A cross-domain debiasing cognitive diagnosis method based on sub-ability perception

Abstract

This invention relates to the field of intelligent education technology and discloses a cross-domain debiased cognitive diagnosis method based on sub-ability perception. It effectively mitigates subject-specific bias by leveraging the rich information and maximum mean difference of the source domain, and alleviates selection bias caused by a sparse student population through IPWE (Individualized Perceived Weaknesses and Entities). This makes the ability distribution of early-start students closer to the overall student distribution. Using early-start students as a bridge, and considering the extreme lack of historical interaction records for cold-start students, it relies on the objectively existing sub-abilities of students to perform high-precision diagnosis of their knowledge mastery status in the target domain, such as a new subject.

Description

Technical Field

[0001] This invention relates to the field of intelligent education technology, and in particular to a cross-domain debiased cognitive diagnosis method based on sub-ability perception. Background Technology

[0002] Cognitive diagnosis plays a crucial role in intelligent education models. Its core objective is to accurately infer students' mastery of various knowledge concepts based on their historical answer logs.

[0003] Early cognitive diagnostics primarily relied on psychometrics. Item Response Theory (IRT) used one-dimensional latent parameters to represent students' abilities and question difficulty, respectively, and used logistic functions to predict students' responses. Deterministic input and noisy AND gates (DINA) directly modeled the relationship between students and knowledge concepts, and introduced slip and guess parameters to characterize student answering behavior. With the development of deep learning technology, the Neural Cross-Domain Bias-Reducing Cognitive Diagnostic Model (NCDM) was the first to introduce neural networks to simulate complex nonlinear interactions, using ID embeddings to simulate students' mastery of specific concepts. Traditional cross-domain bias-reducing cognitive diagnostic models mainly focused on improving the diagnostic accuracy of a single subject by learning student and question characteristics from training data. When online education platforms introduce new subjects, a "cold start" problem occurs, leading to poor model performance. Therefore, cross-domain cognitive diagnostics has become a new research hotspot.

[0004] Existing research on cross-domain cognitive diagnostics mainly focuses on effectively transferring students' cognitive signals from the source domain to the cold-start target domain through cross-domain modeling. The cross-domain debiased cognitive diagnostic model with transferable knowledge concept graph embedding (TechCD) utilizes educational knowledge concept graphs as intermediaries connecting different domains, allowing students' cognitive signals to be transferred from a given domain to a zero-trigger cold-start domain. However, the model's performance is greatly affected by the effectiveness and accuracy of the knowledge link graph. Domain-level zero-shot cognitive diagnostic frameworks (Zero-1-to-3) pre-train the model, decoupling student states into shared and specific domains, transferring shared cognitive signals to the target domain, and enriching the cognitive priors of the new domain. However, this decoupling oversimplifies the complex and multidimensional characteristics of cognitive abilities.

[0005] Existing cross-domain bias-reducing cognitive diagnostic models still suffer from several inherent flaws: 1. Cold-start problem: When introducing a new subject, the lack of student practice records makes it difficult for traditional models to accurately assess student performance. 2. Coarse-grained ability modeling: Existing models often model student abilities in a single way, ignoring the fact that multidimensional cognitive skills may exhibit different emphases in different subjects. 3. Student sample selection bias: Existing cross-domain bias-reducing cognitive diagnostic models typically rely on a small group of "early bird" students with response records in both the source and target domains as a bridge for knowledge transfer. Because these "early bird" students are scarce and randomly distributed, their ability distribution cannot fully cover all sub-ability dimensions, leading to severe sample selection bias and weakening the model's generalization performance and diagnostic accuracy. Summary of the Invention

[0006] To overcome the shortcomings of existing cross-domain models in accurately assessing students' responses during cold starts, this invention proposes a cross-domain debiasing cognitive diagnostic method based on sub-ability perception.

[0007] To achieve the above objectives, the present invention adopts the following technical solution, including: A cross-domain debiasing cognitive diagnostic method based on sub-capability perception includes the following steps: S1: Data Preprocessing and Feature Initialization: Obtain a dataset containing historical interaction records of students, knowledge concepts, and exercises. Exercises are divided into a source domain exercise set with sufficient exercise records and a target domain exercise set with cold start problems. The source domain exercise set and the target domain exercise set share the same group of students but correspond to different knowledge concepts. Students and exercises are initialized into student embedding vectors and exercise embedding vectors, respectively. S2: Construct a cross-domain bias-free cognitive diagnostic model: Construct the student's sub-ability vector and sub-ability matrix; apply orthogonal constraints to the sub-ability matrix to ensure semantic independence of sub-abilities; construct the sub-ability dependency vector of source domain exercises and calculate the sub-ability dependency probability weights; based on the sub-ability vector, sub-ability dependency vector, and sub-ability dependency probability weights, calculate the predicted probability of the student answering the source domain exercises correctly. S3: Cross-domain sub-ability transfer: Calculate the similarity weight between the target domain exercises and the source domain exercises in terms of sub-ability dependency, adjust the student sub-ability matrix according to the similarity weight to obtain the sub-ability enhancement matrix, and at the same time calculate the distribution alignment loss of sub-abilities when crossing domains to alleviate cross-domain distribution shift; S4: Sample selection for the target domain: Distinguish between early bird students and cold start students in the target domain, build a propensity score network to identify student types, and construct an inverse propensity weighted estimator based on the output of the propensity score network to dynamically weight the prediction loss of early bird students and eliminate sample selection bias. S5: Model Training and Optimization: Based on the source domain data, the prediction loss, orthogonal loss, and bias score loss are fused to complete the model pre-training. Then, combined with the target domain data, the bias score loss, weighted prediction loss, orthogonal loss, and distribution alignment loss are fused to complete the model fine-tuning, resulting in the final cross-domain bias-free cognitive diagnosis model, which is then used for cognitive diagnosis prediction.

[0008] Preferably, in step S2, a sub-ability matrix is ​​constructed for student i. Sub-capability matrix Apply orthogonal constraints:

[0009] in, The sub-ability matrix representing student i , Sub-capability matrix The transpose of the matrix, Used to calculate the similarity between any two sub-capability vectors; For K K is the identity matrix, where K is the number of sub-capabilities; This indicates taking the Frobenius norm; This represents the orthogonal loss value, and the sub-capability matrix is ​​adjusted during training. Reduce orthogonal loss value .

[0010] Preferred source domain exercise-sub-capability dependency vector set: This is used to capture the inherent cognitive requirement structure of the exercise itself, where This represents the nth source domain exercise. The dependency vector for the k-th sub-capability; The probability weight of the dependence of the nth source domain exercise on the kth sub-capability The calculation method is as follows:

[0011] in, This represents the nth exercise in the source domain S. The dependency vector of the k-th sub-capability in the sub-capability set; This is an exponential mapping used to convert raw numerical values ​​into positive values; This represents the overall relative dependence of the nth exercise in the source domain S on all sub-capabilities in the sub-capability set.

[0012] Preferably, a basic cross-domain bias-free cognitive diagnostic model is constructed: for the i-th student and the n-th question in the source domain question set S, when only the k-th sub-ability is tested, the probability that student i answers the n-th question correctly is: ② in, This represents student i's response to exercise n. This indicates a correct answer; Indicates an incorrect answer; This represents the sub-capability vector of student i at the k-th sub-capability; This represents the nth problem in the source domain problem set S; This represents a prediction of the probability of answering a question correctly. The cross-domain bias-corrected cognitive diagnostic model is obtained, and the final prediction probability is calculated:

[0013] in, This represents the predicted probability that student i can correctly answer exercise n after the model comprehensively considers all sub-abilities.

[0014] Preferably, in step S3, the target domain exercise set Source Domain Exercise Set Similarity weights in sub-capability dependencies:

[0015] in, This represents the similarity weight between the q-th target domain exercise and the n-th source domain exercise on the k-th sub-ability; This represents the probability weight of the dependency of the q-th target domain exercise on the k-th sub-ability; This represents the probability weight of the dependence of the nth source domain exercise on the kth sub-ability; express and The similarity between them; N is the total number of exercises in the source domain exercise set.

[0016] Preferred cross-domain feature aggregation: Student i's sub-capability enhancement vector for the k-th sub-capability when facing a problem T in the target domain. :

[0017] in, This represents the sub-ability vector of student i for the nth source domain exercise in the kth sub-ability dimension; For the q-th target domain exercise and the source domain exercise set The sum of similarity weights of all exercises on the k-th sub-ability; This represents a sigmoid mapping, which maps the sum of similarity weights to the (0,1) interval; It is an enhancing factor.

[0018] Preferably, the maximum mean difference (MMD) is introduced to measure the degree of shift in the distribution of observed sub-capabilities between the two domains.

[0019] in, Represents a regenerating kernel Hilbert space (RKHS) with an inner product structure. The square norm in the reproducing kernel Hilbert space is used to measure the distance between two distributed features. The feature mapping function projects the sub-capability vectors in the source domain exercise set S and the target domain exercise set T onto the high-dimensional feature vectors in RKHS; This represents the set of sub-capability vectors for the k-th sub-capability observed by the model when a student is working on the source domain exercise set S. This represents the set of sub-capability enhancement vectors for the k-th sub-capability observed by the model when all students are working on the target domain exercise set T. Indicates to Perform the mean operation on the set in the set; This represents the distribution alignment loss when a student crosses the domain for the kth self-capability.

[0020] Preferably, in step S4, Indicator Label When students are early bird students hour, When students are in a cold-start phase, ; The Propensity Score Network PS-Net uses a Multilayer Perceptron (MLP) network. It takes the mean of the sub-ability matrices of all students obtained from the source domain exercise set as input and outputs labels that match the early bird student criteria. Propensity score ; Using cross-entropy loss Training the Propensity Score Network PS-Net:

[0021] in, Index the students, starting from 1, where M is the total number of students; when hour, If the PS-Net predicts the propensity score The closer the score is to 1, the more likely the model will classify the student as an early bird; if the score is biased... The closer the value is to 0, the more the model will classify early bird students as cold start students; when hour, If the PS-Net predicts the propensity score The closer the value is to 1, the more likely the model will misclassify cold-start students as early-bird students; if it tends to score higher... The closer the value is to 0, the more likely the model will classify the student as a cold-start student.

[0022] Preferred prediction loss model based on cross-entropy loss function:

[0023] Where j is any exercise in the exercise set V; Describes the true response of any student in the student set U to any problem in the problem set V, when When, it indicates that the answer is correct; when When the time is up, it indicates an incorrect answer; This represents the predicted probability that a student answers a question correctly, that is, the probability that student i can answer question j correctly, taking into account all sub-abilities. Equals the prediction score of the cross-domain biased cognitive diagnostic model. :

[0024] in, This represents the dependency probability weight between the j-th exercise in all exercise sets and the sub-ability k; This represents the probability that student i answers question j correctly when only the k-th sub-ability is considered; This represents the response log in the target domain; Explain the meanings of i, j, and j in the above formula. All datasets come from the target domain; This represents the result of traversing all interactions between all students and all exercises in the target domain exercise set T; Inverse Propensity Weighted Estimator (IPWE):

[0025] in, Early bird student gathering Size; This indicates that the selected students are early bird students; When students are early bird students hour, ;so ; This represents the probability that student p within the target domain T tends to exhibit early bird student characteristics. The smaller the value, the more reverse weighted. The larger the value, the higher the weight of the cold start student; The larger the value, the more reverse weighted it becomes. The smaller the value, the lower the weight of the cold start student.

[0026] Preferably, in step S5, the cross-domain bias-reduction cognitive diagnostic model is divided into two training phases: a pre-training phase with source domain data as input and a fine-tuning phase with target domain data as input and based on the pre-training results. Total loss function during pre-training phase :

[0027] in, The cross-entropy loss function in step S4; This refers to the orthogonal loss in step S2; The loss for training the propensity score network PS-Net in step S4; Total loss function during fine-tuning phase :

[0028] in, This refers to the cross-entropy loss in step S4; The weighted training loss of the inverse tendency weighted estimator in step S4; For sub-capability enhancement matrix Input, and the resulting orthogonal loss; , and These are learnable hyperparameters and all are positive.

[0029] The advantages of this invention are: (1) Using early bird students as a bridge, in the case of cold start students with extremely lack of student history interaction records, we rely on the objective sub-abilities of students to conduct high-precision knowledge mastery status diagnosis in the target domain, such as new subjects; with the help of the rich information of the source domain and the maximum mean difference, we effectively alleviate the deviation between subjects, and alleviate the selection bias caused by the sparse number of students through IPWE, so that the ability distribution of early bird students is closer to the overall student distribution.

[0030] (2) By modeling sub-abilities in a unified manner and applying orthogonal constraints, the coarse-grained, single-dimensional representation of abilities in traditional cognitive diagnosis is broken. By introducing orthogonal constraints, the semantic independence between different sub-ability dimensions, such as memory, comprehension, and application, is guaranteed, effectively preventing redundancy. This effectively demonstrates the effectiveness of using sub-abilities as a "bridge" for information transfer in cross-domain cognitive diagnosis, enabling the model to accurately capture the differentiated needs of different disciplines for various specific cognitive skills and achieving fine-grained knowledge transfer.

[0031] (3) Student representation enhancement is achieved by relying on question similarity. This method effectively alleviates the subject domain shift problem caused by the differences in knowledge concepts and question features between different disciplines by calculating the similarity of the source domain and target domain questions on the sub-ability dependency distribution and performing feature aggregation.

[0032] (4) By introducing the maximum mean difference (MMD) of sub-capability levels, the marginal distribution of the source and target domains is constrained during the fine-tuning stage, forcing the model to learn a consistent objective capability representation across domains and preventing the model from over-focusing on domain-specific features or biases.

[0033] (5) By using the propensity score network, the representativeness of early bird students in the subject ability distribution of the target domain is obtained, which effectively alleviates the sample selection bias caused by data sparsity. The inverse propensity weighted estimator (IPWE) is constructed to prevent the model from overfitting to specific types of early bird students, thus enhancing the fairness of the model.

[0034] (6) Compared with existing baseline models, the bias-reducing adaptive network of the present invention not only performs better in diagnostic accuracy, but also has more robust generalization performance in different fields, providing extremely reliable support for downstream tasks such as diagnostic report generation and personalized practice recommendation of intelligent education models. Attached Figure Description

[0035] Figure 1 This is an overall flowchart of the present invention; Figure 2 A flowchart illustrating the construction of the basic cross-domain bias-free cognitive diagnostic model for this invention; Figure 3 This is a flowchart of the cross-domain sub-capability migration of the present invention; Figure 4 This is a flowchart of the target domain sample selection process of the present invention; Figure 5 This is a data flow diagram for the present invention. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0037] A cross-domain debiasing cognitive diagnostic method based on sub-ability perception first obtains a dataset of students' historical interaction records based on existing conditions. The dataset includes students, knowledge concepts, and exercises, with each exercise labeled with relevant knowledge concepts. The exercises include a source domain exercise set with sufficient practice records and a target domain exercise set exhibiting a cold-start problem (exercises lacking student practice records). The source and target domain exercise sets share the same group of students who completed the exercises; however, the source and target domain exercise sets correspond to different sets of knowledge concepts.

[0038] It is worth noting that, for ease of distinction, in this embodiment, the student index is i, and for both the target domain exercise set and the source domain exercise set, the exercise index is j. For knowledge concept indexing; in the source domain, n is the exercise index, and... For knowledge concept indexing; in the target domain, q is used as the exercise index, and... Index for knowledge concepts.

[0039] Based on a rich dataset of historical interaction records, a cross-domain bias-correcting cognitive diagnostic model with bias-correcting effect is constructed.

[0040] like Figure 1 and Figure 5 As shown, it includes the following steps: S1: Data Preprocessing and Feature Initialization: Initialize the data into feature embeddings that the model can read, and construct feature representations between students and sub-capabilities.

[0041] S11: Data Preprocessing The student set is denoted as U. Let M represent the i-th student, and the total number of students is M.

[0042] Let the set of exercises in the source domain be denoted as S. Let N represent the nth problem in the source domain, with a total of N problems. The source domain knowledge concept set is denoted as , Represents the first in the source domain There are knowledge concepts, and the total number of knowledge concepts is . ; Source domain student interaction records are recorded as ,in, This represents the interaction result of the i-th student on the n-th exercise. ,when When, it indicates that the answer is correct; when When the time is up, it indicates that the answer is incorrect.

[0043] Construct a matrix to record the relationships between source domain exercises and source domain knowledge concepts. , in, This represents the nth source domain exercise. With the Source domain knowledge concept The correlation, if correlated, then let Otherwise, let ; Let T be the set of exercises for the target domain. Let Q represent the q-th exercise in the target domain, with a total number of exercises. The target domain knowledge concept set is denoted as , Represents the first in the target domain There are knowledge concepts, and the total number of knowledge concepts is . ; Student interaction records in the target domain are recorded as ,in, This represents the interaction result of the i-th student on the q-th exercise. ,when When, it indicates that the answer is correct; when When the time is up, it indicates that the answer is incorrect.

[0044] This represents the q-th target domain exercise. With the Knowledge concepts of the target domain The correlation, if correlated, then let Otherwise, let ; Source Domain Exercise Set and target domain exercise set Composition of exercise sets ; gather students and exercise book Each student and exercise is mapped to a corresponding one-hot encoded vector.

[0045] Student group The one-hot encoded vector is input into the embedding layer of the neural network and transformed into a low-dimensional dense latent feature vector, i.e., the initial student embedding vector.

[0046] Exercise set The one-hot encoded vector is input into the embedding layer of the neural network and transformed into a low-dimensional dense latent feature vector, i.e., the initial problem embedding vector.

[0047] S12: Feature initialization embedding: Quantify the student's abilities and construct the student's sub-ability vectors in sub-abilities.

[0048] Define any seed ability k in the sub-ability set of a student i. There are K sub-abilities in total. The sub-abilities are the individual abilities of students when solving problems, such as memory, comprehension, and application. They can be customized and labeled by the model.

[0049] Since the source domain exercise set and the target domain exercise set share the same group of students doing the exercises, and the students' sub-abilities are inherent attributes of the students, the source domain exercise set and the target domain exercise set share the same sub-ability set.

[0050] The vector dimension of a sub-capability is d, meaning that each seed capability consists of a d-dimensional latent representation vector, which is used to characterize the feature representation of the sub-capability in the latent space.

[0051] The value of d can be customized based on training stability and expressive power, such as d=8, 16, 32, etc.

[0052] like Figure 2 As shown, S2: Constructing a cross-domain de-biased cognitive diagnostic model: Based on the source domain data, a cross-domain de-biased cognitive diagnostic model is constructed. The dependency matrix between exercises and sub-abilities, and the relationship matrix between students and sub-abilities are used as inputs to the cross-domain de-biased cognitive diagnostic model, and the predicted correct answer probability of students in the source domain is output.

[0053] S21: A large number of interaction records based on the source domain The overall ability of students is quantified, and a sub-ability matrix is ​​constructed.

[0054] Reshape the student embedding vector into a sub-capability matrix for student i. K d represents the feature dimension of student i, which is consistent with the dimension of the student embedding vector output by the embedding layer.

[0055] Specifically, Sub-capability vectors , , Let k represent the latent feature representations of student i in the 1st, 2nd, and Kth sub-abilities, respectively, and let k represent the types of sub-abilities of student i. For any sub-ability k, .

[0056] Therefore, for student i, the sub-capability matrix is ​​used. This represents all the sub-abilities that the student possesses.

[0057] S22: Orthogonal Constraint Unit: Construct orthogonal constraint units to enhance the independence and distinguishability of the semantics of each sub-ability, prevent feature redundancy or confusion, and improve the accuracy of the model in diagnosing students' cognitive abilities.

[0058] For the sub-ability matrix of student i Apply orthogonal constraints:

[0059] in, The sub-ability matrix representing student i , Sub-capability matrix The transpose of the matrix, Used to calculate the similarity between any two sub-capability vectors; For K The identity matrix of K; This indicates taking the Frobenius norm; This represents the orthogonal loss value. The larger the value, the worse the independence between sub-capabilities. During training, the sub-capability matrix needs to be adjusted. Make the orthogonal loss value It may be small.

[0060] S23: Calculate the dependency distribution between exercises and sub-abilities

[0061] Different exercises rely on different sub-abilities to varying degrees, especially in interdisciplinary scenarios where the cognitive needs of different fields differ greatly due to the differences in disciplinary systems.

[0062] To obtain the degree of dependency of source domain exercises across different sub-capability dimensions, the source domain exercises are embedded into a vector and input to a learnable mapping function, resulting in a K-dimensional vector set: , This is a set of source domain exercise-sub-ability dependency vectors, used to capture the inherent cognitive requirement structure of the exercises themselves. This represents the nth source domain exercise. The dependency vector for the k-th sub-capability.

[0063] Preferably, the mapping function includes a linear layer or a multilayer perceptron (MLP).

[0064] The source domain exercise-sub-ability dependency vector is analyzed using the softmax function. After normalization, the dependency probability weight of the nth source domain exercise on the kth sub-capability is calculated as follows:

[0065] in, This represents the nth exercise in the source domain S. The dependency probability weight of the kth sub-capability in the sub-capability set represents the degree of dependency of the nth source domain exercise on sub-capability k. Let $\mathbf{n}$ represent the dependency vector of the $n$-th exercise on the $k$-th sub-ability in the source domain $S$. This is an exponential mapping used to convert the original numerical values ​​into positive values ​​to ensure that the final output is a valid probability distribution; This represents the overall relative dependence of the nth exercise in the source domain S on all sub-capabilities in the sub-capability set.

[0066] Traverse the sub-capability sets to obtain the capability dependency vector set of the nth source domain exercise. The capability-dependent vector set This represents the dependency relationship between the nth source domain exercise and each sub-ability.

[0067] S24: Construct a cross-domain bias-reduction cognitive diagnostic model based on the source domain exercise set: weight the sub-ability vector and sub-ability dependency vector, and at the sub-ability level, judge the student's mastery of the source domain knowledge concepts and predict the student's answer probability.

[0068] For the i-th student and the n-th problem in the source domain problem set S, when only the k-th sub-ability is tested, the probability that student i answers the n-th problem correctly is:

[0069] in, This represents student i's response to exercise n. This indicates a correct answer; Indicates an incorrect answer; This represents the sub-capability vector of student i at the k-th sub-capability; This represents the nth problem in the source domain problem set S; This represents a prediction of the probability of answering a question correctly. Let represent the probability that student i answers question n correctly when only the k-th sub-ability is considered.

[0070] The cross-domain bias-corrected cognitive diagnostic model is obtained, and the final prediction probability is calculated:

[0071] in, This represents the predicted probability that student i can correctly answer exercise n after the model comprehensively considers all sub-abilities.

[0072] like Figure 3 As shown, S3: Cross-domain sub-capability transfer: By quantifying the similarity of sub-capability requirements between source domain exercises and target domain exercises, sub-capabilities are transferred to achieve the initial fine-tuning of the basic cross-domain debiased cognitive diagnostic model.

[0073] S31: Construct a sub-capability transfer module and determine the target domain exercise set. Source Domain Exercise Set Similarity in sub-capability dependencies is used for transfer from source domain exercises to target domain in the sub-capability dimension.

[0074] First, calculate the target domain exercise set. Source Domain Exercise Set Similarity weights in sub-capability dependencies:

[0075] in, This represents the similarity weight between the q-th target domain exercise and the n-th source domain exercise performed by the same student on the k-th sub-ability, which is used to weight the sub-abilities that the student has transferred from the source domain in the target domain; The weight represents the probability of dependence of the q-th target domain exercise on the k-th sub-ability (the calculation method is described in step S23). The weight represents the probability of dependence of the nth source domain exercise on the kth sub-ability (the calculation method is described in step S23). express and The similarity between them measures the similarity between the dependency probability weight of the q-th target domain exercise on the k-th sub-capability and the dependency probability weight of the n-th source domain exercise on the k-th sub-capability.

[0076] By traversing the target domain exercise set Source Domain Exercise Set The similarity weights are used to obtain a set of normalized weights. The rich data of the source domain is used to assist in the modeling of exercises in the target domain, so as to realize the transfer of knowledge concepts.

[0077] S32: Cross-domain feature aggregation: In the student representation update stage, the similarity weights obtained in S31 are used as enhancement factors to adjust the student's sub-capability matrix, so that the student's related sub-capabilities are enhanced in a fine-grained manner during the transfer process.

[0078] The student representation update phase is the target domain adaptation phase. For "new exercises" appearing in the target domain, the model no longer relearns, but instead adjusts the model based on the similarity between the target domain and the source domain, i.e., the similarity weights obtained in step S31. Adjust the student's sub-capability matrix to obtain the student's sub-capability enhancement vector in the target domain.

[0079] Specifically, the sub-ability enhancement vector of student i for sub-ability k when facing the target domain exercise T. :

[0080] in, This represents the sub-capability vector of student i in the k-th sub-capability dimension (the calculation method is described in step S21). This indicates that for the q-th target domain exercise and the source domain exercise set... The sum of similarity weights of all exercises on the k-th sub-ability; This represents a sigmoid mapping, which maps the sum of similarity weights to the (0,1) interval; To enhance the factor, the student's sub-ability vector is dynamically amplified based on the sum of the similarity weights between the target domain and the source domain, thereby achieving adaptive enhancement of the student's ability when facing exercises in the target domain.

[0081] The fine-grained enhancement can be understood as: dynamically amplifying the sub-ability vector based on the overall similarity between the target domain exercises and the source domain exercise set, so that students rely more on transferred knowledge concepts when predicting answers to target domain exercises, thereby improving prediction accuracy.

[0082] The sub-capability enhancement vector This can be understood as follows: When student i faces a target domain exercise similar to the source domain exercise, since the student's sub-abilities remain unchanged and the knowledge concepts relied upon by the source domain exercise and the target domain exercise are similar, the cross-domain debiasing cognitive diagnostic model has enhanced predictive ability for student's answer performance on sub-ability k.

[0083] This yields the sub-capability enhancement matrix for student i in the target domain.

[0084] S33: Cross-domain offset mitigation: Measures the degree of distribution offset of sub-capabilities when crossing domains by calculating the maximum mean difference (MMD) loss of each sub-capability in the source and target domains.

[0085] Sub-abilities, as inherent cognitive attributes of students, do not change in definition or connotation when crossing domains. However, the differences between source domain exercises and target domain exercises can lead to a systematic shift in the observed sub-ability distributions of the same group of students across the two domains. Therefore, the maximum mean difference (MMD) is introduced to measure the degree of shift in the observed sub-ability distributions between the two domains.

[0086] Using maximum mean difference (MMD), calculate the distribution alignment loss of the k-th sub-capability when crossing domains. :

[0087] in, Represents a regenerating kernel Hilbert space (RKHS) with an inner product structure. The square norm in the reproducing kernel Hilbert space is used to measure the distance between two distributed features. The feature mapping function projects the sub-capability vectors in the source domain exercise set S and the target domain exercise set T onto the high-dimensional feature vectors in RKHS; This represents the set of sub-capability vectors of the k-th sub-capability observed by the model when a student is working on the source domain exercise set S (the calculation method is described in step S21), and represents the distribution of all students' observations of the k-th sub-capability on the source domain exercise set S. This represents the set of sub-capability enhancement vectors of the k-th sub-capability observed by the model when all students are working on the target domain exercise set T (calculation method refers to step S32), representing the observation distribution of all students on the k-th sub-capability on the target domain exercise set T; Indicates to Perform the mean operation on the set in the set; Distribution Alignment Loss This characterizes the distribution shift of the k-th sub-ability observed by the model when students interact with students in the source domain exercise set S and the target domain exercise set T. If the value is large, then the distribution pattern of students on the k-th sub-ability differs greatly between the source and target domains, making it unsuitable to directly use the source domain model; if If the difference is small, then for the source domain and the target domain, the distribution pattern of students on the kth sub-ability is small, and the source domain model can be directly transferred to the target domain fine-tuning model.

[0088] During model training, the cross-domain alignment problem at the student level can be solved by minimizing the MMD loss and aligning the sub-capability edge distributions of the source and target domains.

[0089] like Figure 4 As shown, S4: Construct a sample selection model for the target domain, input the sub-ability matrix of the student on the source domain exercise set S, construct a propensity score network, and dynamically adjust the training loss of early bird students through propensity scores to alleviate the selection bias caused by insufficient coverage of sub-ability dimensions due to the scarcity of cold start samples.

[0090] When students enter the target domain, they are divided into early bird students who have a small number of answers to the target domain exercises. Cold-start students with no response records .

[0091] Introduce indicator labels When students are early bird students hour, When students are in a cold-start phase, .

[0092] S41: Construct a propensity score network: Train the model to correctly determine the label of the student.

[0093] A propensity scoring network, PS-Net, is constructed using a multilayer perceptron (MLP) network. The mean of the sub-ability matrices of all students obtained from the source domain exercise set is used as input. PS-Net outputs labels indicating early bird students. Propensity score .

[0094] When tending to score The higher the value, the more likely the model is to classify the student as an early bird in the target domain.

[0095] Using cross-entropy loss Training the Propensity Score Network PS-Net:

[0096] Where i is the student index, starting from 1, and M is the total number of students; when hour, If the PS-Net predicts the propensity score The closer the value is to 1, the more accurate the model's assessment of the student as an early bird; a bias towards a higher score indicates a more accurate assessment. The closer the value is to 0, the more likely the model is to classify early bird students as cold start students.

[0097] when hour, If the PS-Net predicts the propensity score The closer the value is to 1, the more likely the model is to classify cold-start students as early-bird students; if the model favors a certain score... The closer the value is to 0, the more accurate it is in identifying the student as a cold-start student.

[0098] Using cross-entropy loss Training to minimize cross-entropy loss This leads to a tendency to score higher. Realistic indicator labels This improves the consistency between the model's judgment results and the actual performance.

[0099] S42: Construct a prediction loss model, train the prediction loss model to improve the prediction accuracy of the cross-domain debiased cognitive diagnostic model, balance the sample selection bias, and make the prediction results of the target domain cross-domain debiased cognitive diagnostic model closer to the real student performance.

[0100] The prediction loss model is based on the cross-entropy loss function:

[0101] Where j is any exercise in the exercise set V; This represents the true response of student i in student set U to problem j in problem set V, when When, it indicates that the answer is correct; when When the time is up, it indicates an incorrect answer; This represents the predicted probability that a student answers a question correctly, that is, the probability that student i can answer question j correctly, taking into account all sub-abilities. Equals the prediction score predicted by the cross-domain biased cognitive diagnostic model in step S24. :

[0102] in, This represents the dependency probability weight between the j-th exercise in all exercise sets and the sub-ability k; Let represent the probability that student i answers question j correctly when only considering the k-th sub-ability.

[0103] This represents the response log in the target domain; Explain the meanings of i, j, and j in the above formula. All datasets come from the target domain; This represents the result of traversing all interactions between all students and all exercises in the target domain exercise set T.

[0104] The predicted loss value represents the student's performance and is used to measure the difference between the model's predicted probability of the student answering correctly and the actual answer. Through training, the loss value is improved. The smaller the value, the closer the model is to the actual student performance during training, thus training a good model that matches the actual student performance and improving the accuracy of model diagnosis.

[0105] S43: Constructing the Inverse Propensity Weighted Estimator (IPWE): Since early bird students have a small number of response records, while cold-start students have no records, if the early bird students' data is used directly to train the target domain fine-tuning model, the output results will be biased towards the early bird students' distribution, causing sample selection bias. Therefore, the propensity score from step S41 is used... The predicted loss values ​​of early bird students are dynamically weighted to construct an inverse bias weighted estimator (IPWE) that reduces the weight of early bird students.

[0106] Inverse Propensity Weighted Estimator (IPWE):

[0107] in, Early bird student gathering Size; This indicates that the selected students are early bird students; when a student is an early bird student hour, ,so ; This represents the probability that student p within the target domain T tends to exhibit early bird student characteristics. The younger the student, the more they are likely to be a cold start student. The older they get, the more they resemble early bird students; To achieve reverse weighting, early bird students who tend to exhibit cold-start characteristics are given higher weights because these students have similar characteristics to cold-start students, and their predictive loss is more valuable for improving the diagnostic performance of cold-start students; typical early bird students are given lower weights to reduce attention to them. This represents the predicted loss value after weighting by the Inverse Propensity Weighted Estimator (IPWE).

[0108] S5: Model Training and Optimization

[0109] S51: Pre-training phase: Using source domain data as input, construct the total loss function of the cross-domain bias-correcting cognitive diagnostic model. :

[0110] in, The cross-entropy loss function in step S42 takes source domain data as input, enabling the model to learn how to predict the probability of students answering questions based on the sub-ability structure. The orthogonal loss in step S22 constrains the orthogonality of the student sub-ability matrix based on the source domain data, making the different sub-ability dimensions semantically independent, and providing a more stable ability space for cross-domain transfer. The loss of the bias score network PS-Net trained in step S41 is reduced through training, making the model's judgment more in line with the real student situation. Source domain total loss function This is used to pre-train a cross-domain debiased cognitive diagnostic model based on source domain data, enabling the model to obtain stable sub-capability representations, reliable cognitive diagnostic capabilities, and a bias score network that can be used for debiasing, providing initial data for the subsequent fine-tuning stage.

[0111] S52: Fine-tuning phase: Using the minimized total source domain loss function Initialize the cross-domain bias-reducing cognitive diagnostic model and construct the final total loss function. :

[0112] in, The cross-entropy loss in step S41 makes the student labels determined by the model closer to the true indicator labels. ; The weighted training loss of the target domain in step S43 is used to make the ability distribution of early bird students closer to the ability distribution of the overall students and reduce sample selection bias. The orthogonal loss obtained by using the sub-capability enhancement matrix obtained in step S32 as the input to step S13 maintains the structural stability of the sub-capability space during the fine-tuning process in the target domain, and avoids multiple sub-capabilities from collapsing into one. The distribution alignment loss in step S33 is used to ensure that the sub-capability distributions of the source domain and the target domain are consistent, so that the student sub-capabilities learned in the source domain can be effectively transferred and applied to the target domain.

[0113] , and For learnable hyperparameters, , and All values ​​are positive and are custom-selected. The purpose is to ensure that the model balances prediction performance with independence and stability among sub-capabilities, and that the distribution of sub-capabilities in the source and target domains is as consistent as possible. This avoids situations where prediction performance is good but sub-capabilities are not independent, or where the distribution of sub-capabilities in the source and target domains differs greatly, or where other aspects are good but prediction performance is poor. To achieve a balance among these three factors, continuous adjustments are needed to optimize the final model performance.

[0114] After pre-training and fine-tuning based on source and target domain data, a cross-domain bias-free cognitive diagnostic model is formed that can be put into use. This model can output the probability of correct answers based on any student's sub-ability and the input questions.

[0115] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0116] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0117] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A cross-domain debiasing cognitive diagnostic method based on sub-ability perception, characterized in that, Includes the following steps: S1: Data Preprocessing and Feature Initialization: Obtain a dataset containing historical interaction records of students, knowledge concepts, and exercises. Exercises are divided into a source domain exercise set with sufficient exercise records and a target domain exercise set with cold start problems. The source domain exercise set and the target domain exercise set share the same group of students but correspond to different knowledge concepts. Students and exercises are initialized into student embedding vectors and exercise embedding vectors, respectively. S2: Construct a cross-domain bias-free cognitive diagnostic model: Construct the student's sub-ability vector and sub-ability matrix; apply orthogonal constraints to the sub-ability matrix to ensure semantic independence of sub-abilities; construct the sub-ability dependency vector of source domain exercises and calculate the sub-ability dependency probability weights; based on the sub-ability vector, sub-ability dependency vector, and sub-ability dependency probability weights, calculate the predicted probability of the student answering the source domain exercises correctly. S3: Cross-domain sub-ability transfer: Calculate the similarity weight between the target domain exercises and the source domain exercises in terms of sub-ability dependency, adjust the student sub-ability matrix according to the similarity weight to obtain the sub-ability enhancement matrix, and at the same time calculate the distribution alignment loss of sub-abilities when crossing domains to alleviate cross-domain distribution shift; S4: Sample selection for the target domain: Distinguish between early bird students and cold start students in the target domain, build a propensity score network to identify student types, and construct an inverse propensity weighted estimator based on the output of the propensity score network to dynamically weight the prediction loss of early bird students and eliminate sample selection bias. S5: Model Training and Optimization: Based on the source domain data, the prediction loss, orthogonal loss, and bias score loss are fused to complete the model pre-training. Then, combined with the target domain data, the bias score loss, weighted prediction loss, orthogonal loss, and distribution alignment loss are fused to complete the model fine-tuning, resulting in the final cross-domain bias-free cognitive diagnosis model, which is then used for cognitive diagnosis prediction.

2. The cross-domain debiasing cognitive diagnosis method based on sub-capability perception as described in claim 1, characterized in that, In step S2, a sub-ability matrix is ​​constructed for student i. Sub-capability matrix Apply orthogonal constraints: in, Sub-ability matrix representing student i , Sub-capability matrix The transpose of the matrix, Used to calculate the similarity between any two sub-capability vectors; For K K is the identity matrix, where K is the number of sub-capabilities; This indicates taking the Frobenius norm; This represents the orthogonal loss value, and the sub-capability matrix is ​​adjusted during training. Reduce orthogonal loss value .

3. The cross-domain debiasing cognitive diagnosis method based on sub-ability perception as described in claim 2, characterized in that, Source domain exercises - sub-capability dependency vector set: This is used to capture the inherent cognitive requirement structure of the exercise itself, where This represents the nth source domain exercise. The dependency vector for the k-th sub-capability; The probability weight of the dependence of the nth source domain exercise on the kth sub-capability The calculation method is as follows: in, This represents the nth exercise in the source domain S. The dependency vector of the k-th sub-capability in the sub-capability set; This is an exponential mapping used to convert raw numerical values ​​into positive values; This represents the overall relative dependence of the nth exercise in the source domain S on all sub-capabilities in the sub-capability set.

4. The cross-domain debiasing cognitive diagnosis method based on sub-ability perception as described in claim 3, characterized in that, Constructing a basic cross-domain bias-reduction cognitive diagnostic model: For the i-th student and the n-th question in the source domain question set S, when only the k-th sub-ability is tested, the probability that student i answers the n-th question correctly is: in, This represents student i's response to exercise n. This indicates a correct answer; Indicates an incorrect answer; This represents the sub-capability vector of student i at the k-th sub-capability; This represents the nth problem in the source domain problem set S; This represents a prediction of the probability of answering a question correctly. The cross-domain bias-corrected cognitive diagnostic model is obtained, and the final prediction probability is calculated: in, This represents the predicted probability that student i can correctly answer exercise n after the model comprehensively considers all sub-abilities.

5. The cross-domain debiasing cognitive diagnosis method based on sub-ability perception as described in claim 4, characterized in that, In step S3, the target domain exercise set Source Domain Exercise Set Similarity weights in sub-capability dependencies: in, This represents the similarity weight between the q-th target domain exercise and the n-th source domain exercise on the k-th sub-ability; This represents the probability weight of the dependency of the q-th target domain exercise on the k-th sub-ability; This represents the probability weight of the dependence of the nth source domain exercise on the kth sub-ability; express and The similarity between them; N is the total number of exercises in the source domain exercise set.

6. The cross-domain debiasing cognitive diagnosis method based on sub-ability perception as described in claim 5, characterized in that, Cross-domain feature aggregation: Sub-capability enhancement vector for student i when facing the target domain exercise T for the k-th sub-capability. : in, This represents the sub-capability vector of student i in the k-th sub-capability dimension; This indicates that for the q-th target domain exercise and the source domain exercise set... The sum of similarity weights of all exercises on the k-th sub-ability; This represents a sigmoid mapping, which maps the sum of similarity weights to the (0,1) interval; It is an enhancing factor.

7. The cross-domain debiasing cognitive diagnosis method based on sub-ability perception as described in claim 6, characterized in that, The maximum mean difference is introduced to measure the degree of shift in the distribution of observed sub-capabilities between two domains: in, This represents a regenerating kernel Hilbert space (RKHS) with an inner product structure. The square norm in the reproducing kernel Hilbert space is used to measure the distance between two distributed features. The feature mapping function projects the sub-capability vectors in the source domain exercise set S and the target domain exercise set T onto the high-dimensional feature vectors in RKHS; This represents the set of sub-capability vectors for the k-th sub-capability observed by the model when a student is working on the source domain exercise set S. This represents the set of sub-capability enhancement vectors for the k-th sub-capability observed by the model when all students are working on the target domain exercise set T. Indicates to Perform the mean operation on the set in the set; This represents the distribution alignment loss when a student crosses the domain for the kth self-capability.

8. The cross-domain debiasing cognitive diagnosis method based on sub-capability perception as described in claim 7, characterized in that, In step S4, an indicator label is introduced. When students are early bird students hour, When students are in a cold-start phase, ; The Propensity Score Network PS-Net uses a Multilayer Perceptron (MLP) network. It takes the mean of the sub-ability matrices of all students obtained from the source domain exercise set as input and outputs labels that match the early bird student criteria. Propensity score ; Using cross-entropy loss Training the Propensity Score Network PS-Net: in, Index the students, starting from 1, where M is the total number of students; when hour, If the PS-Net predicts the propensity score The closer the score is to 1, the more likely the model will classify the student as an early bird; if the score is biased... The closer the value is to 0, the more the model will classify early bird students as cold start students; when hour, If the PS-Net predicts the propensity score The closer the value is to 1, the more likely the model will misclassify cold-start students as early-bird students; if it tends to score higher... The closer the value is to 0, the more likely the model will classify the student as a cold-start student.

9. The cross-domain debiasing cognitive diagnosis method based on sub-capability perception as described in claim 8, characterized in that, Predictive loss model based on cross-entropy loss function: Where j is any exercise in the exercise set V; Describes the true response of any student in the student set U to any problem in the problem set V, when When, it indicates that the answer is correct; when When the time is up, it indicates an incorrect answer; This represents the predicted probability that a student answers a question correctly, that is, the probability that student i can answer question j correctly, taking into account all sub-abilities. Equals the prediction score of the cross-domain biased cognitive diagnostic model. : in, This represents the dependency probability weight between the j-th exercise in all exercise sets and the sub-ability k; This represents the probability that student i answers question j correctly when only the k-th sub-ability is considered; This represents the response log in the target domain; Explain the meanings of i, j, and j in the above formula. All datasets come from the target domain; This represents the result of traversing all interactions between all students and all exercises in the target domain exercise set T; Inverse Propensity Weighted Estimator (IPWE): in, Early bird student gathering Size; This indicates that the selected students are early bird students; When students are early bird students hour, ;so ; This represents the probability that student p within the target domain T tends to exhibit early bird student characteristics. The smaller the value, the more reverse weighted. The larger the value, the higher the weight of the cold start student; The larger the value, the more reverse weighted it becomes. The smaller the value, the lower the weight of the cold start student.

10. The cross-domain debiased cognitive diagnosis method based on sub-ability perception as described in claim 9, characterized in that, In step S5, the cross-domain bias-reduction cognitive diagnostic model is divided into two training phases: a pre-training phase with source domain data as input and a fine-tuning phase with target domain data as input and based on the pre-training results. Total loss function during pre-training phase : in, The cross-entropy loss function in step S4; This refers to the orthogonal loss in step S2; The loss for training the propensity score network PS-Net in step S4; Total loss function during fine-tuning phase : in, This refers to the cross-entropy loss in step S4; The weighted training loss of the inverse tendency weighted estimator in step S4; For sub-capability enhancement matrix Input, and the resulting orthogonal loss; , and These are learnable hyperparameters and all are positive.

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