CN116010718A - Fair personalized recommendation method, equipment and storage medium based on mutual information decoupling - Google Patents

Fair personalized recommendation method, equipment and storage medium based on mutual information decoupling Download PDF

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CN116010718A
CN116010718A CN202310036773.4A CN202310036773A CN116010718A CN 116010718 A CN116010718 A CN 116010718A CN 202310036773 A CN202310036773 A CN 202310036773A CN 116010718 A CN116010718 A CN 116010718A
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product
representing
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吴乐
赵宸
邵鹏阳
张琨
汪萌
洪日昌
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Hefei University of Technology
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Abstract

The invention discloses a fair personalized recommendation method, equipment and storage medium based on mutual information decoupling, wherein the method comprises the following steps: 1. constructing raw data, comprising: a scoring matrix of the user on the product, a user sensitive attribute matrix; 2. forming sensitive embedding of sensitive embedding network learning users and products, comprising: the system comprises a bias independent thermal coding layer, a sensitive information encoder and a sensitive attribute prediction layer; 3. constructing hybrid embedded web learning users and hybrid embedded products of products, comprising: a hybrid single-hot encoding layer, a hybrid information encoder and a preference prediction layer; 4. the method comprises the steps of constructing a non-sensitive embedded network, and learning a non-sensitive embedded user and a product, wherein the non-sensitive embedded network comprises a non-bias independent-heat coding layer, a mutual information lower-bound optimizing layer and a mutual information upper-bound optimizing layer. According to the recommendation method, the fairness constraint of the double mutual information is applied to the embedded vector, so that the fairness of the recommendation system is improved, and the recommendation accuracy is ensured.

Description

Fair personalized recommendation method, equipment and storage medium based on mutual information decoupling
Technical Field
The invention relates to the field of recommendation, in particular to a fair personalized recommendation method based on mutual information decoupling, electronic equipment and a storage medium.
Background
Machine learning algorithms have penetrated all aspects of our lives, and as one of the most common applications of machine learning, recommendation systems are producing a critical impact on human society, and more people use recommendation systems to seek information and decisions. Personalized product recommendation is performed by mining the history of the user based on collaborative filtering models as one of the mainstream recommendation technologies, however, the collaborative filtering based models are driven by data and are easy to generate unfair recommendation results due to data or algorithm deviation.
At the decision level, "fairness" refers to the prejudice that is not based on the innate or acquired nature of any person or group, so that an unfair recommender system is making decisions that are inclined to a particular group. For example, in an job recommendation system, male users would be recommended more high-salary professions and female users would be recommended more low-salary professions, even though they are equally rated.
The existing collaborative filtering recommendation model with fairness as a target mostly only considers the influence of the sensitive information on recommendation fairness, but ignores the influence of the non-sensitive information in the user and product characterization on recommendation accuracy and fairness. Although these approaches achieve fairness to some extent, they result in a significant decrease in recommendation accuracy.
Disclosure of Invention
The invention provides a fair personalized recommendation method, equipment and a storage medium based on mutual information decoupling, aiming at eliminating sensitive information in embedded vectors of users and products and encouraging a model to capture non-sensitive information from interactive data at the same time; the method can relieve the unfairness of recommendation, simultaneously give consideration to the accuracy of recommendation and ensure the quality of recommended content.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention discloses a fair personalized recommendation method based on mutual information decoupling, which is characterized by comprising the following steps of:
step 1, constructing original data, which comprises the following steps: a scoring matrix of users for products, a user sensitive attribute matrix:
let U denote the user set, and u= { U, assuming that there are M users and N products 1 ,...,u m ,...,u M }, where u m Representing the mth user, wherein M is more than or equal to 1 and less than or equal to M; let V denote the product set, and v= { V 1 ,...,v n ,...,v N }, where v n N is not less than 1 and not more than N, which represent the nth product;
let r mn Representing the mth user u m For the nth product v n If there is interaction, if mth user u m For the nth product v n With interaction, let r mn Let r is =1, otherwise mn =0, resulting in a user interaction matrix for the product of r= { R mn } M×N ；
Let the user sensitive attribute matrix s= { S 1 ,...,s m ,...,s M -wherein s m Representing the sensitive attribute value of the mth user;
step 2, constructing a biased embedded network, which comprises the following steps: the polarized independent thermal coding layer, the sensitive information encoder and the sensitive attribute prediction layer are used for learning the polarized embedding of the user and the product and obtaining the sensitive attribute prediction value of the mth user
Figure BDA0004047711710000021
/>
Step 3, calculating a loss function L of the biased embedded network according to the step (1) a (θ a )：
Figure BDA0004047711710000022
In the formula (1), θ a ＝[P,Q,W a ]Is a parameter to be learned;
step 4, training the biased embedded network by using a gradient descent method, and minimizing a loss function L a (θ a ) Until the loss function converges, obtaining a trained biased embedded network and corresponding optimal parameters thereof
Figure BDA0004047711710000023
Wherein P is * Representing an optimal biased embedding matrix for a user, Q * Representing the optimal biased insert matrix of the product,
Figure BDA0004047711710000024
parameters representing optimal inferred sensitivity attributes;
step 5, forming a hybrid embedded network, comprising: the mixed single-heat coding layer, the mixed information coder and the preference prediction layer are used for learning the mixed embedding of the user and the product and obtaining the mth user u m For the nth product v n Predictive preference score of (a)
Figure BDA0004047711710000025
Step 6, calculating a loss function L according to the step (2) r (θ r )：
Figure BDA0004047711710000026
In the formula (2), θ r ＝[W,Z]Is the parameter to be optimized, D m ＝{(i,j)|i∈R m ,j∈V-R m The (m) th user u m Training data of (i, j) represents and u m Ith product v with interaction i And u m No interaction of the jth product v i Is composed ofIs a product pair of (2);
Figure BDA0004047711710000027
representing the mth user u m For the ith product v i Is->
Figure BDA0004047711710000028
Representing the mth user u m For the jth product v j λ is the regularization term coefficient, |·| represents the L2 norm;
step 7, training the hybrid embedded network by using a gradient descent method, and minimizing a loss function L r (θ r ) Until the loss function converges, obtaining a trained hybrid embedded network and corresponding optimal parameters thereof
Figure BDA0004047711710000029
Wherein W is * Representing an optimal hybrid embedding matrix for a user, Z * Representing an optimal hybrid embedding matrix for the product;
step 8, constructing an unbiased embedded network, which comprises the following steps: an unbiased independent heat coding layer, a mutual information lower boundary optimizing layer and a mutual information upper boundary optimizing layer are used for learning unbiased embedding of users and products and obtaining the mutual information lower boundary of the user side
Figure BDA00040477117100000210
And the lower bound of mutual information on the product side->
Figure BDA0004047711710000031
User side mutual information upper bound->
Figure BDA0004047711710000032
And upper bound of mutual information on product side->
Figure BDA0004047711710000033
Step 9, calculating the loss function L (phi) of the optimized user side according to the formula (3) and the formula (4) respectively 1 ) And a loss function L (phi) at the product side 2 )：
Figure BDA0004047711710000034
Figure BDA0004047711710000035
In the formula (3) and the formula (4), phi 1 And phi is equal to 2 Is a parameter to be optimized;
step 10, training an unbiased embedded learning network by using a gradient descent method, and firstly minimizing a loss function L shown in the step (5) in each iteration training h (θ h ) To update the parameter theta h ＝[E,F]The loss function L shown in the formula (6) is minimized φ (phi) to update the parameter phi = [ phi ] 1 ,φ 2 ]Up to the loss function L h (θ h ) Converging to obtain the trained unbiased embedded network and the corresponding optimal parameters
Figure BDA0004047711710000036
Figure BDA0004047711710000037
/>
L φ (φ)＝L(φ 1 )+L(φ 2 )(6)
In the formula (5), gamma corresponds to the super parameter of the lower boundary of the mutual information of the control user and the product, and beta corresponds to the super parameter of the upper boundary of the mutual information of the control user and the product;
step 11, obtaining a scoring matrix of the users meeting fairness requirements on the products through the formula (7)
Figure BDA0004047711710000038
Figure BDA00040477117100000310
The fair personalized recommendation method based on mutual information decoupling is also characterized in that the step 2 comprises the following steps:
step 2.1, the biased independent thermal coding layer maps the user set U and the product set V to the biased embedding space respectively, thereby obtaining a biased embedding matrix p= [ P ] of the user 1 ,...,p m ...,p M ]Biased embedding matrix Q= [ Q ] of product 1 ,...,q n ...,q N ]Wherein p is m Representing the mth user u m Is embedded with a bias vector; q n Represents the nth product v n Is embedded with a bias vector;
step 2.2, constructing a sensitive information encoder, which comprises the following steps: laminating K graph rolls to make the current graph convolution layer be K;
inputting the partial embedded matrix P of the user and the partial embedded matrix Q of the product into a sensitive information encoder, and calculating the mth user u output after the kth picture is laminated by utilizing the method (8) m Is embedded vector with bias
Figure BDA0004047711710000039
With the nth product v n Is embedded vector +.>
Figure BDA0004047711710000041
Figure BDA0004047711710000042
In the formula (8), R m Representation and mth user u m Product set with interactions, T n Representing the nth product v n There is a set of users who have an interaction,
Figure BDA0004047711710000043
mth user u representing the output of the kth-1 graph roll layer m Is a biased embedded vector, ">
Figure BDA0004047711710000044
Nth product representing the output of the (k-1) th picture roll stackProduct v n Is set to be +.>
Figure BDA0004047711710000045
Let->
Figure BDA0004047711710000046
|R m The i represents and mth user u m The number of product collections with interactions, |T n I represents and nth product v n The number of user sets with interactions;
step 2.3, calculating the mth user u by the sensitive attribute prediction layer by using the method (9) m Sensitive attribute predicted value obtained through layering of K volumes
Figure BDA0004047711710000047
Figure BDA0004047711710000048
In the formula (9), W a Parameters representing inferred sensitive properties;
Figure BDA0004047711710000049
mth user u representing the output of the kth picture volume layer m Is embedded with a bias vector; sigma (·) represents a Sigmoid activation function.
The step 5 comprises the following steps:
step 5.1, the hybrid single thermal coding layer maps the user set U and the product set V to the hybrid embedding space respectively, so as to obtain a hybrid embedding matrix w= [ W ] of the user 1 ,...,w m ...,w M ]And product mixed embedding matrix z= [ z ] 1 ,...,z n ...,z N ]Wherein w is m Representing the mth user u m Is used for embedding the mixed embedded vector; z n Represents the nth product v n Is used for embedding the mixed embedded vector;
step 5.2, constructing a mixed information encoder, comprising: laminating K graph rolls to make the current graph convolution layer be K;
step 5.3,The mixed embedded matrix W of the user and the mixed embedded matrix Z of the product are input into a mixed information encoder, and the mth user u output after the kth picture is laminated is calculated by using (10) m Is a mixed embedded vector of (a)
Figure BDA00040477117100000410
With the nth product v n Is>
Figure BDA00040477117100000411
/>
Figure BDA00040477117100000412
In the formula (10), the amino acid sequence of the compound,
Figure BDA00040477117100000413
mth user u representing the output of the kth-1 graph roll layer m Is a mixed embedded vector, ">
Figure BDA00040477117100000414
Nth product v representing the output of the kth-1 graph roll stack n When k=1, initialize
Figure BDA00040477117100000415
Step 5.4, the preference prediction layer calculates the mth user u using equation (11) m For the nth product v n Predictive preference score of (a)
Figure BDA0004047711710000051
Figure BDA0004047711710000052
In the formula (11), </DEG, the expression of > is used to represent the inner product,
Figure BDA0004047711710000053
mth user u representing the output of the kth picture volume layer m Is a mixed embedded vector, ">
Figure BDA0004047711710000054
Nth product v representing the output of the kth picture winding n Is included in the block.
The step 8 includes:
step 8.1, the unbiased independent thermal coding layer maps the user set U and the product set V to unbiased embedding spaces respectively, thereby obtaining an unbiased embedding matrix e= [ E ] of the user 1 ,...,e m ...,e M ]Unbiased embedding matrix f= [ F ] of sum product 1 ,...,f n ...,f N ]Wherein e is m Representing the mth user u m Is embedded vector without bias; f (f) n Represents the nth product v n Is embedded vector without bias;
step 8.2, the mutual information lower bound optimization layer calculates the user side mutual information lower bound by using the method (12) and the method (13) respectively
Figure BDA0004047711710000055
And the lower bound of mutual information on the product side->
Figure BDA0004047711710000056
Figure BDA0004047711710000057
Figure BDA0004047711710000058
In the formulas (12) and (13),
Figure BDA0004047711710000059
representing the mth user u m Is an optimal hybrid embedded vector, ">
Figure BDA00040477117100000510
Represents the mthUser u m Is a biased embedding vector; />
Figure BDA00040477117100000511
Represents the nth product v n Is an optimal hybrid embedded vector, ">
Figure BDA00040477117100000512
Represents the nth product v n Is a biased embedding vector; e, e j Representing from->
Figure BDA00040477117100000513
Randomly sampling in the set to obtain the jth user u j Is embedded vector without bias; />
Figure BDA00040477117100000514
Representing an optimal biased embedding matrix P from a user * Randomly select the jth user u j Is a biased embedded vector of f j Representing from->
Figure BDA00040477117100000515
Randomly sampling in the set to obtain the jth product v j Is embedded vector without bias; />
Figure BDA00040477117100000516
Representing an optimal biased embedding matrix Q from a product * Randomly select the jth product v j Is used for the partial embedding vector of (1), pi (·, ·) represents the pearson correlation coefficient; g (·, ·, ·) is a score function, and has:
Figure BDA0004047711710000061
Figure BDA0004047711710000062
in the formulas (14) and (15), sim (·) is cosine similarity, and α is a hyper-parameter controlling a weight coefficient;
step 8.3, the upper boundary layer of the mutual information calculates the upper boundary of the mutual information of the user side by using the step (16) and the step (17)
Figure BDA0004047711710000063
And upper bound of mutual information on product side->
Figure BDA0004047711710000064
Figure BDA0004047711710000065
Figure BDA0004047711710000066
In the formula (16) and the formula (17), q φ1 (. Cndot. Cndot.). Cndot. Cn. the parameter of the side is phi 1 Is used for the distribution of the gaussian distribution of (c),
Figure BDA0004047711710000067
the parameter representing the product side is phi 2 Is a gaussian distribution of (c).
The electronic device of the invention comprises a memory and a processor, wherein the memory is used for storing a program for supporting the processor to execute any fair personalized recommendation method based on mutual information decoupling, and the processor is configured to execute the program stored in the memory.
The invention relates to a computer readable storage medium, wherein a computer program is stored on the computer readable storage medium, and is characterized in that the computer program is executed by a processor to execute any step of the fair personalized recommendation method based on mutual information decoupling.
Compared with the prior art, the invention has the beneficial effects that:
aiming at recommendation unfairness caused by sensitive information, the invention provides a double constraint based on mutual information, and the method is used for eliminating the sensitive information in the embedded vector of the user and the product and improving the non-sensitive information by using the optimized user and the product embedding of the upper bound and the lower bound of the mutual information. However, the prior art only considers the influence of sensitive information, and even if the recommendation fairness is ensured to a certain extent, the recommendation accuracy is greatly reduced. Therefore, the invention constructs a depolarization frame based on mutual information, and proposes an optimization mode for maximizing the lower bound of the mutual information and minimizing the upper bound of the mutual information, which is used for realizing the dual constraint target based on the mutual information, thereby improving the fairness of any collaborative filtering model based on embedded vectors and simultaneously preventing the recommendation accuracy from being greatly reduced.
Drawings
Fig. 1 is a flowchart of a fair personalized recommendation method based on mutual information decoupling.
Detailed Description
In this embodiment, a fair personalized recommendation method based on mutual information decoupling is constrained by means of constraint between an upper bound of mutual information and a lower bound of mutual information according to embedded vectors of a user and a product, so that the content of non-sensitive information is improved as much as possible while sensitive information is not included, as shown in fig. 1. The method is characterized by comprising the following steps of:
step 1, constructing original data, which comprises the following steps: user interaction matrix for product, user sensitive attribute matrix:
let U denote the user set, and u= { U, assuming that there are M users and N products 1 ,...,u m ,...,u M }, where u m Representing the mth user, wherein M is more than or equal to 1 and less than or equal to M; let V denote the product set, and v= { V 1 ,...,v n ,...,v N }, where v n N is not less than 1 and not more than N, which represent the nth product;
let r mn Representing the mth user u m For the nth product v n If there is interaction, if mth user u m For the nth product v n With interaction, let r mn Let r is =1, otherwise mn =0, resulting in a user interaction matrix for the product of r= { R mn } M×N ；
Let the user sensitive attribute matrix s= { S 1 ,...,s m ,...,s M -wherein s m Representing the sensitive attribute value of the mth user; the embodiment performs training and testing on a public data set MovieLens-1M, wherein the training and testing comprises an interaction matrix of a user on a product and gender characteristics of the user. 70% of each user's interaction record with the product in the MovieLens-1M dataset was used as training and the remaining 30% was used as testing. The user sensitive attribute matrix S is constructed through the sex characteristics of the user, wherein the sex characteristics comprise 'male' and 'female', 0 represents 'male', and 1 represents 'male', and then the user sensitive attribute matrix is represented in a binarized matrix form, as shown in 'user sensitive attribute matrix' in figure 1.
Step 2, constructing a biased embedded network, which comprises the following steps: the device comprises a biased independent thermal coding layer, a sensitive information encoder and a sensitive attribute prediction layer, wherein the biased independent thermal coding layer, the sensitive information encoder and the sensitive attribute prediction layer are used for learning biased embedding of a user and a product:
step 2.1, the biased independent thermal coding layer maps the user set U and the product set V to the biased embedding space respectively, so as to obtain a biased embedding matrix P= [ P ] of the user 1 ,...,p m ...,p M ]Biased embedding matrix Q= [ Q ] of product 1 ,...,q n ...,q N ]Wherein p is m Representing the mth user u m Is embedded with a bias vector; q n Represents the nth product v n Is embedded with a bias vector; the length of the biased insert vector is set to 64 for each user and product.
Step 2.2, constructing a sensitive information encoder, which comprises the following steps: k picture convolution layers are formed, the current picture convolution layer is K, the interactive relation between a user and a product is modeled through the picture convolution layer, and K is set to be 3;
inputting the partial embedded matrix P of the user and the partial embedded matrix Q of the product into a sensitive information encoder, and calculating the mth user u output after the kth picture is laminated by using (1) m Is embedded vector with bias
Figure BDA0004047711710000071
With the nth product v n Is embedded vector +.>
Figure BDA0004047711710000072
Figure BDA0004047711710000081
In the formula (1), R m Representation and mth user u m Product set with interactions, T n Representing the nth product v n There is a set of users who have an interaction,
Figure BDA0004047711710000082
mth user u representing the output of the kth-1 graph roll layer m Is a biased embedded vector, ">
Figure BDA0004047711710000083
Nth product v representing the output of the kth-1 graph roll stack n Is set to be +.>
Figure BDA0004047711710000084
Let->
Figure BDA0004047711710000085
|R m The i represents and mth user u m The number of product collections with interactions, |T n I represents and nth product v n The number of user sets with interactions;
step 2.3, calculating the mth user u by the sensitive attribute prediction layer by using the step (2) m Sensitive attribute predicted value obtained through layering of K volumes
Figure BDA0004047711710000086
Figure BDA0004047711710000087
In the formula (2), W a Parameters representing inferred sensitive properties;
Figure BDA0004047711710000088
mth user u representing the output of the kth picture volume layer m Is embedded with a bias vector; sigma (·) represents Sigmoid activation function;
step 2.4, calculating a loss function L of the biased embedded network according to the step (3) a (θ a )：
Figure BDA0004047711710000089
In the formula (3), θ a ＝[P,Q,W a ]Is a parameter to be learned;
step 2.5 training the biased embedded network by using a gradient descent method and minimizing the loss function L a (θ a ) Until the loss function converges, obtaining a trained biased embedded network and corresponding optimal parameters thereof
Figure BDA00040477117100000810
Wherein P is * Representing an optimal biased embedding matrix for a user, Q * Representing the optimal biased insert matrix of the product,
Figure BDA00040477117100000811
parameters representing optimal inferred sensitivity attributes; in this embodiment, the constructed biased embedded network learns and obtains the optimal biased embedded matrix P of the user through the sensitive attribute prediction task * And optimal biased embedded matrix Q of product * P at this time * And Q * Only sensitive information is contained.
Step 3, forming a hybrid embedded network, comprising: the mixed single-heat coding layer, the mixed information coder and the preference prediction layer are used for learning the mixed embedding of a user and a product:
step 3.1, the mixed single-heat coding layer maps the user set U and the product set V to the mixed embedding space respectively, so as to obtain a mixed embedding matrix W= [ W ] of the user 1 ,...,w m ...,w M ]And product mixed embedding matrix z= [ z ] 1 ,...,z n ...,z N ]Wherein w is m Represents the mthUser u m Is used for embedding the mixed embedded vector; z n Represents the nth product v n For each user and product, the length of the hybrid embedded vector is set to 64;
step 3.2, constructing a mixed information encoder, comprising: laminating K graph rolls to make the current graph convolution layer be K;
step 3.3, inputting the mixed embedded matrix W of the user and the mixed embedded matrix Z of the product into the mixed information encoder, and calculating the mth user u output after the kth picture is laminated by utilizing the (4) m Is a mixed embedded vector of (a)
Figure BDA0004047711710000091
With the nth product v n Is>
Figure BDA0004047711710000092
Figure BDA0004047711710000093
In the formula (4), the amino acid sequence of the compound,
Figure BDA0004047711710000094
mth user u representing the output of the kth-1 graph roll layer m Is a mixed embedded vector, ">
Figure BDA0004047711710000095
Nth product v representing the output of the kth-1 graph roll stack n When k=1, initialize
Figure BDA0004047711710000096
Step 3.4, calculating the mth user u by the preference prediction layer by using the method (5) m For the nth product v n Predictive preference score of (a)
Figure BDA0004047711710000097
Figure BDA0004047711710000098
In the formula (5), the expression "< -, - > represents the inner product,
Figure BDA0004047711710000099
mth user u representing the output of the kth picture volume layer m Is a mixed embedded vector, ">
Figure BDA00040477117100000914
Nth product v representing the output of the kth picture winding n Is used for embedding the mixed embedded vector;
step 3.5, calculating the loss function L according to the step (6) r (θ r )：
Figure BDA00040477117100000910
In the formula (6), θ r ＝[W,Z]Is the parameter to be optimized, D m ＝{(i,j)|i∈R m ,j∈V-R m The (m) th user u m Training data of (i, j) represents and u m Ith product v with interaction i And u m No interaction of the jth product v i A pair of products formed;
Figure BDA00040477117100000911
representing the mth user u m For the ith product v i Is->
Figure BDA00040477117100000912
Representing the mth user u m For the jth product v j λ is a regularization term coefficient set to 0.001, |·| represents the L2 norm;
step 3.6, training the hybrid embedded network by using a gradient descent method, and minimizing the loss function L r (θ r ) Until the loss function converges, thereby obtaining the trained mixed embeddingNetwork access and corresponding optimal parameters
Figure BDA00040477117100000913
Wherein W is * Representing an optimal hybrid embedding matrix for a user, Z * Representing an optimal hybrid embedding matrix for the product; in this embodiment, the optimal hybrid embedded matrix W of the user is learned through the constructed hybrid embedded network * And optimal hybrid embedding matrix Z for a product * W at this time * And Z * Both sensitive and non-sensitive information is included.
Step 4, constructing an unbiased embedded network, which comprises the following steps: the system comprises an unbiased independent heat coding layer, a mutual information lower bound optimizing layer and a mutual information upper bound optimizing layer, wherein the unbiased independent heat coding layer and the mutual information upper bound optimizing layer are used for learning unbiased embedding of users and products:
step 4.1, the unbiased independent thermal coding layer maps the user set U and the product set V to unbiased embedding spaces respectively, so as to obtain unbiased embedding matrixes E= [ E ] of the users 1 ,...,e m ...,e M ]Unbiased embedding matrix f= [ F ] of sum product 1 ,...,f n ...,f N ]Wherein e is m Representing the mth user u m Is embedded vector without bias; f (f) n Represents the nth product v n For each user and product, the length of the unbiased insert vector is set to 64;
step 4.2, the mutual information lower bound optimization layer calculates the mutual information lower bound of the user side by using the formula (7) and the formula (8) respectively
Figure BDA0004047711710000101
And the lower bound of mutual information on the product side->
Figure BDA0004047711710000102
Figure BDA0004047711710000103
Figure BDA0004047711710000104
In the formulas (7) and (8),
Figure BDA0004047711710000105
representing the mth user u m Is an optimal hybrid embedded vector, ">
Figure BDA0004047711710000106
Representing the mth user u m Is a biased embedding vector; />
Figure BDA0004047711710000107
Represents the nth product v n Is an optimal hybrid embedded vector, ">
Figure BDA0004047711710000108
Represents the nth product v n Is a biased embedding vector; e, e j Representing from->
Figure BDA0004047711710000109
Randomly sampling in the set to obtain the jth user u j Is embedded vector without bias; />
Figure BDA00040477117100001010
Representing an optimal biased embedding matrix P from a user * Randomly select the jth user u j Is a biased embedded vector of f j Representing from->
Figure BDA00040477117100001011
Randomly sampling in the set to obtain the jth product v j Is embedded vector without bias; />
Figure BDA00040477117100001012
Representing an optimal biased embedding matrix Q from a product * Randomly select the jth product v j Is used for the partial embedding vector of (1), pi (·, ·) represents the pearson correlation coefficient; g (·, ·, ·) is a score function, and has:
Figure BDA0004047711710000111
Figure BDA0004047711710000112
in the formulas (7) and (8), sim (·) is cosine similarity, α is a hyper-parameter controlling a weight coefficient, and α is set to 0.1; in this embodiment, by optimizing the lower boundary of mutual information between the user side and the product side, the purpose is to make the unbiased embedding matrix E of the user and the unbiased embedding matrix F of the product, respectively from the optimal mixed embedding matrix W of the user * And optimal hybrid embedding matrix Z for a product * In capturing an optimal biased embedding matrix P with a user * And optimal biased embedded matrix Q of product * Irrelevant information, i.e. non-sensitive information.
Step 4.4, calculating the upper boundary of the user side mutual information by using the upper boundary layer of the mutual information (11) and the upper boundary layer of the mutual information (12)
Figure BDA0004047711710000113
And upper bound of mutual information on product side->
Figure BDA0004047711710000114
Figure BDA0004047711710000115
Figure BDA0004047711710000116
/>
In the formulas (11) and (12),
Figure BDA0004047711710000117
the parameter representing the user side is phi 1 Conditional gaussian distribution of->
Figure BDA0004047711710000118
Representing the yieldThe parameter on the product side is phi 2 Conditional gaussian distribution of (2); in this embodiment, by optimizing the upper boundary of the mutual information between the user side and the product side, the purpose is to make the unbiased embedding matrix E of the user and the unbiased embedding matrix F of the product, and eliminate the optimal biased embedding matrix P with the user * And optimal biased embedded matrix Q of product * Related information, i.e. sensitive information.
Step 4.5, calculating the loss function L (phi) of the optimized user side according to the formula (13) and the formula (14), respectively 1 ) And a loss function L (phi) at the product side 2 )：
Figure BDA0004047711710000119
Figure BDA00040477117100001110
In the formula (13) and the formula (14), phi 1 And phi is equal to 2 Is a parameter to be optimized;
step 4.6, training the unbiased embedded learning network by using a gradient descent method, and firstly minimizing a loss function L shown in the step (15) in each iteration training h (θ h ) To update the parameter theta h ＝[E,F]The loss function L shown in the formula (16) is minimized again φ (phi) to update the parameter phi = [ phi ] 1 ,φ 2 ]Up to the loss function L h (θ h ) Converging to obtain the trained unbiased embedded network and the corresponding optimal parameters
Figure BDA0004047711710000121
Figure BDA0004047711710000122
L φ (φ)＝L(φ 1 )+L(φ 2 ) (16)
In the formula (15), gamma corresponds to the super parameter of the lower boundary of the mutual information of the control user and the product, and beta corresponds to the super parameter of the upper boundary of the mutual information of the control user and the product; both γ and β are set to 0.1;
step 4.7, obtaining a scoring matrix of the users meeting the fairness requirement from the formula (17)
Figure BDA0004047711710000123
Figure BDA0004047711710000124
In this embodiment, an electronic device includes a memory for storing a program for supporting the processor to execute the above-described product fairness recommendation method, and a processor configured for executing the program stored in the memory.
In this embodiment, a computer-readable storage medium stores a computer program that, when executed by a processor, performs the steps of the product fairness recommendation method described above.
Examples:
in order to verify the effectiveness of the method, the invention adopts two public data sets commonly used in the field of fairness of recommendation systems: movielens-1M, lastFM-360K. The invention adopts widely used NDCG and RECALL as the evaluation index of the recommendation accuracy, and the larger the value of the index is, the better the recommendation accuracy is; meanwhile, a fairness index suitable for TopK product recommendation is defined by adopting the Demographic Parity principle and the Equal Opportunity principle: the smaller the value of the index, the more fair the recommendation is, dp@k and eo@k.
TABLE 1 recommendation accuracy and fairness on methods of the invention and comparison methods
Figure BDA0004047711710000125
Figure BDA0004047711710000131
TABLE 2 recommendation accuracy and fairness on LastFM-360K for the inventive and comparative methods
Figure BDA0004047711710000132
As shown in table 1, table 2, compared with other fairness methods, the invention obtains the optimal result on the tradeoff of recommendation accuracy and fairness on the MovieLens-1m, lastfm-360K public data set; the experimental result fully verifies the effectiveness of the invention in improving the recommended fairness.

Claims (6)

1. A fair personalized recommendation method based on mutual information decoupling is characterized by comprising the following steps:
step 1, constructing original data, which comprises the following steps: a scoring matrix of users for products, a user sensitive attribute matrix:
let U denote the user set, and u= { U, assuming that there are M users and N products 1 ,...,u m ,...,u M }, where u m Representing the mth user, wherein M is more than or equal to 1 and less than or equal to M; let V denote the product set, and v= { V 1 ,...,v n ,...,v N }, where v n N is not less than 1 and not more than N, which represent the nth product;
let r mn Representing the mth user u m For the nth product v n If there is interaction, if mth user u m For the nth product v n With interaction, let r mn Let r is =1, otherwise mn =0, resulting in a user interaction matrix for the product of r= { R mn } M×N ；
Let the user sensitive attribute matrix s= { S 1 ,...,s m ,...,s M -wherein s m Representing the sensitive attribute value of the mth user;
step 2, constructing a biased embedded network, which comprises the following steps: the polarized independent thermal coding layer, the sensitive information encoder and the sensitive attribute prediction layer are used for learning the polarized embedding of a user and a productEntering and obtaining the sensitivity attribute predicted value of the mth user
Figure FDA0004047711700000015
Step 3, calculating a loss function L of the biased embedded network according to the step (1) a (θ a )：
Figure FDA0004047711700000011
In the formula (1), θ a ＝[P,Q,W a ]Is a parameter to be learned;
step 4, training the biased embedded network by using a gradient descent method, and minimizing a loss function L a (θ a ) Until the loss function converges, obtaining a trained biased embedded network and corresponding optimal parameters thereof
Figure FDA0004047711700000012
Wherein P is * Representing an optimal biased embedding matrix for a user, Q * Representing an optimal biased insert matrix of the product,>
Figure FDA0004047711700000013
parameters representing optimal inferred sensitivity attributes;
step 5, forming a hybrid embedded network, comprising: the mixed single-heat coding layer, the mixed information coder and the preference prediction layer are used for learning the mixed embedding of the user and the product and obtaining the mth user u m For the nth product v n Predictive preference score of (a)
Figure FDA0004047711700000016
Step 6, calculating a loss function L according to the step (2) r (θ r )：
Figure FDA0004047711700000014
In the formula (2), θ r ＝[W,Z]Is the parameter to be optimized, D m ＝{(i,j)|i∈R m ,j∈V-R m The (m) th user u m Training data of (i, j) represents and u m Ith product v with interaction i And u m No interaction of the jth product v i A pair of products formed;
Figure FDA0004047711700000021
representing the mth user u m For the ith product v i Is->
Figure FDA0004047711700000022
Representing the mth user u m For the jth product v j λ is the regularized term coefficient, representing the L2 norm;
step 7, training the hybrid embedded network by using a gradient descent method, and minimizing a loss function L r (θ r ) Until the loss function converges, obtaining a trained hybrid embedded network and corresponding optimal parameters thereof
Figure FDA0004047711700000023
Wherein W is * Representing an optimal hybrid embedding matrix for a user, Z * Representing an optimal hybrid embedding matrix for the product;
step 8, constructing an unbiased embedded network, which comprises the following steps: an unbiased independent heat coding layer, a mutual information lower boundary optimizing layer and a mutual information upper boundary optimizing layer are used for learning unbiased embedding of users and products and obtaining the mutual information lower boundary of the user side
Figure FDA0004047711700000024
And the lower bound of mutual information on the product side->
Figure FDA0004047711700000025
User side mutual information upper bound->
Figure FDA0004047711700000026
And upper bound of mutual information on product side->
Figure FDA0004047711700000027
Step 9, calculating the loss function L (phi) of the optimized user side according to the formula (3) and the formula (4) respectively 1 ) And a loss function L (phi) at the product side 2 )：
Figure FDA0004047711700000028
Figure FDA0004047711700000029
In the formula (3) and the formula (4), phi 1 And phi is equal to 2 Is a parameter to be optimized;
step 10, training an unbiased embedded learning network by using a gradient descent method, and firstly minimizing a loss function L shown in the step (5) in each iteration training h (θ h ) To update the parameter theta h ＝[E,F]The loss function L shown in the formula (6) is minimized φ (phi) to update the parameter phi = [ phi ] 1 ,φ 2 ]Up to the loss function L h (θ h ) Converging to obtain the trained unbiased embedded network and the corresponding optimal parameters
Figure FDA00040477117000000210
Figure FDA00040477117000000211
L φ (φ)＝L(φ 1 )+L(φ 2 )(6)
In the formula (5), gamma corresponds to the super parameter of the lower boundary of the mutual information of the control user and the product, and beta corresponds to the super parameter of the upper boundary of the mutual information of the control user and the product;
step 11, obtaining a scoring matrix of the users meeting fairness requirements on the products through the formula (7)
Figure FDA00040477117000000212
Figure FDA0004047711700000031
2. The fair personalized recommendation method based on mutual information decoupling according to claim 1, wherein the step 2 comprises:
step 2.1, the biased independent thermal coding layer maps the user set U and the product set V to the biased embedding space respectively, thereby obtaining a biased embedding matrix p= [ P ] of the user 1 ,...,p m ...,p M ]Biased embedding matrix Q= [ Q ] of product 1 ,...,q n ...,q N ]Wherein p is m Representing the mth user u m Is embedded with a bias vector; q n Represents the nth product v n Is embedded with a bias vector;
step 2.2, constructing a sensitive information encoder, which comprises the following steps: laminating K graph rolls to make the current graph convolution layer be K;
inputting the partial embedded matrix P of the user and the partial embedded matrix Q of the product into a sensitive information encoder, and calculating the mth user u output after the kth picture is laminated by utilizing the method (8) m Is embedded vector with bias
Figure FDA0004047711700000032
With the nth product v n Is embedded vector +.>
Figure FDA0004047711700000033
Figure FDA0004047711700000034
In the formula (8), R m Representation and mth user u m Product set with interactions, T n Representing the nth product v n There is a set of users who have an interaction,
Figure FDA0004047711700000035
mth user u representing the output of the kth-1 graph roll layer m Is a biased embedded vector, ">
Figure FDA0004047711700000036
Nth product v representing the output of the kth-1 graph roll stack n Is set to be +.>
Figure FDA0004047711700000037
Let->
Figure FDA0004047711700000038
R m Representation and mth user u m Quantity of product sets with interactions, T n Representing the nth product v n The number of user sets with interactions;
step 2.3, calculating the mth user u by the sensitive attribute prediction layer by using the method (9) m Sensitive attribute predicted value obtained through layering of K volumes
Figure FDA0004047711700000039
Figure FDA00040477117000000310
In the formula (9), W a Parameters representing inferred sensitive properties;
Figure FDA00040477117000000311
mth user u representing the output of the kth picture volume layer m Is embedded with a bias vector;sigma (·) represents a Sigmoid activation function.
3. The fair personalized recommendation method based on mutual information decoupling according to claim 2, wherein the step 5 comprises:
step 5.1, the hybrid single thermal coding layer maps the user set U and the product set V to the hybrid embedding space respectively, so as to obtain a hybrid embedding matrix w= [ W ] of the user 1 ,...,w m ...,w M ]And product mixed embedding matrix z= [ z ] 1 ,...,z n ...,z N ]Wherein w is m Representing the mth user u m Is used for embedding the mixed embedded vector; z n Represents the nth product v n Is used for embedding the mixed embedded vector;
step 5.2, constructing a mixed information encoder, comprising: laminating K graph rolls to make the current graph convolution layer be K;
step 5.3, inputting the mixed embedded matrix W of the user and the mixed embedded matrix Z of the product into the mixed information encoder, and calculating the mth user u output after the kth picture is laminated by using the method (10) m Is a mixed embedded vector of (a)
Figure FDA0004047711700000041
With the nth product v n Is>
Figure FDA0004047711700000042
Figure FDA0004047711700000043
In the formula (10), the amino acid sequence of the compound,
Figure FDA0004047711700000044
mth user u representing the output of the kth-1 graph roll layer m Is a mixed embedded vector, ">
Figure FDA0004047711700000045
Nth product v representing the output of the kth-1 graph roll stack n Is initialized when k=1 +.>
Figure FDA0004047711700000046
Step 5.4, the preference prediction layer calculates the mth user u using equation (11) m For the nth product v n Predictive preference score of (a)
Figure FDA0004047711700000047
Figure FDA0004047711700000048
In the formula (11), </DEG, the expression of > is used to represent the inner product,
Figure FDA0004047711700000049
mth user u representing the output of the kth picture volume layer m Is a mixed embedded vector, ">
Figure FDA00040477117000000410
Nth product v representing the output of the kth picture winding n Is included in the block.
4. The fair personalized recommendation method based on mutual information decoupling according to claim 3, wherein the step 8 comprises:
step 8.1, the unbiased independent thermal coding layer maps the user set U and the product set V to unbiased embedding spaces respectively, thereby obtaining an unbiased embedding matrix e= [ E ] of the user 1 ,...,e m ...,e M ]Unbiased embedding matrix f= [ F ] of sum product 1 ,...,f n ...,f N ]Wherein e is m Representing the mth user u m Is embedded vector without bias; f (f) n Represents the nth product v n Is embedded vector without bias;
step 8.2, the mutual trustThe lower-bound information optimization layer calculates the lower bound of the mutual information at the user side by using the formula (12) and the formula (13) respectively
Figure FDA00040477117000000411
And the lower bound of mutual information on the product side->
Figure FDA00040477117000000412
Figure FDA00040477117000000413
Figure FDA0004047711700000051
In the formulas (12) and (13),
Figure FDA0004047711700000052
representing the mth user u m Is an optimal hybrid embedded vector, ">
Figure FDA0004047711700000053
Representing the mth user u m Is a biased embedding vector; />
Figure FDA0004047711700000054
Represents the nth product v n Is an optimal hybrid embedded vector, ">
Figure FDA0004047711700000055
Represents the nth product v n Is a biased embedding vector; e, e j Representing from->
Figure FDA0004047711700000056
Randomly sampling in the set to obtain the jth user u j Is embedded vector without bias; />
Figure FDA0004047711700000057
Representing an optimal biased embedding matrix P from a user * Randomly select the jth user u j Is a biased embedded vector of f j Representing from->
Figure FDA0004047711700000058
Randomly sampling in the set to obtain the jth product v j Is embedded vector without bias; />
Figure FDA0004047711700000059
Representing an optimal biased embedding matrix Q from a product * Randomly select the jth product v j Is used for the partial embedding vector of (1), pi (·, ·) represents the pearson correlation coefficient; g (·, ·, ·) is a score function, and has:
Figure FDA00040477117000000510
Figure FDA00040477117000000511
in the formulas (14) and (15), sim (·) is cosine similarity, and α is a hyper-parameter controlling a weight coefficient;
step 8.3, the upper boundary layer of the mutual information calculates the upper boundary of the mutual information of the user side by using the step (16) and the step (17)
Figure FDA00040477117000000512
And upper bound of mutual information on product side->
Figure FDA00040477117000000513
Figure FDA00040477117000000514
Figure FDA00040477117000000515
In the formulas (16) and (17),
Figure FDA00040477117000000516
the parameter representing the user side is phi 1 Gaussian distribution of->
Figure FDA00040477117000000517
The parameter representing the product side is phi 2 Is a gaussian distribution of (c).
5. An electronic device comprising a memory and a processor, wherein the memory is configured to store a program that supports the processor to perform the fair personalized recommendation method based on mutual information decoupling of any one of claims 1-4, the processor being configured to execute the program stored in the memory.
6. A computer readable storage medium having stored thereon a computer program, characterized in that the computer program when executed by a processor performs the steps of the fair personalized recommendation method based on mutual information decoupling according to any one of claims 1-4.
CN202310036773.4A 2023-01-10 2023-01-10 Fair personalized recommendation method, equipment and storage medium based on mutual information decoupling Pending CN116010718A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116645174A (en) * 2023-07-27 2023-08-25 山东省人工智能研究院 Personalized recommendation method based on decoupling multi-behavior characterization learning
CN116720006A (en) * 2023-08-10 2023-09-08 数据空间研究院 Fair recommendation method, device and medium based on limited user sensitivity attribute

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116645174A (en) * 2023-07-27 2023-08-25 山东省人工智能研究院 Personalized recommendation method based on decoupling multi-behavior characterization learning
CN116645174B (en) * 2023-07-27 2023-10-17 山东省人工智能研究院 Personalized recommendation method based on decoupling multi-behavior characterization learning
CN116720006A (en) * 2023-08-10 2023-09-08 数据空间研究院 Fair recommendation method, device and medium based on limited user sensitivity attribute
CN116720006B (en) * 2023-08-10 2023-11-03 数据空间研究院 Fair recommendation method, device and medium based on limited user sensitivity attribute

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