper bound of the l1 norm of the user vector and the item vector. This represents the regularization coefficient of the positive feedback project vector. This represents the regularization coefficient of the non-positive feedback item vector.

[0084] Step 7: Calculate the similarity between the latent factor vector of project interest and the latent factor vector of project conformity to determine the size of the privacy budget allocated to the project interest matrix and the project conformity matrix. The calculation method is as follows:

[0085]

[0086] After determining the privacy budget, distribute it from Laplace. and Sampling noise Gradient of project interest matrix and project conformity matrix and The perturbation is applied, where ∈ represents the overall privacy budget. The gradient after the Laplace noise perturbation. and as follows:

[0087]

[0088] Based on all the noisy gradient vectors and Update matrix and Where η2 is the learning rate, and then the updated value will be used to... and The final project matrix is ​​obtained by splicing.

[0089] Step 8: Calculate the prediction vector for the u-th user. The prediction results of non-positive feedback items in the implicit feedback matrix R are sorted, and the top-N items are recommended to the u-th user.

[0090] Example

[0091] The causal inference matrix factorization recommendation method based on differential privacy described in this invention specifically includes the following steps:

[0092] Step 1: Transform the implicit user feedback data for the project into an implicit feedback matrix with values ​​of 0 or 1. A value of 0 represents non-positive user feedback to the project, and a value of 1 represents positive user feedback. Initialize the user latent factor matrix P based on the number of users |U| and the number of projects |I| contained in the implicit inverse matrix. int P con and the project latent factor matrix Q int Q con Construct the objective function L, and solve for P using the gradient descent method. int P con Q int Q con And save it. The solution process is as follows: Figure 1 As shown.

[0093] Step 2: Take the P obtained in Step 1 int P con Substitute L and randomly initialize matrix Q. int , to obtain information about Q int Q con Objective function L(Q) int |D) and L(Q) con|D), consider the objective function for each item i∈I. and calculate and With regard to the gradient of the objective function, calculate the coefficient sensitivity Δ in adjacent datasets D and D' respectively. int and Δ con . respectively from Laplace distribution and Sampling noise noise gradient and To perform the perturbation, the specific process is as follows: Figure 2 As shown.

[0094] Step 3: Calculate the user's prediction vector according to the formula in S6, sort the prediction results of non-positive feedback items in the implicit feedback matrix R, and recommend the top-N items to the u-th user. The recommendation process is as follows: Figure 3 As shown.

[0095] Finally, it should be noted that 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A causal inference matrix factorization recommendation method based on differential privacy, characterized in that, The method specifically includes the following steps: S1: Implicit feedback data of users to items is represented by an implicit feedback matrix with values ​​of 0 or 1, where 0 indicates user feedback to items. The purpose is not positive feedback; 1 indicates positive feedback from the user to the project. S2: Randomly initialize the matrix , , , ; It is a latent factor matrix of user interests. Representation matrix The Line, representing the first The latent interest factor vector of each user; It is a user-following latent factor matrix. Representation matrix The Line, representing the first The conformity latent factor vector of each user; It is a latent factor matrix of project interests. Representation matrix The Line, representing the first The interest latent factor vector of each project; It is the project's hidden factor matrix. Representation matrix The Line, representing the first The latent factor vector of each project's conformity; It is a noisy latent factor matrix of project interests. Representation matrix The Line, representing the first Noisy latent factor vectors for each project's interest; It is a noisy latent factor matrix of project interests. Representation matrix The Line, representing the first The latent factor vector of each project that adds noise by conforming to the crowd; Represents the dimension of the latent factor vector; S3: Divide user clicks into two cases: Case 1: The user clicked on a less popular item. In this case, it can be inferred that the user has a high interest in the item. Loss functions can be constructed separately for user interest and conformity reasons. and Case 1: Bayesian personalized ranking is used to maximize the score difference between the two; Case 2: The user clicked on a more popular item. In this case, it is impossible to infer the user's true interest, so a loss function can only be constructed based on the herd mentality. We use Bayesian feasibility ranking to maximize the score difference between the two; finally, we construct a click loss function based on the actual click situation. Therefore, it can be based on , , as well as Loss function for building the model Solve , , and ,Will and The user matrix is ​​obtained by splicing. , and The project matrix is ​​obtained by splicing. Specifically, it includes the following steps: S31: Decompose the implicit feedback matrix into four low-dimensional matrices , , and For case 1, construct a matrix... and Objective function: ， Construct about the matrix and Objective function: ， in, Indicates the first One user, Indicates the first One project, Representing a matrix Norm; for case 2, construct norm about the matrix and Objective function: ， Construct a matrix based on actual project clicks by end users. and Objective function: ， in, Depend on and composition, Depend on and composition, Depend on and Composition; the final loss function is obtained from all the loss functions: = ； S32: Regarding the loss function Gradient descent is performed, calculating the user interest and conformity latent factor vectors for each user, and the item interest and conformity latent factor vectors for each item. The gradient with respect to the objective function is then calculated based on all user and item latent factor vectors, and the matrix is ​​updated. , , and ;No. User interests and latent factor vectors and gradient and the first Interest and conformity latent factor vector items and The calculation formula is as follows: ， ， ， ， ， ， in This represents the learning rate, and ， ， ， ， ， ， in, and Indicates user Positive feedback projects gradient, and Indicates user For non-positive feedback projects The gradient, based on the calculated gradient... Perform the update; repeat step S32. , , and Perform iterations. , , and The iteration ends and the matrix is ​​saved when the stopping condition is met. , ; S4: The matrix obtained in S3 , and Fixed, randomly initialized matrix and Substitute into the loss function And recalculate the matrix and Through the loss function Find the matrix and gradient and and calculate the dataset and The sensitivity is calculated and assigned to and The privacy budget is used to sample noise from the Laplace distribution and apply it to the gradient. and By perturbing the gradient, we obtain a noisy gradient. and ; S5: Using the gradient obtained after perturbation, apply it to the loss function. Gradient descent is used to obtain the final matrix. and ,Will and By splicing together, a differential privacy-preserving project matrix is ​​obtained. ; S6: According to the formula Make predictions, sort the prediction results of non-positive feedback items in the implicit feedback matrix described in S1, and recommend the TOP-N items to the user.

2. The causal inference matrix factorization recommendation method based on differential privacy according to claim 1, characterized in that: In step S1, the implicit feedback data of users to the project is transformed into an implicit feedback matrix with values ​​of 0 or 1. A value of 0 indicates negative user feedback on the project, while a value of 1 indicates positive user feedback. It is a collection that includes all users. It is a collection that includes all projects. express The number of users in China express The number of projects in the middle.

3. The causal inference matrix factorization recommendation method based on differential privacy according to claim 2, characterized in that: In step S4, the product obtained in S3 is... and Perform random initialization and save the matrix , Fixed, Substitute , get about and loss function and neighboring datasets and Calculate sensitivity, for and Allocate a privacy budget, and sample noise from the Laplace distribution according to the privacy budget. and By perturbing the gradient, we obtain a noisy gradient. and Specifically, it includes the following steps: S41: Obtained from S3 Fixed substitution , get about A new loss function, thus affecting the objective function. The new objective function is obtained by rewriting it. and : ， ， S42: The formula for calculating the gradient of the objective function is as follows: ， ， ， ， ， ， in, , Indicates user Positive feedback projects gradient, , Indicates user For non-positive feedback projects The gradient, based on the calculated gradient... , , and Update; S43: Calculate the objective function respectively medium dataset and dataset sensitivity and The calculation formula is as follows: ， ， ， ， ， ， in, , and , Representing user vectors and item vectors respectively The upper bound of the norm; S44: Calculate the similarity between the latent factor vector of project interest and the latent factor vector of project conformity to determine the size of the privacy budget allocated to the project interest matrix and the project conformity matrix. The calculation method is as follows: ， ， ， ， After determining the privacy budget, distribute it from Laplace. and Sampling noise Gradient of project interest matrix and project conformity matrix and To cause a disturbance. For the overall privacy budget; gradient after Laplace noise perturbation and as follows: ， ， ， ， Based on all the noisy gradient vectors and Update matrix and ,in The learning rate will be updated later. and The final project matrix is ​​obtained by splicing. .

4. The causal inference matrix factorization recommendation method based on differential privacy according to claim 1, characterized in that: In step S6, the first... Prediction vector for each user For implicit feedback matrix The prediction results of the China-Africa positive feedback project are ranked, and the top-N projects are recommended to the next project. One user.

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