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CN112949935B - Knowledge tracking method and system fusing student knowledge point question interaction information - Google Patents

Knowledge tracking method and system fusing student knowledge point question interaction information Download PDF

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CN112949935B
CN112949935B CN202110326338.6A CN202110326338A CN112949935B CN 112949935 B CN112949935 B CN 112949935B CN 202110326338 A CN202110326338 A CN 202110326338A CN 112949935 B CN112949935 B CN 112949935B
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孙建文
刘三女牙
邹睿
张凯
蒋路路
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Abstract

The invention discloses a knowledge tracking method and a knowledge tracking system fusing interactive information among students, knowledge points and questions. The method comprises the following steps: acquiring a historical student answer record set; coding data in a historical student answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector; decoding interaction parameters between students and subjects and interaction parameters between students and knowledge points from the output vector, and decoding interaction parameters between knowledge points and subjects from next subject information coding; and inputting all the interaction parameters into the Bayesian probability model, and outputting an answer prediction result. The invention integrates the deep learning model and the Bayesian probability model, models the interaction between students and knowledge points, the interaction between students and questions, and the interaction between knowledge points and questions, provides good interpretability for explaining the learning process, and improves the accuracy of knowledge tracking.

Description

Knowledge tracking method and system fusing student knowledge point question interaction information
Technical Field
The invention belongs to the technical field of knowledge tracking, and particularly relates to a knowledge tracking method and a knowledge tracking system fusing interactive information among students, knowledge points and questions.
Background
Knowledge tracking tracks the change of knowledge point mastery level of students according to historical learning records of the students, and then accurately predicts the performance of the students in future learning. Essentially, knowledge tracking is the interaction among modeling students (students), knowledge points (concepts) and topics (Question). Therefore, the three types of interactions for comprehensively modeling are the key for improving the performance of the knowledge tracking model.
Most existing knowledge tracking models cannot describe these interactions simultaneously.
The Knowledge tracking field has two types of classical models, the first type of classical model is a Deep Knowledge tracking model (DKTs), the DKTs can better predict results by means of strong model capability of Deep learning, but from the explanatory point of view, most of the DKTs do not model interaction between students and subjects and interaction between Knowledge points and subjects. The second class of classical models is the Bayesian Knowledge tracking model and its variants (Bayesian Knowledge tracking models, BKTs for short). BKTs uses a set of parameters to explain the learning process, but BKTs ignores the interaction of knowledge points with topics, and moreover, BKTs statically describes the performance of all students on the same knowledge point with the same set of parameters, neither personalizing students nor considering the change of parameters with time, which is one of the main reasons why BKTs' predicted performance is inferior to DKTs.
Disclosure of Invention
Aiming at least one defect or improvement requirement in the prior art, the invention provides a knowledge tracking method and a knowledge tracking system fusing interaction information among a student knowledge point topic, a deep learning model and a Bayesian probability model are fused, interaction between the student and a knowledge point, interaction between the student and a topic, and interaction between the knowledge point and the topic are modeled, so that good interpretability is provided for explaining a learning process, and the accuracy of knowledge tracking is improved.
In order to achieve the above object, according to a first aspect of the present invention, there is provided a knowledge tracking method for fusing interactive information among students, knowledge points, and topics, comprising:
acquiring a historical student answer record set;
coding data in a historical student answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector;
decoding interaction parameters between students and subjects and interaction parameters between students and knowledge points from the output vector, and decoding interaction parameters between knowledge points and subjects from next subject information codes;
and inputting all the interaction parameters into the Bayesian probability model, and outputting an answer prediction result.
Preferably, the method for outputting the answer prediction result by the bayesian probability model comprises the steps of:
obtaining the probability of solving the question by the student according to the interaction parameters between the student and the knowledge point and the interaction parameters between the knowledge point and the question;
and outputting an answer prediction result according to the probability of solving the question by the student, the interactive parameters between the student and the question and the one-hot coding of the next question associated knowledge point.
Preferably, the method further comprises the steps of:
and respectively establishing a grading penalty loss function of the interaction parameters between the students and the subjects, a grading penalty loss function of the interaction parameters between the students and the knowledge points, and a grading penalty loss function of the interaction parameters between the knowledge points and the subjects.
Preferably, the encoding the data in the student historical answer record set comprises the following steps:
recording the answer record of the current time step in the historical answer record set of the students as x<t>,x<t>=(c<t>,q<t>,a<t>) Wherein c is<t>Is the current topic associated knowledge point number, a<t>Is the current student answer situation, q<t>The current question number is used for recording the question information of the next time step in the historical answer record set of the students as (c)<t+1>,q<t+1>) Wherein c is<t+1>Is the next topic associated knowledge point number, q<t+1>Is the next question number;
to (c)<t>,a<t>) Encoding is carried out, and the content after encoding is recorded as
Figure BDA0002994794560000021
Will (q)<t>,a<t>) Encoding is carried out, and the content after encoding is recorded as
Figure BDA0002994794560000022
Combining the two parts of coding results, and recording the combined content as
Figure BDA0002994794560000023
Wherein, the + is a broadcast operator, the combined content is input into an input LSTM network, and the current answer record code is output;
to c<t+1>Coding is carried out, and the coded content is recorded as
Figure BDA0002994794560000031
To q is<t+1>Encoding is carried out, and the content after encoding is recorded as
Figure BDA0002994794560000032
Combining the two part coding results, the combined content
Figure BDA0002994794560000033
I.e., the next title information, where + is the broadcast operator.
Preferably, the interaction parameters between the student and the question comprise the error probability of the student on the question and the guess-to-correct probability of the student on the question, the interaction parameters between the student and the knowledge point comprise the probability of the student mastering the knowledge point, and the interaction parameters between the knowledge point and the question comprise the complexity of the question related to the knowledge point.
Preferably, the interaction parameters between the student and the question comprise a student error probability and a student guess-to-correct probability on the question, the student error probability on the question is recorded as S, the student guess-to-correct probability on the question is recorded as G, the interaction parameters between the student and the knowledge points comprise a student knowledge point mastering probability, the student knowledge point mastering probability is recorded as L, the interaction parameters between the knowledge points and the question comprise question-to-knowledge point correlation complexity and are recorded as R, and the calculation formula of inputting all the interaction parameters into the bayesian probability model is as follows:
Lq=L*(1-R),
wherein L isqProbability of solving the problem for the student;
Figure BDA0002994794560000034
wherein,
Figure BDA0002994794560000035
for the probability of the student answering the next question,
Figure BDA0002994794560000036
one-hot coding of knowledge points is associated for the next topic.
Preferably, the grading penalty loss function of the interaction parameter between the student and the subject is as follows:
and recording the grading penalty loss function of the interaction parameters between the students and the knowledge points as lossL,jThe calculation formula is as follows:
Figure BDA0002994794560000037
wherein, Δ LjA variation value, Γ, representing the probability of a student grasping the jth knowledge point between two time stepslower,ΓupperIs divided into Δ LjLower and upper limits of the normal variation range;
and the grading penalty loss function of the interaction parameters between the students and the subjects is recorded as lossS,jThe calculation formula is as follows:
Figure BDA0002994794560000041
wherein
Figure BDA0002994794560000042
Is the probability of failure, λ, of the associated knowledge point of the topic at the τ -th time stepS∈[0,1]Is a preset average probability of failure, len, on each topicjThe number of topics appearing at the jth knowledge point;
and the grading penalty loss function of the interaction parameters between the students and the knowledge points is recorded as lossG,jThe calculation formula is as follows:
Figure BDA0002994794560000043
wherein
Figure BDA0002994794560000044
Is the guess-to-probability, λ, of the associated knowledge point of the topic at the τ -th time stepG∈[0,1]Is a preset average probability, len, of guessing pairs on each topicjIs the number of topics that appear at the jth knowledge point.
Preferably, if each answer record in the student historical answer record set only comprises a knowledge point number and a student answer condition, replacing the question number with the knowledge point number in all subsequent processing.
According to a second aspect of the present invention, there is provided a knowledge tracking system for fusing interactive information among students, knowledge points, and topics, comprising:
the data acquisition module is used for acquiring a historical answer record set of students;
the coding module is used for coding data in the student historical answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector;
the decoding module is used for decoding the interaction parameters between the students and the subjects and the interaction parameters between the students and the knowledge points from the output vector and decoding the interaction parameters between the knowledge points and the subjects from the next subject information coding;
and the prediction module is used for inputting all the interaction parameters into the Bayesian probability model and outputting an answer prediction result.
According to a third aspect of the invention, there is provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method of any of the above.
Overall, the invention has the advantages over the prior art:
(1) the invention uses the mastery degree (expressed by a parameter Learning, L for short) of the student to the knowledge points to model S-C; S-Q is modeled by Guessing (G for short) and missing (S for short) behaviors in the student answering process. Besides, the Correlation complexity (expressed by a parameter Correlation complexity, R for short) between the topic and the associated knowledge point is introduced to model C-Q, for example, the topic Q relates to the knowledge points C _1 and C _2, and by adopting the method of the invention, the Correlation complexity R _1 and R _2 of Q on the knowledge points C _1 and C _2 can be obtained, and the larger the value is, the more complex the Correlation complexity is. In summary, the present invention can model three interactions simultaneously.
(2) The invention dynamically generates the three interactive related parameters by using a deep learning technology, thereby solving the problem that BKT can only statically model students, and the invention can personalize and dynamically model students, which is beneficial to the problem and the prediction performance of the model also reaches an advanced level.
(3) Experiments were performed on four open knowledge pursuit datasets to conclude that: (1) the prediction result of the method exceeds most of the existing KT models, and the advanced prediction level is achieved. (2) The invention has excellent explanatory property and can analyze the learning process of students in more detail.
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FIG. 1 is a schematic diagram of a knowledge tracking method of an embodiment of the invention;
FIG. 2 is a visual learning process of an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a deep bayesian probability model (DBKT for short) is used in the knowledge tracking method for fusing the mutual information among students, knowledge points, and topics according to the embodiment of the present invention. DBKT employs a "coder-decoder" architecture. The encoder encodes the student history as an intermediate representation and then uses three decoders (S-C, C-Q and S-Q decoders) to decode the parameters that model the three interactions. Finally, the parameters are input into a Bayesian conditional probability formula to obtain the prediction of the future performance of the student.
The knowledge tracking method for fusing the mutual information among students, knowledge points and questions comprises the following steps:
and S1, acquiring a historical answer record set of the students.
And acquiring historical learning records of students as DBKT input. The historical learning record of the student is recorded as X ═ X<1>,...,x<t>,...,x<T>]Wherein x is<t>Is the learning record of the T time step, and there are T records in total. For the sake of simplicity, x will be used hereinafter<t>Collectively referred to as "current" records, with x<t+1>Collectively referred to as the "next" record.
x<t>=(c<t>,q<t>,a<t>) Wherein c is<t>Is the current topic associated knowledge point number, a<t>Is the current student's answer condition, q<t>Is the current title number.
When the student answers the next question, x<t+1>Is only (c)<t+1>,q<t+1>) Wherein c is<t+1>Is the next topic associated knowledge point number, q<t+1>Is the next question number;
tracking tasks can be divided into two types according to whether topic information knowledge is used or not: knowledge point level tasks and topic level tasks. The main difference between the two types of tasks is that the former uses knowledge point data but does not use topic data; the latter uses both knowledge point data and topic data. The input of the knowledge point level task is x<t>=(c<t>,a<t>) Wherein c is<t>∈N+Is the ID of the current knowledge point, a<t>E {0, 1} is the current student answer case (1 means student answer pair, 0 means answer wrong). The input of the subject level task is x<t>=(c<t>,q<t>,a<t>) Wherein q is<t>∈N+Is the ID of the current topic. DBKT is mainly suitable for topic-level tasks, but it can also be used to process knowledge point-level tasks. In the following steps, taking the processing of the topic-level task as an example, if the processing of the knowledge point-level task is performed, that is, if there is no topic number in the answer record, all the processing steps are not changed, but only when the processing of the topic number is involved in all the subsequent processing steps, the knowledge point number is used to replace the topic number.
And S2, coding data in the student historical answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector.
The encoder encodes the student's historical learning records. The encoder encodes the current recording and the next recording separately and then concatenates the two partial encoding results.
For the current record, will (c)<t>,a<t>) Is coded into
Figure BDA0002994794560000071
Will (q)<t>,a<t>) Is coded into
Figure BDA0002994794560000072
Wherein N is a neural networkThe hidden layer size of (2). Then, the two part coding results are combined into
Figure BDA0002994794560000073
Where "+" here is the addition of the broadcast, the broadcast operator appearing hereinafter will not be particularly emphasized for convenience. Then the combined result is input into LSTM, output ocurrent
For the next recording, similarly, c<t+1>Is coded into
Figure BDA0002994794560000074
Then q is added<t+1>Is coded into
Figure BDA0002994794560000075
The two part encoding results are then combined into
Figure BDA0002994794560000076
Finally, o iscurrentAnd onextAnd performing splicing operation to obtain a final output vector o of the encoder.
S3, decoding the interaction parameters between students and subjects and the interaction parameters between students and knowledge points from the output vector, and decoding the interaction parameters between knowledge points and subjects from the next subject information coding.
The S31, S-Q decoder decodes the parameters S, G from the encoder output o, which model the student' S interaction with the topic (S-Q). In particular, it decodes o through a series of linear layers and an activation function, resulting in
Figure BDA0002994794560000077
Wherein SjE [0, 1 is the probability of student miss on the jth topic, NCIs the total number of knowledge points; and also obtain
Figure BDA0002994794560000078
Wherein G isjE [0, 1 is the guess pair probability of the jth knowledge point associated topic.
S32,The S-C decoder models student interaction with the topic (S-C). It decodes the parameter vector from the output o of the encoder
Figure BDA0002994794560000079
Wherein L isjE [0, 1 is the probability of the student grasping the jth knowledge point.
S33, the C-Q decoder models the interaction of knowledge points and topics (C-Q). It will follow the next topic q by linear layers and activation functions<t+1>Decoding to associated complexity
Figure BDA00029947945600000710
Wherein R isjE [0, 1 is the associated complexity of the current topic at its jth associated knowledge point.
And S4, inputting all the interaction parameters into the Bayes probability model, and outputting the answer prediction result.
After the four parameters are decoded, the parameters are input into a Bayes conditional probability formula to model the learning process of the student, and finally the future performance of the student is predicted.
Preferably, the method for outputting the answer prediction result by the bayesian probability model comprises the following steps:
and S41, obtaining the probability of solving the question by the student according to the interaction parameters between the student and the knowledge point and the interaction parameters between the knowledge point and the question.
Converting the probability (L) of the student mastering the knowledge point into the probability (L) of the student solving the problemq):
Lq=L*(1-R)
Wherein probability of solving the problem
Figure BDA0002994794560000081
Wherein L isq,jE [0, 1 is the resolving power of the student to the jth associated knowledge point of the student to the topic. The meaning of the formula is: the necessary condition for a student to solve a topic is that the student has knowledge points (L) associated with the topic, and the associated complexity (R) cannot be too difficult for the student.
And S42, outputting an answer prediction result according to the probability of solving the question by the student, the interaction parameters between the student and the question and the unique hot coding of the next question associated knowledge point.
After the student solves the probability of the question, the prediction result is calculated by the following probability formula, namely the probability that the student answers the next question
Figure BDA0002994794560000082
Figure BDA0002994794560000083
Where "·" is a dot product. The left side of the dot product is the bayesian conditional probability formula. Dot product right side
Figure BDA0002994794560000084
Is the one-hot encoding of the next time step knowledge point. The meaning of the probability formula is that the student answers the question in two situations, namely, the student can solve the question without errors; secondly, students can not solve the problem, but guess right.
The knowledge tracking method for fusing the mutual information among the students, the knowledge points and the subjects, provided by the embodiment of the invention, further comprises the following steps: and respectively establishing a grading penalty loss function of the interaction parameters between the students and the subjects, a grading penalty loss function of the interaction parameters between the students and the knowledge points, and a grading penalty loss function of the interaction parameters between the knowledge points and the subjects.
Most of the training goals of depth knowledge tracking models are prediction accuracy. Unlike them, DBKT requires, in addition to pursuing prediction accuracy, more rational modeling of three interactions in the learning process. For this purpose, graded penalty loss functions are introduced into the DBKT, and these functions are used for constraining the above-mentioned parametric performances to make them more in line with the real learning process of students. The design idea of the graded penalty loss function is that when the variation range of the parameters is within a reasonable range, no penalty is needed, and when the variation exceeds the reasonable range, the penalty is given to the exceeding part. Specifically, the loss function is designed for the parameters L, G, S, respectively. Taking L as an example, the following hierarchical penalty functions are designed:
Figure BDA0002994794560000091
wherein
Figure BDA0002994794560000092
Is the change value of the learning probability of the jth knowledge point between two time steps. [ gamma ] islower,Γupper]Denotes the normal range, whereinlower∈[-1,0],Γupper∈[0,1]。ΔLj∈(-∞,Γlower) The mastery degree of the student on the knowledge points is shown to be stepped back, the stepping back is beyond a reasonable range, and the loss value at the moment is
Figure BDA0002994794560000095
Multiplying by 2 represents twice the penalty factor for stepping back as for stepping forward. Δ Lj∈[Γlower,Γupper]The change of the mastery degree is reasonable, and no punishment is given. L isj∈(Γupper, + ∞) indicates that the student's mastery of the knowledge points has progressed beyond a reasonable range. In the experiment, a hyper-parameter gamma is setupper=0.8,Γlower0.2. Loss function loss in calculating each knowledge pointL,jThen, they are summed to get the total loss function:
Figure BDA0002994794560000093
the overall loss function is calculated. Similarly to L, a hierarchical penalty function loss is also calculated for the parameters G and SG,lossSTheir calculation method and lossLLike
Loss function for S:
Figure BDA0002994794560000094
wherein the fault loss function of the j-th knowledge point is recorded as
Figure BDA0002994794560000101
Wherein
Figure BDA0002994794560000102
Is the probability of failure of the associated knowledge point of the topic at the τ th time step (i.e., the jth knowledge point). LambdaS∈[0,1]Is a preset average probability of failure on each topic. len (a)j∈N+Is the number of topics that appear at the jth knowledge point. Thus, Δ SjIs the difference between the probability of failure generated by the model and the maximum allowed failure reference value. When the difference is greater than 0, the mistake is considered to be unreasonable, and is marked as lossS,j
Similarly, we have
Figure BDA0002994794560000103
Figure BDA0002994794560000104
Figure BDA0002994794560000105
Wherein
Figure BDA0002994794560000106
Is the guess pair probability of the associated knowledge point of the topic at the τ th time step (i.e., the jth knowledge point). Lambda [ alpha ]G∈[0,1]Is a preset average probability of guessing pairs on each topic. len (a)j∈N+Is the number of topics that appear at the jth knowledge point. Therefore, Δ GjIs the difference between the model-generated guess-to-probability and the maximum allowed guess-to-reference value. When the difference is greater than 0, recognizeIs an unreasonable mistake.
The predicted loss and the loss of these parameters are then combined into a total loss:
loss=lossL+lossS+lossG+lossPred
wherein lossPredTo predict the loss, it is calculated from the predicted value and the target value.
And finally, training the DBKT by using a back propagation algorithm for the total loss.
Experiment (1) was performed using the method described above.
Table 1 shows the predicted results of DBKT and the existing advanced knowledge tracking model for the learner's answering situation. As shown in table 1, experiments are performed on four data sets, namely, assement 2009, assement 2015, assement 2017 and Statics2011, to perform corresponding prediction, wherein BKT represents a bayesian knowledge tracking method, DKT +, DKVMN, SAKT and AKT represent the existing depth knowledge tracking method, DBKT represents the knowledge tracking method of the present invention, and a metric of an experimental result is Area Under Curve (AUC), which is defined as an Area enclosed by coordinate axes Under an ROC Curve. As can be seen from the table, the predicted results for DBKT are superior to those for the comparative model.
Specifically, because the Assist15 and Static11 data sets do not have topic data, they have knowledge-point level tasks. Bold represents the best performing model, DBKT achieved the best results on almost all datasets, and DBKT achieved a great advance on Assist17 on the knowledge point level task.
Figure BDA0002994794560000111
Experiment (2) was performed using the method described above.
The DBKT visualizes the learning process. As shown in fig. 2, four examples of learning processes are listed to illustrate the explanatory ability of the DBKT.
Fig. 1 is a graph of four randomly chosen student learning processes analyzed using DBKT. L is mastered by studentsThe probability of a knowledge point, G is the probability of a student guessing, S is the probability of a student missing, and R is the associated complexity of the topic. (a) In response to the situation that the student does not know the knowledge point, the student exercises 7 questions with topic IDs 332, 310, 237, 351, 347, 261 and 21 in sequence for the knowledge point "CircleGraph", answers are 0, 0, 0, 1, 0, 0 and 0 in sequence, and only the fourth question is answered. In (b), students performed exercises at knowledge point "Conversion of fractions demols centers". (c) The student in (1) exercises the knowledge point "Least Common Multiplt". In (d), the student exercises the knowledge point "Proavailability of a Single Event". For a clearer display of the individual parameters, the histogram portion is divided by 2, i.e.
Figure BDA0002994794560000112
Taking (a) as an example, on the one hand, according to the horizontal axis "answer situation" display, the student answers seven questions in total, and all but the fourth question are answered in error, and it can be judged that the degree of grasp of the relevant knowledge point by the student is low. On the other hand, in the model of the embodiment of the present invention, the range of the parameter L is [0, 0.3], that is, the model considers that the degree of knowledge points mastered by the student is also low, which is consistent with the actual situation. It can be inferred that DBKT can better restore the true learning process.
In particular, it is unreasonable for the fourth topic, the student still answered the topic without having knowledge of the point of knowledge. In combination with the graph analysis, the key factor of student answer is found to be a larger parameter G, namely the model considers that students guess at a larger probability, which is consistent with the cognitive experience. This indicates that DBKT can explain some special learning cases.
The knowledge tracking system for fusing the mutual information among students, knowledge points and questions, provided by the embodiment of the invention, comprises:
the data acquisition module is used for acquiring a historical answer record set of students;
the coding module is used for acquiring a current answer record code and a next question information code for data in a student historical answer record set, and splicing the current answer record code and the next question information code to obtain an output vector;
the decoding module is used for decoding the interaction parameters between the students and the subjects and the interaction parameters between the students and the knowledge points from the output vector and decoding the interaction parameters between the knowledge points and the subjects from the next subject information coding;
and the prediction module is used for inputting all the interaction parameters into the Bayesian probability model and outputting the answer prediction result.
The realization principle and technical effect of the knowledge tracking system are the same as those of the knowledge tracking method, and the details are not repeated here.
Embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor to implement any of the technical solutions of the embodiments of the knowledge tracking method. The implementation principle and technical effect are the same as those of the method, and are not described herein again.
It must be noted that in any of the above embodiments, the methods are not necessarily executed in order of sequence number, and as long as it cannot be assumed from the execution logic that they are necessarily executed in a certain order, it means that they can be executed in any other possible order.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A knowledge tracking method for fusing interactive information among students, knowledge points and questions is characterized by comprising the following steps:
acquiring a historical student answer record set;
coding data in a historical student answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector;
decoding interaction parameters between students and subjects and interaction parameters between students and knowledge points from the output vector, and decoding interaction parameters between knowledge points and subjects from next subject information coding;
inputting all interaction parameters into a Bayesian probability model, and outputting an answer prediction result;
the method for outputting the answer prediction result by the Bayesian probability model comprises the following steps:
obtaining the probability of solving the question by the student according to the interaction parameters between the student and the knowledge point and the interaction parameters between the knowledge point and the question;
outputting an answer prediction result according to the probability of solving the question by the student, the interactive parameters between the student and the question and the one-hot coding of the next question associated knowledge point;
the interactive parameters between the students and the questions comprise the error probability of the students on the questions and the guess-to-correct probability of the students on the questions, the error probability of the students on the questions is recorded as S, the guess-to-correct probability of the students on the questions is recorded as G, the interactive parameters between the students and the knowledge points comprise the probability of the students mastering the knowledge points, the probability of the students mastering the knowledge points is recorded as L, the interactive parameters between the knowledge points and the questions comprise the complexity related to the questions and the knowledge points, which is recorded as R, and the calculation formula of inputting all the interactive parameters into the Bayesian probability model is as follows:
Lq=L*(1-R),
wherein L isqProbability of solving the problem for the student;
Figure FDA0003611705310000011
wherein,
Figure FDA0003611705310000012
for the probability of the student answering the next question,
Figure FDA0003611705310000013
one-hot coding of knowledge points is associated for the next topic.
2. The knowledge tracking method for fusing the mutual information among the students, the knowledge points and the subjects as claimed in claim 1, further comprising the steps of:
and respectively establishing a grading penalty loss function of the interaction parameters between the students and the subjects, a grading penalty loss function of the interaction parameters between the students and the knowledge points, and a grading penalty loss function of the interaction parameters between the knowledge points and the subjects.
3. The knowledge tracking method for integrating the mutual information among the students, the knowledge points and the questions as claimed in claim 1, wherein said encoding the data in the student's historical answer record set comprises the steps of:
recording the answer records of the current time step in the historical answer record set of the students as x<t>,x<t>=(c<t>,q<t>,a<t>) Wherein c is<t>Is the number of knowledge points associated with the current topic, a<t>Is the current student answer situation, q<t>The current question number is used for recording the question information of the next time step in the historical answer record set of the students as (c)<t+t>,q<t+1>) Wherein c is<t+1>Is the next topic associated knowledge point number, q<t+1>Is the next question number;
to (c)<t>,a<t>) Encoding is carried out, and the content after encoding is recorded as
Figure FDA0003611705310000021
Will (q) be<t>,a<t>) Encoding is carried out, and the content after encoding is recorded as
Figure FDA0003611705310000022
Combining the two parts of coding results, and recording the combined content as
Figure FDA0003611705310000023
Wherein, the + is a broadcast operator, the combined content is input into an input LSTM network, and the current answer record code is output;
to c<t+1>Encoding is carried out, and the content after encoding is recorded as
Figure FDA0003611705310000024
To q is<t+1>Coding is carried out, and the coded content is recorded as
Figure FDA0003611705310000025
Combining the two part coding results, the combined content
Figure FDA0003611705310000026
I.e., the next title information, where + is the broadcast operator.
4. The knowledge tracking method integrating interaction information among students, knowledge points and subjects as claimed in claim 2, wherein the level penalty loss function of the interaction parameters among the students and the knowledge points is recorded as lossL,jThe calculation formula is as follows:
Figure FDA0003611705310000031
wherein, Δ LjA variation value, Γ, representing the probability of a student grasping the jth knowledge point between two time stepslower,ΓupperIs divided into Δ LjLower and upper limits of the normal variation range;
the graded penalty loss function of the student's failure probability on the subject is recorded as lossS,jThe calculation formula is as follows:
Figure FDA0003611705310000032
wherein
Figure FDA0003611705310000033
Is the probability of failure, λ, of the associated knowledge point of the topic at the τ -th time stepS∈[0,1]Is a preset average probability of failure, len, on each topicjThe number of topics appearing at the jth knowledge point;
the grading penalty loss function of the guessing probability of the students on the subject is recorded as lossG,jThe calculation formula is as follows:
Figure FDA0003611705310000034
wherein
Figure FDA0003611705310000035
Figure FDA0003611705310000036
Is the guess-to-probability, λ, of the associated knowledge point of the topic at the τ -th time stepG∈[0,1]Is a preset average probability, len, of guessing pairs on each topicjIs the number of topics that appear at the jth knowledge point.
5. The knowledge tracking method for fusing the mutual information among the students, the knowledge points and the questions as claimed in claim 1, wherein if each answer record in the student history answer record set includes only the knowledge point number and the student answer condition, the knowledge point number is used to replace the question number in all subsequent processing.
6. The utility model provides a fuse knowledge tracking system of mutual information between student, knowledge point, topic three which characterized in that includes:
the data acquisition module is used for acquiring a historical answer record set of students;
the coding module is used for coding data in the student historical answer record set, acquiring a current answer record code and a next question information code, and splicing the current answer record code and the next question information code to obtain an output vector;
the decoding module is used for decoding interaction parameters between students and subjects and interaction parameters between students and knowledge points from the output vector and decoding interaction parameters between knowledge points and subjects from the next subject information coding;
the prediction module is used for inputting all the interaction parameters into the Bayesian probability model and outputting an answer prediction result;
the method for outputting the answer prediction result by the Bayesian probability model comprises the following steps:
obtaining the probability of solving the question by the student according to the interaction parameters between the student and the knowledge point and the interaction parameters between the knowledge point and the question;
outputting an answer prediction result according to the probability of solving the question by the student, the interactive parameters between the student and the question and the one-hot coding of the next question associated knowledge point;
the interactive parameters between the students and the questions comprise the error probability of the students on the questions and the guess-to-correct probability of the students on the questions, the error probability of the students on the questions is recorded as S, the guess-to-correct probability of the students on the questions is recorded as G, the interactive parameters between the students and the knowledge points comprise the probability of the students mastering the knowledge points, the probability of the students mastering the knowledge points is recorded as L, the interactive parameters between the knowledge points and the questions comprise the complexity related to the questions and the knowledge points, which is recorded as R, and the calculation formula of inputting all the interactive parameters into the Bayesian probability model is as follows:
Lq=L*(1-R),
wherein L isqProbability of solving the problem for the student;
Figure FDA0003611705310000041
wherein,
Figure FDA0003611705310000042
for the probability of the student answering the next question,
Figure FDA0003611705310000043
one-hot coding of knowledge points is associated for the next topic.
7. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1 to 5.
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