A training method, a recommendation method and a recommendation system for a recommendation model

By adopting the cross-pairing sorting algorithm and unbiased loss function in the recommendation model, combined with the dynamic sampling strategy, the problem of popular items occupying too much exposure opportunities in the recommendation system is solved, and the recommendation quality and prediction accuracy of niche items are improved.

CN113987358BActive Publication Date: 2025-05-27UNIV OF SCI & TECH OF CHINA
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Patent Information

Application Number
CN202111346460.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-11-15
Publication Date
2025-05-27
Estimated Expiration
2041-11-15

AI Technical Summary

Technical Problem

Existing recommendation models are susceptible to bias inherent in observation data when optimizing parameters, resulting in popular items occupying too much exposure opportunities and damaging the recommended quality of niche items.

Method used

Using an unbiased learning method based on the cross-pair sorting algorithm, we ensure unbiased learning of each sample and reduce popularity bias by constructing a new unbiased loss function and dynamic sampling strategy.

Benefits of technology

It improves the prediction accuracy of the recommendation system on niche items, reduces popularity deviation, and improves the overall performance of the recommendation system.

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Abstract

The present invention discloses a training method for a recommendation model, including: obtaining training sample data, wherein the training sample data includes user-item pairs, and the user-item pairs include user information, item information, and interaction information between the user and the item; constructing a recommendation model based on a cross-pair ranking algorithm and initializing the parameters of the recommendation model; using the recommendation model to process the training sample data, and optimizing the parameters of the recommendation model according to an unbiased loss function to obtain a trained recommendation model. The present invention also discloses an unbiased recommendation method, an unbiased recommendation system, an electronic device, and a computer program product.
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Description

Technical Field

[0001] The present invention relates to the fields of machine learning and data mining, and particularly to a training method for a recommendation model, a recommendation method, a recommendation system, an electronic device, and a computer program product. Background Art

[0002] For many online platforms, including e-commerce, streaming media, social networks, etc., recommendation systems play a core role. Most existing recommendation models follow the paradigm of supervised learning, using the historical interactions of users (implicit feedback such as clicks and purchases) as labeled data, and learning the user-item correlation by fitting the labeled data. Existing technologies usually use point loss and pairwise loss to optimize the parameters of the recommendation model. However, these standard loss functions are easily affected by the biases inherent in the observed data. Interaction data usually exhibits a long-tailed distribution with respect to item popularity, that is, a few popular items account for most of the interactions. The mainstream loss functions only focus on the recovery of historical data and do not consider the bias effect. When using these loss functions to build a recommendation system, a few popular items will occupy more and more exposure opportunities, seriously damaging the recommendation quality of niche items. In the prior art, to solve the above problems, the common practice is to use the Inverse Propensity Score (IPS), which re-weights each data sample by the propensity score (i.e., the exposure probability). But it has limitations in practice: (1) It is difficult to accurately estimate the propensity score for each sample because the exposure mechanism is often unknown; (2) The re-weighted loss values usually have a high variance, which means that the loss value of a single sample fluctuates greatly relative to the expected value. Summary of the Invention

[0003] To solve the above problems, the present invention provides a training method for a recommendation model, a recommendation method, a recommendation system, an electronic device, and a computer program product.

[0004] According to a first aspect of the present invention, there is provided a training method for a recommendation model, including:

[0005] Obtaining training sample data, where the training sample data includes user-item pairs, and the user-item pairs include user information, item information, and interaction information between the user and the item;

[0006] Constructing a recommendation model based on a cross-pair ranking algorithm and initializing the parameters of the recommendation model;

[0007] Processing the training sample data using the recommendation model, and optimizing the parameters of the recommendation model according to an unbiased loss function to obtain a trained recommendation model;

[0008] where the unbiased loss function is represented by Equation (1):

[0009]

[0010] Among them, k represents the number of user-item pairs with interaction relationships in the training sample data, u k represents the k-th user, i k represents the k-th item, represents the relevance score between the k-th user and the k-th item, is the training sample data, and σ is the activation function of the recommendation model.

[0011] According to an embodiment of the present invention, the above-mentioned training sample data is represented by Equation (2):

[0012]

[0013] Among them, represents that the m-th user and the n-th item have an interaction relationship, represents that the m-th user and the n-th item do not have an interaction relationship.

[0014] According to an embodiment of the present invention, the above-mentioned unbiased loss function is defined by Equation (3) and Equation (4):

[0015] P(Y u,i = 1) = P(R u,i = 1)P(Q u,i = 1|R u,i = 1) (3),

[0016] P(Q u,i = 1|R u,i = 1) = p u ·p i ·P(R u,i = 1) α (4),

[0017] Among them, R u,i = 1 indicates that user u likes item i, O u,i = 1 indicates that user u can see item i, Y u,i = R u,i ·O u,i , P(R u,i = 1) is the relevance probability, P(O u,i = 1|R u,i = 1) is the exposure rate; α is a positive constant.

[0018] According to an embodiment of the present invention, the above-mentioned exposure rate can be decomposed into user tendency, item tendency, and user-item relevance.

[0019] According to an embodiment of the present invention, the obtaining of the training sample data includes:

[0020] Obtaining a plurality of sample data according to a preset sampling batch value, a dynamic sampling rate, and a selection rate, where the sample data includes a plurality of user-item pairs with interaction relationships;

[0021] Preprocessing the sample data, screening out user-item pairs in which the user has no interaction information with other items or the item has no interaction information with other users, and obtaining the screened sample data;

[0022] Processing the screened sample data by using a recommendation model to obtain an average relevance value of the user-item pairs;

[0023] Selecting the screened sample data with the smallest average relevance value as the training sample data.

[0024] According to an embodiment of the present invention, the above average relevance value is represented by formula (5):

[0025]

[0026] where k represents the number of user-item pairs with interaction relationships in the sample data, u k represents the k-th user, i k represents the k-th item, represents the relevance score of the k-th user and the k-th item.

[0027] According to a second aspect of the present invention, an unbiased recommendation method is provided, including:

[0028] Obtaining data to be processed, where the data to be processed includes user-item pairs, and the user-item pairs include user information, item information, and interaction information between the user and the item;

[0029] Constructing an unbiased recommendation model based on a cross-pairing sorting algorithm and initializing the parameters of the recommendation model;

[0030] Processing the data to be processed by using the recommendation model, where the recommendation model is trained by the above method.

[0031] According to a third aspect of the present invention, an unbiased recommendation system is provided, including:

[0032] A data acquisition module for acquiring user-item pair data;

[0033] A recommendation model based on a cross-pairing sorting algorithm for processing user-item pair data to recommend relevant items to users, where the recommendation model is trained by the above method.

[0034] According to a fourth aspect of the present invention, there is provided an electronic device, comprising:

[0035] one or more processors;

[0036] a storage device for storing one or more programs,

[0037] wherein, when the one or more programs are executed by the one or more processors, the one or more processors are caused to execute the above method.

[0038] According to a fifth aspect of the present invention, there is provided a computer program product comprising a computer program which, when executed by a processor, implements the above method.

[0039] The recommendation model training method provided by the present invention is based on the Cross Pair Rank (CPR) algorithm. Compared with IPS, CPR can ensure unbiased learning for each sample when the exposure mechanism is unknown. At the same time, the loss function of the recommendation model provided by the present invention can be applied to a variety of underlying recommendation models, greatly improving the performance of these models on unbiased data, and the effect exceeds the current optimal debiasing method. The recommendation system obtained by applying the recommendation model training method provided by the present invention has higher prediction accuracy, especially when applied to the recommendation of niche products, and can better alleviate the popularity bias. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematically shows a flowchart of a method for training a recommendation model according to an embodiment of the present invention;

[0041] Figure 2 Schematically shows a flowchart of obtaining training sample data according to an embodiment of the present invention;

[0042] Figure 3 is a schematic diagram of training sample data obtained by a dynamic sampling strategy according to an embodiment of the present invention;

[0043] Figure 4 Schematically shows a flowchart of an unbiased recommendation method according to an embodiment of the present invention;

[0044] Figure 5 Schematically shows a structural diagram of an unbiased recommendation system according to an embodiment of the present invention;

[0045] Figure 6 Schematically shows a block diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0046] To make the objectives, technical solutions, and advantages of the present invention more clear and understandable, the following further elaborates on the present invention in detail with reference to specific embodiments and the accompanying drawings.

[0047] Recommendation systems are widely used on platforms such as streaming media, e-commerce, and social networks. Currently, loss functions are usually used to optimize the parameters of recommendation models. Among them, there are two types of loss functions: (1) Point loss, which captures the user's preference for a single item by minimizing the difference between the target and the predicted user-item correlation score, such as binary cross-entropy and mean squared error. (2) Pairwise loss, which simulates the user's preference for two items by encouraging the predicted value of the positive sample to be higher than that of the negative sample, such as Bayesian personalized ranking. The present invention provides an unbiased learning method based on the cross-pair ranking algorithm (CPR) to ensure unbiased learning during the training process of the recommendation model.

[0048] Figure 1 The flowchart of a method for training a recommendation model according to an embodiment of the present invention is schematically shown.

[0049] As Figure 1 shown, it includes operation S110 to operation S130.

[0050] In operation S110, training sample data is obtained, where the training sample data includes user-item pairs, and the user-item pairs include user information, item information, and the interaction information between the user and the item;

[0051] The above user-item pairs are data pairs with an interaction relationship (such as purchase, collection, click, browsing, etc.).

[0052] In operation S120, a recommendation model based on the cross-pair ranking algorithm is constructed and the parameters of the recommendation model are initialized;

[0053] In operation S130, the training sample data is processed using the recommendation model, and the parameters of the recommendation model are optimized according to the unbiased loss function to obtain a trained recommendation model;

[0054] Among them, the unbiased loss function is represented by Equation (1):

[0055]

[0056] Among them, k represents the number of user-item pairs with an interaction relationship in the training sample data, u k represents the k-th user, i k represents the k-th item, represents the correlation score between the k-th user and the k-th item, is the training sample data, and σ is the activation function of the recommendation model.

[0057] In the above loss function for unbiasedness, The user-item correlation score predicted by the friend recommendation model is generally obtained by inputting the embeddings of the user and the item into an interaction function, such as the inner product or a deep network, etc., to obtain the predicted score. The purpose of this score is to fit the true correlation score between the user and the item.

[0058] The training method of the above recommendation model provided by the present invention constructs a new loss function with small unbiasedness, thereby removing the popularity bias problem brought by the training sample data to the recommendation result in the case where the exposure mechanism is unknown, and improving the proportion and quality of the recommendation of niche items.

[0059] According to an embodiment of the present invention, the above training sample data is represented by Equation (2):

[0060]

[0061] where, indicates that the ith user and the nth item have an interaction relationship, indicates that the ith user and the nth item do not have an interaction relationship.

[0062] For example, indicates that the 1st user and the 1st item have an interaction relationship, indicates that the 1st user and the 2nd item do not have an interaction relationship.

[0063] According to an embodiment of the present invention, the above unbiased loss function is defined by Equation (3) and Equation (4):

[0064] P(Y u,i = 1) = P(R u,i = 1)P(O u,i = 1|R u,i = 1) (3),

[0065] P(O u,i = 1|R u,i = 1) = p u ·p i ·P(R u,i = 1) α (4),

[0066] where, R u,i = 1 indicates that user u likes item i, O u,i = 1 indicates that user u can see item i, Y u,i = R u,i ·O u,i , P(R u,i= 1) is the relevance probability, P(O u,i = 1|R u,i = 1) is the exposure rate; α is a positive constant.

[0067] In the above formulas (3) and (4), two binary variables R u,i and O u,i are introduced; P(R u,i = 1) is the relevance probability, s u,i = ln P(R u,i = 1) is the value that the recommendation model provided by the present invention attempts to fit; P(O u,i = 1|R u,i = 1) is the exposure probability. Popular items and active users generally have a greater exposure probability, so they have a greater interaction probability P(Y u,i = 1) and occupy more interactions in the observed data.

[0068] According to an embodiment of the present invention, the above exposure rate can be decomposed into user preference, item preference, and user-item relevance.

[0069] The decomposition of the above exposure rate can be represented by the above formula (4). According to the decomposition formula of the exposure rate, the unbiased loss function provided by the present invention can eliminate the popularity bias caused by the preferences of users and items, so that the prediction score can be used to accurately fit the true score s u,i .

[0070] To construct an unbiased loss function, a new sampling method is needed to obtain training sample data The method adopted in the prior art is random sampling: First, k non-overlapping user-item pairs are drawn. If their cross combinations have not occurred in interactions, they are accepted as a sample; otherwise, they are discarded and samples are redrawn. However, in this way, all samples are selected with the same probability, and some difficult samples may require more iterations to converge, affecting the efficiency of model training.

[0071] To solve the above problems, the present invention provides a dynamic sampling strategy for CPR, aiming to assign a higher sampling probability to difficult samples and train them more frequently.

[0072] Figure 2 Schematically shows a flowchart of obtaining training sample data according to an embodiment of the present invention.

[0073] As Figure 2 shown, it includes operation S210 to operation S240.

[0074] In operation S210, multiple sample data are obtained according to a preset sampling batch value, a dynamic sampling rate, and a selection rate, where the sample data includes multiple user-item pairs with interaction relationships;

[0075] Let b, β, and γ (γ > 1) represent the batch value (i.e., batch size), the dynamic sampling rate, and the selection rate respectively; First, randomly select bβγ samples, and each sample contains k pairs of interacting user-item data pairs. The selection rate y is to increase the number of initial samples to ensure that after discarding inappropriate samples in the subsequent operations, the required number of samples can still be collected.

[0076] In operation S220, the sample data is preprocessed to filter out the user-item pairs in which the user has no interaction information with other items or the item has no interaction information with other users, and the filtered sample data is obtained;

[0077] In the above operations, if a user has a cross relationship with all items in the sample data, then the user-item pair data is discarded; similarly, similar operations are performed on the items.

[0078] In operation S230, the filtered sample data is processed using a recommendation model to obtain the average correlation of the user-item pairs;

[0079] For the recommendation model constructed by the above method, the model parameters have been initialized. First, use this recommendation model for prediction, and then perform multiple rounds of optimization on the parameters of the recommendation model according to the unbiased loss function.

[0080] In operation S240, the filtered sample data with the smallest average correlation is selected as the training sample data.

[0081] The smaller the above average correlation, the more difficult it is for the sample to reach its target ranking. Therefore, select those samples with the minimum average correlation as a batch of sample data.

[0082] Figure 3 It is a schematic diagram of the training sample data obtained according to the dynamic sampling strategy of the embodiment of the present invention. Next, in conjunction with Figure 3 The data structure of the obtained training sample data will be further explained.

[0083] As Figure 3 shown, in the training sample data, the solid line represents that there is an interaction relationship between the user and the item, and the dotted line represents that there is no interaction relationship between the user and the item. The dynamic sampling strategy provided by the embodiment of the present invention aims to obtain a large number of user-item pair data without interaction relationships to facilitate the training of the recommendation model provided by the embodiment of the present invention.

[0084] According to an embodiment of the present invention, the above-mentioned average correlation value is represented by formula (5):

[0085]

[0086] where k represents the number of user-item pairs with interaction relationships in the sample data, u k represents the k-th user, and i k represents the k-th item, represents the correlation score between the k-th user and the k-th item.

[0087] By adopting the above dynamic sampling strategy to obtain the training sample data, it can enable the training to converge faster, achieve the best effect in a shorter time, and have good generalization ability for training sets with different degrees of deviation.

[0088] Figure 4 The flowchart of an unbiased recommendation method according to an embodiment of the present invention is schematically shown.

[0089] As Figure 4 shown, it includes operation S410 to operation S430.

[0090] In operation S410, the data to be processed is obtained, where the data to be processed includes user-item pairs, and the user-item pairs include user information, item information, and the interaction information between the user and the item;

[0091] In operation S420, an unbiased recommendation model based on the cross-pair ranking algorithm is constructed and the parameters of the recommendation model are initialized;

[0092] In operation S430, the data to be processed is processed by using the recommendation model, where the recommendation model is obtained by training with the above method.

[0093] To verify the conclusion, based on the matrix factorization model (MF) as the basic recommendation model, three public datasets, MovieLens, Netflix, and iFashion, are selected for experiments. Two traditional training methods, BPR and Mult-VAE, and four debiasing methods, CausE, Rel-MF, UBPR, and DICE, are compared. To measure the debiasing effect, when constructing the validation set and the test set, the same sampling probability is given to each item to construct simulated unbiased data, and two common metrics, Recall@K and NDCG@K, are calculated on the unbiased data. The higher these two metrics are, the higher the accuracy of the recommendation is, especially for the recommendation accuracy of niche items. The embodiment of the present invention also calculates the ARP@K metric, that is, the average popularity of the top-K recommended items. The lower this metric is, the smaller the popularity bias of the recommendation is. K is taken as 20.

[0094] The experimental results are shown in Table 1. The methods provided by the embodiments of the present invention are CPR-rand and CPR. CPR-rand uses random sampling, while CPR uses dynamic sampling. CPR-rand outperforms all baselines on MovieLens and Netflix. On iFashion, CPR-rand achieves a Recall similar to the best baseline, but has a lower ARP, indicating that its recommended bias is smaller. CPR further improves the performance of CPR-rand on all datasets and is significantly better than all baselines in terms of Recall and NDCG.

[0095] Table 1 Overall Comparison

[0096]

[0097] Compared with other methods, the higher Recall and NDCG of CPR on the unbiased test set indicate that it has higher prediction accuracy, especially for niche items. The lower ARP of CPR further indicates that CPR tends to recommend more niche items. In other words, it can better alleviate the popularity bias.

[0098] Figure 5 Schematically shows a structural diagram of an unbiased recommendation system according to an embodiment of the present invention. As Figure 5 shown, the recommendation system 500 includes a data acquisition module 510 and a recommendation model 520.

[0099] The data acquisition module 510 is used to acquire user-item pair data;

[0100] The recommendation model 520 based on the cross-pair ranking algorithm is used to process the user-item pair data and recommend relevant items to users. Among them, the recommendation model is obtained by training with the above method.

[0101] The recommendation system provided by the present invention can be applied to e-commerce, streaming media, social networks, etc. Using the unbiased loss function provided by the present invention, the recommendation system can more accurately recommend more niche items, improve the user experience, and increase the platform revenue.

[0102] According to the fourth aspect of the present invention, one or more processors are provided;

[0103] A storage device for storing one or more programs,

[0104] wherein, when the one or more programs are executed by the one or more processors, the one or more processors are caused to execute the above method.

[0105] Figure 6 Schematically shows a block diagram of an electronic device according to an embodiment of the present invention.

[0106] As shown Figure 6 As shown in FIG. Figure 6 , the electronic device 600 according to an embodiment of the present disclosure includes a processor 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 602 or a program loaded from a storage section 608 into a random access memory (RAM) 603. The processor 601 may include, for example, a general-purpose microprocessor (e.g., CPU), an instruction set processor, and / or a related chipset, and / or a dedicated microprocessor (e.g., an application specific integrated circuit (ASIC)), etc. The processor 601 may also include on-board memory for caching purposes. The processor 601 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present disclosure.

[0107] In the RAM 603, various programs and data required for the operation of the electronic device 600 are stored. The processor 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. The processor 601 performs various operations of the method flow according to an embodiment of the present disclosure by executing the programs in the ROM 602 and / or the RAM 603. It should be noted that the programs may also be stored in one or more memories other than the ROM 602 and the RAM 603. The processor 601 may also perform various operations of the method flow according to an embodiment of the present disclosure by executing the programs stored in the one or more memories.

[0108] According to an embodiment of the present disclosure, the electronic device 600 may further include an input / output (I / O) interface 605, and the input / output (I / O) interface 605 is also connected to the bus 604. The electronic device 600 may further include one or more of the following components connected to the I / O interface 505: an input section 606 including a keyboard, a mouse, etc.; an output section 607 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc. and a speaker, etc.; a storage section 608 including a hard disk, etc.; and a communication section 609 including a network interface card such as a LAN card, a modem, etc. The communication section 609 performs communication processing via a network such as the Internet. A drive 610 is also connected to the I / O interface 605 as needed. A removable medium 611, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 610 as needed so that a computer program read therefrom can be installed into the storage section 608 as needed.

[0109] According to a fifth aspect of the present invention, there is provided a computer program product including a computer program, which when executed by a processor implements the above method.

[0110] When the computer program product runs in a computer system, the program code causes the computer system to implement the item recommendation method provided by the embodiments of the present disclosure.

[0111] When the computer program is executed by the processor 601, the above functions defined in the system / apparatus of the embodiments of the present disclosure are executed. According to the embodiments of the present disclosure, the above-described systems, apparatuses, modules, units, etc. can be implemented by computer program modules.

[0112] In one embodiment, the computer program can rely on tangible storage media such as optical storage devices, magnetic storage devices, etc. In another embodiment, the computer program can also be transmitted and distributed in the form of a signal on a network medium, and downloaded and installed through the communication part 609, and / or installed from the removable medium 611. The program code included in the computer program can be transmitted by any suitable network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0113] In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 609, and / or installed from the removable medium 611. When the computer program is executed by the processor 601, the above functions defined in the system of the embodiments of the present disclosure are executed. According to the embodiments of the present disclosure, the above-described systems, devices, apparatuses, modules, units, etc. can be implemented by computer program modules.

[0114] According to the embodiments of the present disclosure, the program code for executing the computer program provided by the embodiments of the present disclosure can be written in any combination of one or more programming languages. Specifically, these computing programs can be implemented using high-level procedures and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages include but are not limited to, such as Java, C++, python, the "C" language, or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (for example, by using an Internet service provider to connect through the Internet).

[0115] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A training method for a recommendation model, comprising: Obtaining training sample data, wherein the training sample data includes user-item pairs, and the user-item pairs include user information, item information, and interaction information between the user and the item; Constructing a recommendation model based on a cross-pairwise ranking unbiased loss function and initializing the parameters of the recommendation model; Processing the training sample data using the recommendation model, and optimizing the parameters of the recommendation model according to the unbiased loss function to obtain a trained recommendation model; wherein the unbiased loss function is represented by Equation (1): (1), Among them, represents the number of user-item pairs with interaction relationships in the training sample data, represents the th user, represents the th item, represents the relevance score between the th user and the th item, is the training sample data, is the activation function of the recommendation model; Among them, the is represented by Equation (2): (2), Among them, indicates that there is an interaction relationship between the m-th user and the n-th item, indicates that there is no interaction relationship between the m-th user and the n-th item; wherein the unbiased loss function is defined by Equations (3) and (4): (3), (4), Among them, represents the user likes the item , represents the user can see the item , , is the relevance probability, is the exposure rate; is a positive constant; wherein the exposure rate can be decomposed into user propensity, item propensity, and user-item correlation; wherein the obtaining of the training sample data includes: Obtaining a plurality of sample data according to a preset sampling batch value, a dynamic sampling rate, and a selection rate, wherein the sample data includes a plurality of user-item pairs with interaction relationships; Preprocessing the sample data, screening out the user-item pairs in which the user has no interaction information with other items or the item has no interaction information with other users, to obtain the screened sample data; Processing the screened sample data using the recommendation model to obtain the average correlation of the user-item pairs; Selecting the screened sample data with the smallest average correlation as the training sample data.

2. The method according to claim 1, wherein, the average correlation is represented by formula (5): (5), Among them, represents the number of user-item pairs with interaction relationships in the sample data, represents the th user, represents the th item, represents the relevance score between the kth user and the th item.

3. An unbiased recommendation method, comprising: Obtaining data to be processed, wherein the data to be processed includes user-item pairs, and the user-item pairs include user information, item information, and interaction information between the user and the item; Constructing a recommendation model based on a cross-pairwise ranking unbiased loss function and initializing the parameters of the recommendation model; Processing the data to be processed using the recommendation model, wherein the recommendation model is trained according to the method described in any one of claims 1 and 2.

4. An unbiased recommendation system, comprising: A data acquisition module for acquiring user-item pair data; A recommendation model based on a cross-pairwise ranking unbiased loss function for processing the user-item pair data to recommend relevant items to the user, wherein the recommendation model is trained according to the method described in any one of claims 1 and 2.

5. An electronic device, comprising: One or more processors; A storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors execute the method described in any one of claims 1 to 3.

6. A computer program product, comprising a computer program which, when executed by a processor, implements the method described in any one of claims 1 to 3.

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