Information bottleneck based debiased recommendation method

Abstract

The application discloses a kind of based on information bottleneck's debiasing recommendation method, comprising:1. Construct original data: user-product interaction matrix of user interaction to product, user biased attribute matrix;2. Using biased attribute encoder learns user biased representation in user-product interaction data;3. Based on deep graph neural network learns user and product representation matrix;4. Based on information bottleneck theory minimizes the mutual information between user representation and biased representation, user subgraph representation and biased representation, calculates loss function;5. Recomputes interaction matrix based on user and product representation matrix, calculates loss function;6. The loss function of joint step 4-step 5 is carried out information bottleneck learning, and model parameter is updated to model convergence.The application is based on the thought of information bottleneck, learns unbiased user representation under the demand of meeting recommendation task, so as to effectively reduce recommendation bias, guarantee the accuracy of recommendation.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of recommendation, in particular to a bias-eliminating recommendation method based on information bottleneck. BACKGROUND

[0002] Recommendation systems have permeated various fields of real life, seamlessly providing personalized content. With complex algorithms and user-centric models, these systems have excelled in predicting user preferences, enhancing overall user experience and engagement. While recommendation systems have achieved remarkable success in customizing recommendations to individual users, data-driven recommendation systems are susceptible to biased recommendation results due to historical interaction data bias.

[0003] A biased recommendation system is one that leans towards a particular group of people, such as in a career recommendation system, where women are more likely to be recommended low-paying careers. Traditional recommendation methods focus solely on improving recommendation accuracy, inevitably amplifying existing biases in the data, leading to biased recommendations. Existing bias-eliminating recommendation methods have not effectively balanced recommendation accuracy and bias, resulting in suboptimal outcomes. How to better balance recommendation accuracy and bias is a key issue in improving recommendation system bias. SUMMARY

[0004] To address the shortcomings of the prior art, the present application proposes a bias-eliminating recommendation method based on information bottleneck, encouraging the model to learn beneficial information for recommendation prediction from interaction data while eliminating biased information in user representation, achieving a better balance between recommendation accuracy and bias.

[0005] To solve the technical problems, the present application adopts the following technical solutions:

[0006] The bias-eliminating recommendation method based on information bottleneck of the present application is characterized by the following steps:

[0007] Step 1, construct original data, including: user-product interaction matrix, user bias attribute matrix;

[0008] Step 1.1, let U represent the user set, and U = {u1,…u a ,…u M}, u a represents the a-th user, M represents the total number of users, 1 ≤ a ≤ M; let V represent the product set, and V = {v1,…,v i ,…,v N}, v i represents the i-th product, N represents the total number of products, 1 ≤ i ≤ N; let r ai represent the a-th user ua the interaction data of the ith product v i , the user-product interaction matrix R = {r ai} M×N a if the a-th user u i has interaction record with the ith product v ai , r ai = 1, otherwise, r a = 0; represent the predicted interaction relationship between the a-th user u i and the ith product v a ; according to the user-product interaction matrix R, a user-product bipartite graph G = <U, V, R> is constructed, taking users and products as nodes, and interaction records as edges;

[0009] Step 1.2, let the binary biased attribute matrix of users S = {s1, …s M}, where s a ∈{0,1} represents the biased attribute value of the a-th user u a ; according to the biased attribute value, the user set U can be divided into 2 subsets, namely U0 and U1, U0 represents the user subset with biased attribute value of 0, and U1 represents the user subset with biased attribute value of 1;

[0010] Step 2, learn the user biased representation in the user-product interaction data using the biased attribute encoder, so as to train the biased attribute encoder and obtain the optimal parameters and the corresponding binary biased attribute representation e s ;

[0011] Step 3, learn the user and product representation matrices using the deep graph neural network, so as to obtain the final user representation matrix X and the final product representation matrix Y;

[0012] Step 4, based on the information bottleneck theory, minimize the mutual information between the user representation and the biased representation, and the mutual information between the user subgraph representation and the biased representation, and calculate the loss function:

[0013] Step 4.1, construct the information bottleneck loss function L HSIC between the user representation and the biased representation according to formula (9):

[0014]

[0015] In formula (9), U b represents the user set in the current training batch, x a represents the a-th row representation vector in the final user representation matrix X, and HSIC(,) represents the Hilbert-Schmidt independence criterion; ​Represents the a-th user u a The representation of the binary biased property s;

[0016] Step 4.2: Calculate the user's subgraph representation Gu according to equation (10):

[0017] G u =g(X) 1 ,…,X l ,…,X L+1 (10)

[0018] In equation (10), X l Let g() represent the user's representation at layer l of the graph neural network, and g() represent the aggregation function of the subgraph representation.

[0019] Step 4.3: Construct the user subgraph representation G according to equation (11). u and biased representation e s Information bottleneck loss function L' HSIC :

[0020]

[0021] In equation (11), The subgraph representation G of the user u The subgraph in row a represents the vector;

[0022] Step 5: Reconstruct the interaction matrix based on the user and product representation matrices, and calculate the reconstruction loss function L. rec ;

[0023] Step 6: Combine various loss functions to perform information bottleneck learning, update the network parameters until the loss functions converge, and thus obtain the optimal parameters θ. * This is used to enable users to recommend products that meet the bias removal requirements.

[0024] The bias-removal recommendation method based on information bottlenecks described in this invention is also characterized in that step 2 includes:

[0025] Step 2.1: Randomly initialize the user biased representation matrix C = {c1,...,c...} using a Gaussian distribution. a ,...,c M}, where c a Represents the a-th user u a Biased representation;

[0026] The product partial representation matrix Z = {z1,...,z2} is randomly initialized using a Gaussian distribution. i ,...,z N}, where z i v represents the i-th product i Biased representation;

[0027] Step 2.2: Construct a biased attribute encoder;

[0028] Input the user biased representation matrix C and the product biased representation matrix Z into the biased attribute encoder, and calculate the a-th user u after passing through the (k+1)-th graph convolutional layer according to Equation (1). a Biased representation and the i-th product v i Biased representation

[0029]

[0030] In equation (1), R a Represents the a-th user u a An interactive product collection, H i Indicates the relationship with the i-th product v i An interactive set of users This represents the output of the a-th user u after the k-th graph convolutional layer. a Biased representation, The i-th product v is output after the k-th graph convolutional layer. i Biased representation, |R a | represents the a-th user u a Size of the interactive product collection, |H i | indicates the relationship with the i-th product v i Size of the user set with interaction; initialization when k=1.

[0031] Step 2.3: Construct a biased attribute classifier;

[0032] Calculate the a-th user u using equation (2) a The biased attribute prediction value obtained after the (k+1)th graph convolutional layer

[0033]

[0034] In equation (2), W represents the parameters of the fully connected layer of the biased attribute classifier. This represents the output of the (k+1)th graph convolutional layer, representing the a-th user u. a The biased representation of σ() is the Sigmoid activation function.

[0035] Step 2.4: Calculate the loss function of the biased attribute encoder according to equation (3);

[0036]

[0037] In equation (3), θ s=[C,Z,W] represents the parameters to be learned;

[0038] Step 2.5: Train the biased attribute encoder using gradient descent and minimize the loss function L in equation (3). s (θ s This process continues until the loss function converges, thus obtaining the corresponding optimal parameters. Among them, C * Z represents the optimal user-biased representation matrix. * W represents the optimal product partial characterization matrix. * This represents the optimal parameters for the fully connected layer;

[0039] Based on optimal parameters Get the a-th user u a Biased representation

[0040] Step 2.6: Calculate the binary biased attribute representation e using equation (4). s ;

[0041]

[0042] In equation (4), s∈{0,1} represents a binary biased attribute value, U s This represents a set of users with different biased attribute values.

[0043] Step 3 includes:

[0044] Step 3.1: Randomly initialize the user representation matrix P = {p1,...,p} using a Gaussian distribution. a ,...,p M}, where p a Represents the a-th user u a The product co-representation matrix Q = {q1,...,q} is randomly initialized using a Gaussian distribution. i ,...,q N}, where q i v represents the i-th product i The representation;

[0045] Step 3.2: Calculate the connection matrix A according to equation (5):

[0046]

[0047] Step 3.3: Define the graph neural network as having L convolutional layers, with the current convolutional layer being layer l;

[0048] Initialize the node representation matrix H of layer 0 0 ={P,Q};

[0049] Step 3.4: Represent the node representation matrix H of the l-th layer. l The input is fed into the graph neural network, and the representation matrix H of the nodes in the (l+1)th layer is calculated according to equation (6). l+1 :

[0050]

[0051] In equation (6), D represents the degree matrix of the connection matrix A;

[0052] Step 3.5: Aggregate the outputs of each graph convolutional layer according to equation (7) to obtain the final node representation matrix H:

[0053]

[0054] Step 3.6: Obtain the final user representation matrix X and the final product representation matrix Y according to equation (8):

[0055] X=H[:M],Y=H[M:] (8)

[0056] In equation (8), H[:M] represents the first to M rows of matrix H, and H[M:] represents the (M+1) to (M+N) rows of matrix H.

[0057] Step 5 includes:

[0058] Step 5.1: Predict the a-th user u according to equation (12). a For the i-th product v i Interaction probability

[0059]

[0060] In equation (12), σ is the Sigmoid activation function; x a y represents the representation vector in the a-th row of the user's final representation matrix X; i This represents the representation vector in the i-th row of the final product representation matrix Y;

[0061] Step 5.2: Calculate the reconstruction loss function L according to equation (13). rec :

[0062]

[0063] In equation (13), D a It is the a-th user u a All training data, and D a ={(i,j)|i∈R a ,j∈VR a};R a Represents the a-th user u aThe set of interactive products; (i,j) represents a user-product pair; j represents the a-th user u a A product number in the set of non-interactive products.

[0064] Step 6 includes:

[0065] Step 6.1: Establish the overall optimization objective L(θ) according to equation (14):

[0066] L(θ)=L rec +βL HSIC +γL' HSIC (14)

[0067] In equation (14), θ = [P, Q] are all the parameters to be optimized, and β and γ are used to adjust the information bottleneck loss function on the user side and the subgraph side, respectively.

[0068] Step 6.2: Solve the optimization objective L(θ) in equation (14) using the gradient descent method to update the parameter θ until L(θ) converges to the minimum value, thereby obtaining the optimal parameter θ. * ;

[0069] Step 6.3: Predict the optimal parameter θ according to equation (15). * Next user a a For the i-th product v i Optimal interaction probability This yields the interaction matrix for predicting the relationship between user set U and product set V. Used to achieve user-recommended products that meet the bias correction requirements:

[0070]

[0071] In equation (15), Represents the a-th user u a The optimal representation vector, v represents the i-th product i The optimal representation vector.

[0072] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the bias removal recommendation method, and the processor is configured to execute the program stored in the memory.

[0073] This invention discloses a computer-readable storage medium on which a computer program is stored, characterized in that the computer program, when executed by a processor, performs the steps of the bias-reduction recommendation method. Compared with existing technologies, the advantages of this invention are reflected in:

[0074] 1. This invention proposes a bias-reduction recommendation method based on information bottlenecks. By constraining both the user representation and the user subgraph representation through information bottlenecks, biased information in the learned representations is eliminated. This method can effectively balance recommendation accuracy and unbiasedness, thereby improving the recommendation bias problem while ensuring accuracy.

[0075] 2. The bias removal method based on information bottleneck proposed in this invention has universality and can be applied to any recommendation method based on representation learning.

[0076] 3. The information bottleneck-based recommendation method proposed in this invention does not require the introduction of any model parameters and has strong application prospects. Attached Figure Description

[0077] Figure 1 This is a flowchart of the bias-removal recommendation method based on information bottlenecks according to the present invention. Detailed Implementation

[0078] In this embodiment, a bias-free recommendation method based on information bottlenecks addresses the recommendation bias problem inherent in traditional recommendation systems. From the perspective of unbiased representation learning, it designs a user representation and user subgraph representation information bottleneck learning module based on Hilbert-Schmidt independence constraints to obtain accurate and unbiased user representations that satisfy the recommendation task, thereby achieving unbiased recommendation results. Specifically, as... Figure 1 As shown, the procedure is as follows:

[0079] Step 1: Construct the raw data, including: user interaction matrix with the product, and user biased attribute matrix;

[0080] Step 1.1: Let U denote the user set, and U = {u1, ..., u2} a ,…u M}, u a Let a represent the a-th user, M represent the total number of users, 1 ≤ a ≤ M; let V represent the product set, and V = {v1, ..., v2} i ,…,v N}, v i Let r represent the i-th product, N represent the total number of products, 1 ≤ i ≤ N; ai Represents the a-th user u a For the i-th product v i The interaction data, then the user's interaction matrix with the product R = {r ai} M×N If the a-th user u a For the i-th product v i If there is an interaction record, then r ai =1, otherwise, r ai =0; Represents the a-th user ua and the i-th product v i The predicted interaction relationships; based on the user-product interaction matrix R, construct a user-product bipartite graph G with users and products as nodes and their interaction records as edges.<U,V,R> .

[0081] Step 1.2: Let the user's binary biased attribute matrix S = {s1, ... s2} a ,…s M}, where s a ∈{0,1} represents the a-th user u a The biased attribute values; based on the biased attribute values, the user set U can be divided into two subsets, namely U0 and U1, where U0 represents the subset of users with a biased attribute value of 0 and U1 represents the subset of users with a biased attribute value of 1.

[0082] In this embodiment, testing is conducted on the real-world dataset MovieLens-1M. 80% of each user's interaction records with the product in the dataset are used for training, and the remaining 20% ​​are used for testing. A binary biased attribute is used to select gender; a biased attribute value of 0 represents male, and a biased attribute value of 1 represents female. The elements in the user's biased attribute matrix are either 0 or 1. Figure 1 The partial attribute matrix for the user is shown below.

[0083] Step 2: Use a biased attribute encoder to learn biased user representations from user-product interaction data:

[0084] Step 2.1: Randomly initialize the user biased representation matrix C = {c1,...,c...} using a Gaussian distribution. a ,...,c M}, where c a Represents the a-th user u a Biased representation; the biased representation matrix Z = {z1,...,z2} is randomly initialized using a Gaussian distribution. i ,...,z N}, where z i v represents the i-th product i Biased representation.

[0085] Step 2.2: Construct a biased attribute encoder;

[0086] Input the user biased representation matrix C and the product biased representation matrix Z into the biased attribute encoder, and calculate the a-th user u after passing through the (k+1)-th graph convolutional layer according to Equation (1). a Biased representation and the i-th product v i Biased representation

[0087]

[0088] In equation (1), R a Represents the a-th user u a An interactive product collection, H i Indicates the relationship with the i-th product v i An interactive set of users This represents the output of the a-th user u after the k-th graph convolutional layer. a Biased representation, The i-th product v is output after the k-th graph convolutional layer. i Biased representation, |R a | represents the a-th user u a Size of the interactive product collection, |H i | indicates the relationship with the i-th product v i Size of the user set with interaction; initialization when k=1.

[0089] Step 2.3: Construct a biased attribute classifier; calculate the value of u for the a-th user using equation (2). a The biased attribute prediction value obtained after the (k+1)th graph convolutional layer

[0090]

[0091] In equation (2), W represents the parameters of the fully connected layer of the biased attribute classifier. This represents the output of the (k+1)th graph convolutional layer, representing the a-th user u. a The biased representation of σ() is the Sigmoid activation function.

[0092] Step 2.4: Calculate the loss function of the biased attribute encoder according to equation (3);

[0093]

[0094] In equation (3), θ s =[C,Z,W] are the parameters to be learned.

[0095] Step 2.5: Train the biased attribute encoder using gradient descent and minimize the loss function L in equation (3). s (θ s This process continues until the loss function converges, thus obtaining the corresponding optimal parameters. Based on optimal parameters Get the a-th user u a Biased representation Among them, C * Z represents the optimal user-biased representation matrix. *W represents the optimal product partial characterization matrix. * This represents the optimal parameters for the fully connected layer.

[0096] Step 2.6: Calculate the binary biased attribute representation using equation (4);

[0097]

[0098] In equation (4), s∈{0,1} represents a binary biased attribute value, U s This represents a set of users with different biased attribute values.

[0099] Step 3: Use a deep graphical neural network to learn the user and product representation matrices:

[0100] Step 3.1: Randomly initialize the user representation matrix P = {p1,...,p} using a Gaussian distribution. a ,...,p M}, where p a Represents the a-th user u a The product co-representation matrix Q = {q1,...,q} is randomly initialized using a Gaussian distribution. i ,...,q N}, where q i v represents the i-th product i The representation of.

[0101] Step 3.2: Calculate the connection matrix A according to equation (5):

[0102]

[0103] Step 3.3: Define the graph neural network as having L convolutional layers, with the current convolutional layer being layer l;

[0104] Initialize the node representation matrix H of layer 0 0 ={P,Q};

[0105] Step 3.4: Represent the node representation matrix H of the l-th layer. l The input is fed into the graph neural network, and the representation matrix H of the nodes in the (l+1)th layer is calculated according to equation (6). l+1 :

[0106]

[0107] In equation (6), D represents the degree matrix of the connection matrix A;

[0108] Step 3.5: Aggregate the outputs of each graph convolutional layer according to equation (7) to obtain the final node representation matrix H:

[0109]

[0110] Step 3.6: Obtain the final user representation matrix X and the final product representation matrix Y according to equation (8):

[0111] X=H[:M],Y=H[M:] (8)

[0112] In equation (8), H[:M] represents the first to M rows of matrix H, and H[M:] represents the (M+1) to (M+N) rows of matrix H.

[0113] Step 4: Based on the information bottleneck theory, minimize the mutual information between user representation and biased representation, and between user subgraph representation and biased representation, and calculate the loss function:

[0114] Step 4.1: Construct the information bottleneck loss function L between the user representation and the biased representation according to equation (9). HSIC :

[0115]

[0116] In equation (9), U b Let x represent the set of users in the current training batch. a This represents the representation vector in the a-th row of the user's final representation matrix X. Represents the a-th user u a The binary biased property s is represented by HSIC(,), which represents the Hilbert-Schmidt independence index.

[0117] Step 4.2: Calculate the user's subgraph representation G according to equation (10). u :

[0118] G u =g(X) 1 ,…,X l ,…,X L+1 (10)

[0119] In equation (10), X l Let g() represent the user's representation at layer l of the graph neural network, and g() represent the aggregation function of the subgraph representation.

[0120] Step 4.3: Construct the user subgraph representation G according to equation (11). u and biased representation e s Information bottleneck loss function L' HSIC :

[0121]

[0122] In equation (11), U b This represents the set of users in the current training batch. Let represent the subgraph representation of user a, and HSIC(,) represent the Hilbert-Schmidt independence index.

[0123] This embodiment uses the Hilbert-Schmidt independence index to eliminate biased information from the perspective of users and their subgraphs, thereby ensuring that the final user representation matrix X contains as little biased information as possible.

[0124] Step 5: Reconstruct the interaction matrix based on the user and product representation matrices, and calculate the loss function:

[0125] Step 5.1: Predict the a-th user u according to equation (12). a For the i-th product v i Interaction probability

[0126]

[0127] In equation (12), σ is the Sigmoid activation function; x a y represents the representation vector in the a-th row of the user's final representation matrix X; i This represents the representation vector in the i-th row of the final product representation matrix Y.

[0128] Step 5.2: Calculate the reconstruction loss function L according to equation (13). rec :

[0129]

[0130] In equation (13), D a It is the a-th user u a All training data, and D a ={(i,j)|i∈R a ,j∈VR a};R a Represents the a-th user u a The set of interactive products; (i,j) represents a user-product pair; j represents the a-th user u a A product number in the set of non-interactive products.

[0131] Step 6: Combine the various loss functions to learn the information bottleneck, and update the model parameters until the model converges:

[0132] Step 6.1: Establish the overall optimization objective L(θ) according to equation (14):

[0133] L(θ)=L rec +βL HSIC +γL' HSIC (14)

[0134] In equation (14), θ = [P, Q] are all parameters to be optimized, and β and γ are used to adjust the information bottleneck loss function on the user side and the subgraph side, respectively.

[0135] Step 6.2: Solve the optimization objective L(θ) in equation (14) using the gradient descent method to update the parameter θ until L(θ) converges to the minimum value, thereby obtaining the optimal parameter θ. * ;

[0136] Step 6.3: Predict the optimal parameter θ according to equation (15). * Next user a a For the i-th product v i Optimal interaction probability This yields the interaction matrix for predicting the relationship between user set U and product set V. Used to achieve user-recommended products that meet the bias correction requirements:

[0137]

[0138] In equation (15), Represents the a-th user u a The optimal representation vector, v represents the i-th product i The optimal representation vector.

[0139] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0140] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0141] Example:

[0142] To verify the effectiveness of this method, this invention selects two commonly used datasets in the field of bias removal in recommender systems, namely MovieLens-1M and Lastfm, for experiments. This invention selects all products that the user has not interacted with and sorts them, using Recall@K and Normalized Discounted Cumulative Gain (NDCG@K) as evaluation metrics for recommender system accuracy; higher values ​​for both metrics indicate higher recommendation accuracy. Simultaneously, to measure the bias removal effect, Demographic Parity (DP@K) and Equal Opportunity (EO@K) are defined as bias removal metrics; lower values ​​for both metrics indicate better bias removal.

[0143] This invention uses LightGCN as the base model and compares the performance of four related methods: Adv, FairGO, FairRec, and FairMI. Specifically, Tables 1 and 2 show the experimental results on the two datasets mentioned above.

[0144] Table 1 Comparison of recommendation results between the proposed method and the comparative method on the MovieLens-1M dataset.

[0145] Models Recall@10 NDCG@10 DP@10 EO@10 Adv 0.1469 0.1963 0.1532 0.2694 FairRec 0.1472 0.1950 0.1536 0.2590 FairGO 0.1336 0.1822 0.2728 0.3382 FairMI 0.1480 0.1979 0.1436 0.2560 FairIB (the invention) 0.1502 0.2003 0.1408 0.2045

[0146] Table 2 Comparison of recommendation results of the proposed method and the comparative method on the Lastfm dataset.

[0147] Models Recall@10 NDCG@10 DP@10 EO@10 Adv 0.1499 0.1887 0.1382 0.2682 FairRec 0.1505 0.1892 0.1397 0.2700 FairGO 0.1371 0.1693 0.2626 0.3282 FairMI 0.1506 0.1888 0.1381 0.2690 FairIB (the invention) 0.1520 0.1900 0.1313 0.2325

[0148] As can be seen from the two tables above, on both datasets, the FairIB method proposed in this invention significantly outperforms the comparison methods in all four metrics: Recall@10, NDCG@10, DP@10, and EO@10.

Claims

1. A bias-reduction recommendation method based on information bottlenecks, characterized in that, The procedure is as follows: Step 1: Construct the raw data, including: user interaction matrix with the product, and user biased attribute matrix; Step 1.1: Let U denote the user set, and U = {u1, ... u2} a ,...u M }, u a Let a represent the a-th user, M represent the total number of users, 1 ≤ a ≤ M; let V represent the product set, and V = {v1, ..., v2} i , ..., v N }, v i Let r represent the i-th product, N represent the total number of products, 1 ≤ i ≤ N; ai Represents the a-th user u a For the i-th product v i The interaction data, then the user's interaction matrix with the product R = {r ai } M×N If the a-th user u a For the i-th product v i If there is an interaction record, then r ai =1, otherwise, r ai =0; Represents the a-th user u a and the i-th product v i The predicted interaction relationships; based on the user-product interaction matrix R, construct a user-product bipartite graph G with users and products as nodes and their interaction records as edges.<U,V,R> ; Step 1.2: Let the user's binary biased attribute matrix be v = {s1, ... s2}. a ,...s M }, where s a ∈{0,1} represents the a-th user u a The biased attribute values; based on the biased attribute values, the user set U can be divided into two subsets, namely U0 and U1, where U0 represents the subset of users with a biased attribute value of 0 and U1 represents the subset of users with a biased attribute value of 1. Step 2: Use a biased attribute encoder to learn biased user representations from user-product interaction data, thereby training the biased attribute encoder to obtain optimal parameters. and its corresponding binary biased property representation e s ; Step 3: Use a deep graph neural network to learn user and product representation matrices, thereby obtaining the final user representation matrix X and the final product representation matrix Y; Step 4: Based on the information bottleneck theory, minimize the mutual information between user representation and biased representation, and between user subgraph representation and biased representation, and calculate the loss function: Step 4.1: Construct the information bottleneck loss function L between the user representation and the biased representation according to equation (9). HSIC : In equation (9), U b Let x represent the set of users in the current training batch. a Let represent the representation vector in the a-th row of the user's final representation matrix X, and HSIC(,) represent the Hilbert-Schmidt independence index; Represents the a-th user u a The representation of the binary biased property s; Step 4.2: Calculate the user's subgraph representation G according to equation (10). u : G u =g(X 1 ,...,X l ,...,X L+1 ) (10) In equation (10), X l This represents the user's representation at the l-th layer of the graph neural network, where g() represents the aggregation function of the subgraph representation. Step 4.3: Construct the user subgraph representation G according to equation (11). u and biased representation e s Information bottleneck loss function L′ HSIC : In equation (11), The subgraph representation G of the user u The subgraph in row a represents the vector; Step 5: Reconstruct the interaction matrix based on the user and product representation matrices, and calculate the reconstruction loss function L. rec ; Step 6: Combine various loss functions to perform information bottleneck learning, update the network parameters until the loss functions converge, and thus obtain the optimal parameters θ. * This is used to enable users to recommend products that meet the bias removal requirements.

2. The bias-removal recommendation method based on information bottlenecks according to claim 1, characterized in that, Step 2 includes: Step 2.1: Randomly initialize the user-biased representation matrix C = {c1, ..., c2} using a Gaussian distribution. a c M }, where c a Represents the a-th user u a Biased representation; The product partial representation matrix Z = {z1, ..., z2} is randomly initialized using a Gaussian distribution. i , ..., z N }, where z i v represents the i-th product i Biased representation; Step 2.2: Construct a biased attribute encoder; Input the user biased representation matrix C and the product biased representation matrix Z into the biased attribute encoder, and calculate the a-th user u after passing through the (k+1)-th graph convolutional layer according to Equation (1). a Biased representation and the i-th product v i Biased representation In equation (1), R a Represents the a-th user u a An interactive product collection, H i Indicates the relationship with the i-th product v i An interactive set of users This represents the output of the a-th user u after the k-th graph convolutional layer. a Biased representation, The i-th product v is output after the k-th graph convolutional layer. i The biased representation, |R a | represents the a-th user u a Size of the interactive product collection, |H i | indicates the relationship with the i-th product v i Size of the set of interactive users; initialization when k=1. Step 2.3: Construct a biased attribute classifier; Calculate the a-th user u using equation (2) a The biased attribute prediction value obtained after the (k+1)th graph convolutional layer In equation (2), W represents the parameters of the fully connected layer of the biased attribute classifier. This represents the output of the a-th user u after the (k+1)-th graph convolutional layer. a The biased representation, σ() represents the Sigmoid activation function; Step 2.4: Calculate the loss function of the biased attribute encoder according to equation (3); In equation (3), θ s =[C, Z, W] are the parameters to be learned; Step 2.5: Train the biased attribute encoder using gradient descent and minimize the loss function L in equation (3). s (θ s This process continues until the loss function converges, thus obtaining the corresponding optimal parameters. Among them, C * Z represents the optimal user-biased representation matrix. * W represents the optimal product partial characterization matrix. * This represents the optimal parameters for the fully connected layer; Based on optimal parameters Get the a-th user u a Biased representation Step 2.6: Calculate the binary biased attribute representation e using equation (4). s ; In equation (4), s∈{0,1} represents a binary biased attribute value, U s This represents a set of users with different biased attribute values.

3. The bias-removal recommendation method based on information bottlenecks according to claim 2, characterized in that, Step 3 includes: Step 3.1: Randomly initialize the user representation matrix P = {p1, ..., p2} using a Gaussian distribution. a , ..., p M }, where p a Represents the a-th user u a The product co-representation matrix Q = {q1, ..., q2} is randomly initialized using a Gaussian distribution. i , ..., q N }, where q i v represents the i-th product i The representation; Step 3.2: Calculate the connection matrix A according to equation (5): Step 3.3: Define the graph neural network as having L convolutional layers, with the current convolutional layer being layer l; Initialize the node representation matrix H of layer 0 0 = {P, Q}; Step 3.4: Represent the node representation matrix H of the l-th layer. l The input is fed into the graph neural network, and the representation matrix H of the nodes in the (l+1)th layer is calculated according to equation (6). l+1 : In equation (6), D represents the degree matrix of the connection matrix A; Step 3.5: Aggregate the outputs of each graph convolutional layer according to equation (7) to obtain the final node representation matrix H: Step 3.6: Obtain the final user representation matrix X and the final product representation matrix Y according to equation (8): X = H[:M], Y = H[M:] (8) In equation (8), H[:M] represents the first to the Mth rows of matrix H, and H[M:] represents the (M+1)th to (M+N)th rows of matrix H.

4. The bias-removal recommendation method based on information bottlenecks according to claim 3, characterized in that, Step 5 includes: Step 5.1: Predict the a-th user u according to equation (12). a For the i-th product v i Interaction probability In equation (12), σ is the Sigmoid activation function; x a y represents the representation vector in the a-th row of the user's final representation matrix X; i This represents the representation vector in the i-th row of the final product representation matrix Y; Step 5.2: Calculate the reconstruction loss function L according to equation (13). rec : In equation (13), D a It is the a-th user u a All training data, and D a ={(i, j)|i∈R a ,j∈VR a };R a Represents the a-th user u a The set of interactive products; (i, j) represents a user-product pair; j represents the a-th user u a A product number in the set of non-interactive products.

5. The bias-removal recommendation method based on information bottlenecks according to claim 4, characterized in that, Step 6 includes: Step 6.1: Establish the overall optimization objective L(θ) according to equation (14): L(θ)=L rec +βL HSIC +γL′ HSIC (14) In equation (14), θ = [P, Q] are all parameters to be optimized, and β and γ are used to regulate the information bottleneck loss function on the user side and the subgraph side, respectively. Step 6.2: Solve the optimization objective L(θ) in equation (14) using the gradient descent method to update the parameter θ until L(θ) converges to the minimum value, thereby obtaining the optimal parameter θ. * ; Step 6.3: Predict the optimal parameter θ according to equation (15). * Next user a a For the i-th product v i Optimal interaction probability This yields the interaction matrix for predicting the relationship between user set U and product set V. Used to achieve user-recommended products that meet the bias correction requirements: In equation (15), Represents the a-th user u a The optimal representation vector, v represents the i-th product i The optimal representation vector.

6. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing any of the bias-reduction recommendation methods of claims 1-5, and the processor is configured to execute the program stored in the memory.

7. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it performs the steps of any of the bias-reduction recommendation methods described in claims 1-5.

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