Prediction Method and System Based on Multi-View Task Relationship-Aware Meta-Learning

Abstract

A prediction method and system based on multi-view task relationship-aware meta-learning. For the recommendation task of a given cold-start user, while learning the user's personalized preference representation using the context interaction information of the task itself, the multi-view association relationship between this task and other recommendation tasks is utilized to aggregate the representations of similar tasks. Based on the learned task representation, the present invention generates the initial parameters of a personalized customized scoring prediction model for this task by querying the task-aware fast weight memory learned during the historical model training process. Finally, the scoring prediction model obtains the scoring prediction model unique to this user by performing local parameter updates on a small number of observable interactions, and can generate personalized recommendation results.

Description

Technical Field

[0001] The present invention relates to a technology in the field of information processing, and specifically to a prediction method and system based on multi-view task relationship-aware meta-learning. Background Art

[0002] In many current online services, prediction methods and systems are usually used to accurately predict users' preferences for items, so as to recommend interesting items for them, achieving the purpose of alleviating the problem of information overload. In addition to the rating prediction method for regular user recommendations, the cold-start user recommendation problem often suffers from insufficient user interaction records, making it impossible for many existing rating prediction methods to obtain good model training or training biases, resulting in inaccurate recommendation results for cold-start users.

[0003] Existing rating prediction methods usually use auxiliary information or transfer information of input users / items to alleviate the cold-start problem. Specifically, a common strategy is to use additional user / item-side information to supplement the association between users and items, as well as user-item interactions. For example, user profiles and item contents can be encoded into user / item representations to implicitly learn the content-based similarity between users and items. In addition, graph-structured data (such as knowledge, heterogeneous information networks, etc.) can also provide semantic associations through explicit graph connections. However, these methods focus on making recommendations by combining additional user similarities or item correlations, but still lack the design of discovering personal preferences from the limited interactions of cold-start users. Another popular strategy is to transfer knowledge about cold-start users from other domains, which is the core idea of cross-domain methods. The limitation is that due to the heterogeneity and isolation between different domains, a large number of shared users are not always available. In addition, traditional methods usually follow the general supervised learning paradigm and train a unified model for all users. When making recommendations for cold-start users, the performance may be very poor due to data imbalance and long-tail problems.

[0004] Meta learning, also known as "learning to learn", is inspired by the human learning process and can quickly learn new tasks based on a small number of examples. Meta learning can be divided into three types: metric-based, memory-based, and optimization-based. In recent years, meta learning has shown effectiveness in solving the cold start problem in recommendation. Generally speaking, meta learning focuses on obtaining globally shared meta-knowledge (such as model initialization, external meta-learners, etc.) in different training tasks. The learned meta-knowledge should have strong generalization ability and ensure quick adaptation to new tasks through a small number of samples. Inspired by the idea of optimization-based meta learning, the model-agnostic meta learning (MAML) framework is introduced into cold start recommendation, aiming to learn the global initialization of the base model as prior knowledge. In addition to the user cold start scenario, some studies also focus on the click-through rate (CTR) prediction problem and the item cold start problem in online recommendation based on optimization meta learning.

[0005] Existing recommendation systems based on collaborative filtering techniques such as matrix factorization utilize rich interaction data of users and items to model users' preferences for items and achieve good recommendation effects. However, for cold start users, that is, users with a small number of observed interactions, these methods do not have good personalized recommendation capabilities. Some recommendation methods based on meta learning attempt to learn the initialization recommendation model parameters with strong generalization ability, enabling the personalized recommendation models for different cold start users to locally adapt the parameters on a small number of interactions and accurately capture the preferences of different cold start users. However, due to the differences in user preferences, the recommendation tasks for different users are usually heterogeneous, and a single initialization parameter shared by all tasks is difficult to apply to the recommendation tasks for all users. Summary of the Invention

[0006] In view of the deficiencies of the prior art that a large amount of user interaction data is required as training samples and the recommendation effect for cold-start users in actual industrial application scenarios is not considered, that is, users with fewer interactions will have poor results due to insufficient training samples; it is impossible to distinguish the characteristics of recommendation tasks for different users, and it is difficult to achieve good results in scenarios with severe heterogeneity of recommendation tasks, etc., the present invention proposes a prediction method and system based on multi-view task relationship-aware meta-learning. For the recommendation task of a given cold-start user, while learning the user's personalized preference representation using the context interaction information of the task itself, the multi-view association relationship between this task and other recommendation tasks is utilized to aggregate the representations of similar tasks. Based on the learned task representations, the present invention generates the initial parameters of a personalized scoring prediction model for this task by querying the task-aware fast weight memory learned during the historical model training process. Finally, the scoring prediction model obtains the scoring prediction model unique to this user by performing local parameter updates on a small number of observable interactions, and can generate personalized recommendation results.

[0007] The present invention is realized through the following technical solutions:

[0008] The present invention relates to a prediction method based on multi-view task relationship-aware meta-learning, including:

[0009] Step 1) Unify the format of the user's interaction data as the input part for subsequent recommendation task representation learning and local adaptation of the scoring prediction model. Specifically: The data of user-item interactions and the feature data of users and items must first be subjected to data cleaning to remove possible noisy data. At the same time, the interaction records should be sorted according to the specified format, and a set of observable interactions should be generated for each user according to the time stamp of the record.

[0010] Step 2) Utilize the context interaction information of the task itself and the multi-angle association relationship with other tasks to learn a fixed-dimensional vector representation for the current recommendation task as the task characteristic representation. Specifically: Through the context-based task representation learning module, model the user's interest from the user's interaction information to obtain the user interest representation of this task; through the multi-view task relationship modeling module, construct a heterogeneous information network using the user profile, item attributes, and user-item interactions, and mine task associations from user similarity, interaction item similarity, and interaction item attribute similarity, and combine the information of similar tasks to represent the current recommendation task.

[0011] The context-based task representation learning module described above includes: an encoder, a decoder, and an interaction aggregation unit, where: The encoder performs encoding processing based on user interaction information to obtain a low-dimensional vector representation of each interaction. The decoder decodes and reconstructs the original interaction information based on the obtained low-dimensional vector representation, and combines the reconstruction loss to improve the quality of the low-dimensional vector representation. The interaction aggregation unit performs representation aggregation on the vector representations of multiple interactions using average pooling to obtain the final user interest representation of the task.

[0012] The multi-view task relationship modeling module described above includes: a heterogeneous information network construction unit, a meta-path extraction unit, and a two-layer attention aggregation unit, where: The heterogeneous information network construction unit constructs a heterogeneous information network based on user interaction information, user attribute information, and item attribute information to obtain a structured task relationship graph; The meta-path extraction unit extracts neighbor information between target tasks based on the heterogeneous information network based on meta-paths to obtain a set of related task nodes from multiple perspectives; The two-layer attention aggregation unit uses the set of task nodes to perform relationship representation learning based on meta-paths, aggregates the neighborhood information of the target task on the heterogeneous graph, and obtains the relationship representation of the task.

[0013] Step 3) Based on the recommendation task representation obtained in Step 2), use the parameter initialization customization module to obtain an initialization parameter offset, which is used as the initialization parameter of the subsequent personalized scoring prediction model for this task.

[0014] The parameter initialization customization module described above includes: a key-value memory network and a weight generation unit, where: The key-value memory network stores the fast weights of the prediction model using multiple memory units according to historical task learning information to obtain a fast weight memory for fast adaptation of the task; The weight generation unit performs memory queries for cold-start tasks based on the learned fast weight memory, and combines the globally learned initial parameters to generate task-specific initialization parameters.

[0015] Step 4) Use a small amount of interactions of the task itself and perform local adaptation of the parameters through conventional gradient optimization methods to obtain the personalized scoring prediction model of the task, which serves as the basis for subsequent model updates; After the personalized scoring prediction model is locally adapted through training, the meta-learning model will be trained through global updates on multiple tasks.

[0016] The personalized scoring prediction model is implemented by a neural collaborative filtering model (NCF), specifically:

[0017] Where: is the learned user representation, is the learned item representation Emb u and Emb vIt is a learning function for user and item representation, which takes user and item attributes, such as and as inputs, is the predicted score, and rec θ is implemented by a multi-layer perceptron.

[0018] The training of the meta-learning model mentioned above refers to: updating the parameters of the recommendation model rec θ and the parameters of multiple modules including the context-based task representation learning module, the multi-view task relationship modeling module, and the parameter initialization customization module through global gradient descent on the query sets of multiple tasks. The globally optimized loss function

[0019] where: is the set of all training samples, Q i is the query set of a single task, is the predicted score for a single interaction (v1, y i,1 ), and y i,j is the true score of this interaction.

[0020] Step 5) Based on the personalized score prediction model obtained in step 4), generate a recommendation result for a specified user. Specifically: first predict the preference score between the user and the candidate items, and select the item with the highest preference score as the recommendation result to be recommended to the user.

[0021] Technical effects

[0022] The present invention can utilize the heterogeneous information network to mine the task relationships from multiple perspectives, thereby generating personalized parameter initializations for different user score prediction models to alleviate the problem that the model training is insufficient due to insufficient cold-start user interactions. Description of the drawings

[0023] Figure 1 is the flowchart of the method of the present invention;

[0024] Figure 2 is the system structure diagram of the present invention. Detailed implementation manners

[0025] As Figure 1 shown, this embodiment relates to a cold-start score prediction method based on multi-view task relationship-aware meta-learning, including:

[0026] Step 1) Unify the format of the user's interaction data as the input part for subsequent recommendation task representation learning and local adaptation of the score prediction model.

[0027] The so-called format unification means that for a cold-start user ui A recommendation is regarded as an independent recommendation task Its historical interaction record is denoted as I i ={(v1, y i,1 ),(v2, y i,2 ),...,(v n , y i,n )}, where y i,n is the preference score of the user for the nth interactive item v n . In this embodiment, the interaction quantity threshold K is used as the basis for determining a cold-start user. For example, if K is 20, it means that a user with an interaction quantity less than 20 is a cold-start user, and cold-start users are selected as the data for model training and verification

[0028] In this embodiment, each cold-start user u i has associated user portrait information And each item v k has associated item attribute information where o and q are the numbers of domains of user portraits and item attributes respectively

[0029] Step 2) Use the context interaction information of the task itself and the multi-angle association relationship with other tasks to learn a fixed-dimensional vector representation for the current recommendation task as the task feature representation

[0030] Step 3) Based on the recommendation task representation obtained in Step 2, query the continuously updated fast weight memory unit to obtain the initialization parameter offset as the initialization parameter of the subsequent personalized scoring prediction model for this task

[0031] Step 4) Use a small amount of interactions of the task itself for local adaptation of the parameters. Through gradient optimization of the parameters, obtain the personalized scoring prediction model of the task as the basis for subsequent model updates. When in the model training stage, after local adaptation, the meta-learning model will be trained through global updates on multiple tasks

[0032] Step 5) Based on the personalized scoring prediction model obtained in Step 4, generate recommendation results for the specified user. Specifically, first predict the preference scores between the user and the candidate items, and select the item with the highest preference score as the recommendation result to recommend to the user

[0033] Such as Figure 2As shown in the figure, this embodiment relates to a system for implementing the above method, including: a context-based task representation learning module, a multi-view task relationship modeling module, a parameter initialization customization module, and a local adaptation module, where: the context-based task representation learning module models user interests based on task-specific interaction information to obtain a user interest vector representation of the task; the multi-view task relationship modeling module models task association relationships from multiple perspectives by constructing a heterogeneous information network using meta-paths, and finally finds existing tasks closely related to the current recommended task, aggregates their representations to obtain a final task relationship vector representation; the parameter initialization customization module learns task-adaptive initialization scoring prediction model parameters for each task to obtain task-specific initialization parameters, enabling it to quickly and effectively perform local adaptation during the subsequent local adaptation process of the scoring prediction model. The local adaptation module uses the support set of the current recommended task to perform local adaptation of the scoring prediction model according to the task-specific initialization parameters using an optimization-based meta-learning method to obtain a personalized scoring prediction model.

[0034] The context-based task representation learning module described above includes: an encoder AE enc , a decoder AE dec and an interaction aggregation unit, where: the autoencoder divides the interaction of a recommended task into two parts, including a support set S i and a query set Q i uses the support set S i as context interaction information, performs encoding processing to obtain a low-dimensional vector representation o i,j of each interaction, that is the decoder reconstructs S i,j according to o i and uses the reconstruction loss for constraint to improve the quality of o i,j . The constraint mentioned above refers to: the difference between the original representation and the interaction representation after decoding by the decoder, that is, the reconstruction loss is as follows: where: the interaction (u i , v1, y i,1 ) ∈ S i , u i is the user, v1 is the item, and y i,1 is the score. Finally, the interaction aggregation unit can obtain a context-based task representation

[0035] The multi-view task relationship modeling module described above includes: a heterogeneous information network construction unit, a meta-path extraction unit, and a double-layer attention aggregation unit, where: The heterogeneous information network construction unit constructs a heterogeneous information network based on user interaction information, user attribute information, and item attribute information, and obtains a structured task relationship graph; The meta-path extraction unit, based on the heterogeneous information network, extracts neighbor information between target tasks based on meta-paths, and obtains a set of relevant task nodes from multiple perspectives; The double-layer attention aggregation unit uses the set of task nodes to perform relationship representation learning based on meta-paths, aggregates the neighborhood information of the target task on the heterogeneous graph, and obtains the relationship representation of this task.

[0036] The heterogeneous information network construction unit described above uses the support sets of all cold-start recommendation tasks in the training set to construct a heterogeneous information network where: V is a heterogeneous node set including all task nodes, item nodes, and user attribute / item attribute nodes, and E represents the heterogeneous edge set, which is constructed based on the associations between corresponding heterogeneous nodes; Based on this heterogeneous information network The meta-path extraction unit adopts the method of meta-path to design three different types of meta-paths to model the task association relationship from multiple different perspectives, including (1) task-user attribute-task (2) task-item-task (3) task-item-attribute-item-task. For each type of meta-path, an indefinite number of specific meta-path instances can be obtained according to the actual scenario. Finally, MP = {mp1, mp2..., mp P}, a total of P different meta-paths, are used as P different task relationship perspectives.

[0037] To aggregate similar task representations from all task relationship perspectives, the double-layer attention aggregation unit designs a double-layer attention aggregation structure, including task-level attention and perspective-level attention. Specifically, for each perspective mp p , first use a graph search algorithm, such as the breadth-first search algorithm, to find all neighbor task nodes, denoted as Subsequently, use the task-level attention mechanism to aggregate the task representations under this perspective mp p to obtain the representation of this perspective Specifically: the attention weight of neighbor task node where: β i,l is the attention weight corresponding to neighbor task node , indicating the importance of this task node for the representation learning of the current task node. e l is the learnable vector representation of neighbor task node . After that, based on all the learned perspective representations ​The information aggregation is performed by using the perspective-level attention mechanism to obtain the task representation r modeled based on the multi-perspective task relationship. i , specifically: the perspective mp p The attention weight Among them: η i,p is the attention weight corresponding to the perspective mp p , indicating the importance of this perspective for the learning of the current task node representation. Finally, using the above two modules, the final recommendation task representation learning can be learned as t i = [c i ; r i , as the recognition of the characteristics of this task.

[0038] The parameter initialization customization module described above includes: a key-value memory network and a weight generation unit. Among them: the key-value memory network stores the fast weights of the prediction model using multiple memory units according to the historical task learning information to obtain a weight memory network for fast adaptation of the task; the weight generation unit performs memory queries for cold-start tasks according to the learned weight memory network, and combines the globally learned initial parameters to generate task-specific initialization parameters.

[0039] The key-value memory network is Among them: k m is the key vector, used to store the task representation, and m m is the value memory unit, used to store the fast weights of the score prediction model; M is the number of predefined memory units, which can be set to 4, 8, 16.... etc. The key-value memory network is updated during the learning process of each recommendation task. Specifically: k m = λπ j,m t i + (1 - λ)k m , Among them: is the task-specific parameter learned through local adaptation on the task . For a new task First, use the final task representation t i , generate task-specific fast weights by querying the fast weight memory network After that, combine the task-specific initialization parameters with the globally shared initialization parameter θ. Specifically: Among them: τ is the update control factor.

[0040] The described local adaptation module includes: a scoring prediction model unit, a parameter optimization unit, and a recommendation generation unit, where: the scoring prediction model unit uses the basic neural collaborative filtering model (NCF) based on the interaction pair information, and obtains the scoring prediction result through a neural network structure; the parameter optimization unit uses the mean squared error and the reconstruction loss as loss functions according to... information, and uses gradient descent to optimize the parameters to obtain the updated parameters The preference prediction unit is based on the updated parameters As the parameters of the personalized scoring prediction model for this task, the user preferences are predicted. The scoring unit ranks the candidate items according to the prediction results and generates a top-K recommendation list.

[0041] The described neural collaborative filtering model (NCF) is specifically: where: rec θ is implemented by a multi-layer perceptron.

[0042] The described parameter optimization is specifically: where is the set of all training samples, is the reconstruction loss, and ξ is the discount factor.

[0043] The described recommendation generation unit is based on As the preference score, the candidate items are ranked to generate a top-K recommendation list, where K is customarily set according to the actual application scenario.

[0044] Through specific actual experiments, this method is evaluated on three real-world recommendation datasets, including MovieLens, Dbook, and Yelp. The MovieLens dataset contains 1 million movie rating records from the MovieLens website. The Dbook dataset is a book rating dataset extracted from the Douban2 platform. The Yelp dataset contains user business ratings from Yelp3. The user ratings of all three datasets are between 1 and 5.

[0045] In this embodiment, the fixed dimension of all embedded representations is set to 32, and the local update learning rate is set to 0.005. To learn the multi-view task relationship, three types of meta-paths (i.e., TPT, TIT, TIAIT) are designed according to the available auxiliary information in different datasets. Regarding the initialization customization, the number M of fast weight memory units is set to 8, and the memory update rate λ is default set to 0.01. In addition, the local update step is default set to 2, and the parameter customization ratio τ is default set to 0.2. For the training process, the batch size and the training time are set to 32 and 20 respectively, and the Adam optimizer is used as the optimizer.

[0046] Evaluation criteria: For each dataset, truncate the historical interactions of each user to the range of 15 to 100 to construct the user cold-start recommendation task. For each user, leave 10 interactions as the query set, and assign the other interactions to the support set. To generate the meta-training set and meta-test set, split all tasks in each dataset at a ratio of 0.8:0.2. For the MovieLens and Yelp datasets, sort the users according to the timestamp of the first interaction, and divide the last 20% of the tasks into the meta-test set. For the Dbook dataset, since there is no interaction time information, randomly split the tasks. Regarding the evaluation criteria, use three widely used evaluation metrics in terms of rating prediction and top-K recommendation, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Normalized Discounted Cumulative Gain (NDCG). The lower the MAE and RMSE, the higher the prediction accuracy. The higher the NDCG, the better the recommendation performance. For each metric, give the average result of all cold-start users in the meta-test set. Here, NDCG is implemented as NDCG@3.

[0047] Table 1: Comparison effects between the present invention and the prior art

[0048]

[0049] The comparison methods in Table 1 are all rating prediction algorithms in existing recommendation systems.

[0050] As can be seen from Table 1, compared with non-cold-start methods (i.e., NCF, DeepFM, and HAN), the meta-learning-based cold-start method generally achieves better performance. These methods are trained using samples from all meta-training tasks and fine-tuned using samples in the support set of the meta-test tasks. By learning personalized rating prediction models for different users, the effectiveness of meta-learning in dealing with the user cold-start problem is demonstrated. Among the meta-learning-based methods, the proposed method MeCM always achieves the best performance on all datasets. Specifically, compared with the strongest baselines on the three datasets, MeCM obtains improvements respectively (e.g., weighted average errors of 4.10%, 1.99%, and 1.53%). By dividing the meta-test tasks into support sets of different sizes, compare the performance of meta-learning-based methods under different degrees of cold-start scenarios. Additionally, according to the additional grouping experiments, it can be observed that when the interactions in the support set (such as 5, 10, and 20) are relatively few, the present invention is significantly better than other models (such as TaNP and MetaHIN), and can better improve the adaptability of users to the cold-start recommendation tasks with sparse interactions.

[0051] The above specific embodiments can be locally adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific embodiments. All implementation solutions within its scope are subject to the present invention.

Claims

1. A prediction method based on multi-view task relationship-aware meta-learning, characterized in that, Including: Step 1) Unify the format of the user's interaction data, which serves as the input part for subsequent representation learning of the recommendation task and local adaptation of the scoring prediction model. Specifically: The data of user-item interactions and the feature data of users and items need to be cleaned first to remove possible noisy data; at the same time, the interaction records need to be further organized according to the specified format, and based on the timestamps of the records, an observable interaction set is generated for each user. Step 2) Utilize the context interaction information of the task itself and the multi-angle correlation relationships with other tasks to learn a fixed-dimensional vector representation for the current recommendation task as the task characteristic representation. Specifically: Through the context-based task representation learning module, model the user's interest in the interaction information of the user to obtain the user interest representation of this task; through the multi-view task relationship modeling module, use the user profile, item attributes, and user-item interactions to construct a heterogeneous information network, and mine task associations from user similarity, interaction item similarity, and interaction item attribute similarity, and combine the information of similar tasks to represent the current recommendation task. The described multi-view task relationship modeling module includes: a heterogeneous information network construction unit, a meta-path extraction unit, and a two-layer attention aggregation unit. Among them: The heterogeneous information network construction unit constructs a heterogeneous information network based on user interaction information, user attribute information, and item attribute information to obtain a structured task relationship graph; the meta-path extraction unit, based on the heterogeneous information network, extracts neighbor information between target tasks based on meta-paths to obtain a set of relevant task nodes from multiple perspectives; the two-layer attention aggregation unit uses the set of task nodes to perform relationship representation learning based on meta-paths, aggregates the neighborhood information of the target task on the heterogeneous graph, and obtains the relationship representation of this task. Step 4) Based on the recommendation task representation obtained in Step 2), use the parameter initialization customization module to query the continuously updated fast weight memory unit to obtain the initialization parameter offset, which serves as the initialization parameter of the subsequent personalized scoring prediction model for this task. Specifically, through the fast weight memory network, during the historical training process, save the fast weights perceived by the task representation as additional memory for parameter initialization, and assist in generating the initialization parameters of the personalized scoring prediction model. Step 5) Utilize a small amount of interactions of the task itself to perform local adaptation of the parameters. Through gradient optimization of the parameters, obtain the personalized scoring prediction model of the task, which serves as the basis for subsequent model updates; after the personalized scoring prediction model is locally adapted through training, the meta-learning model will be trained through global updates on multiple tasks. Step 6) Based on the personalized scoring prediction model obtained in Step 5), generate a recommendation result for the specified user. Specifically: First, predict the preference score between the user and the candidate item, and select the item with the highest preference score as the recommendation result to be recommended to the user.

2. The prediction method based on multi-view task relationship-aware meta-learning according to claim 1, characterized in that The context-based task representation learning module described above includes: an encoder, a decoder, and an interaction aggregation unit, where: the encoder performs encoding processing based on user interaction information to obtain a low-dimensional vector representation of each interaction; the decoder decodes and reconstructs the original interaction information based on the obtained low-dimensional vector representation, and combines the reconstruction loss to improve the quality of the low-dimensional vector representation; the interaction aggregation unit performs representation aggregation on the vector representations of multiple interactions in an average pooling manner to obtain the final user interest representation of the task.

3. The prediction method based on multi-view task relationship-aware meta-learning according to claim 1, characterized in that The parameter initialization customization module described above includes: a key-value memory network and a weight generation unit, where: the key-value memory network stores the fast weights of the prediction model using multiple memory units according to historical task learning information to obtain a fast weight memory for rapid adaptation to tasks; the weight generation unit performs memory queries for cold-start tasks based on the learned fast weight memory, and combines the globally learned initial parameters to generate task-specific initialization parameters.

4. The prediction method based on multi-view task relationship-aware meta-learning according to claim 1, characterized in that, The personalized rating prediction model is implemented by a Neural Collaborative Filtering model (NCF), specifically as follows: , , is the learned user representation, is the learned item representation and are the user and item representation learning functions, taking user and item attributes, such as and as inputs, is the predicted rating, which is implemented by a multi-layer perceptron.

5. The prediction method based on multi-view task relationship-aware meta-learning according to claim 1, characterized in that, Training the meta - learning model means: updating the parameters of the recommendation model and the parameters of multiple modules including the context - based task representation learning module, the multi - view task relationship modeling module, and the parameter initialization customization module through global gradient descent on the query sets of multiple tasks. The globally optimized loss function , where: is the set of all training samples, is the query set of a single task, is the predicted score of a single interaction ( ), is the true score of this interaction.

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