CN113361685A - Knowledge tracking method and system based on learner knowledge state evolution expression - Google Patents
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Abstract
The invention provides a knowledge tracking method and a knowledge tracking system based on learner knowledge state evolution expression, wherein the method comprises the following steps: acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples; generating knowledge state representation of learners and building a knowledge tracking model; generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner; generating an evolution item; the evolution item is incorporated into the loss function and optimized, the training goal of the knowledge tracking model is to generate accurate predicted values of the learner's future answer performance and accurately model the gradual change of the knowledge state, and the goal is characterized by defining the loss function.
Description
Technical Field
The invention belongs to the field of knowledge tracking, and particularly relates to a knowledge tracking method and system based on learner knowledge state evolution expression.
Background
Knowledge tracking is an important learner modeling method, which models a learner's historical answer sequence, tracks the learner's knowledge state, and then predicts the learner's future answer performance. Specifically, the knowledge state of the learner refers to the mastery degree of the knowledge point of the learner, and the knowledge state of the learner changes along with the answering situation. Generally speaking, in the process of adjacent answers, the knowledge state should be gradually transited and gradually evolves. How to restore the process of the gradual change of the knowledge state is a key problem of the knowledge tracking task.
Existing knowledge tracking models mainly include two types. The first type is a probabilistic knowledge tracking model, represented by classical Bayesian Knowledge Tracking (BKT), which uses state parameters with specific semantics to represent the knowledge state of a learner, and calculates the change of the knowledge state through the state parameters. The model has the advantages that the state parameter semantics are clear, and the interpretability is higher; the disadvantage is that there is no gradual change in the state of knowledge modeled. The second type is a Deep learning Knowledge tracking model, which is represented by classical Deep Knowledge Tracking (DKT), and uses a distributed vector or matrix generated by a Deep neural network to represent the Knowledge state of a learner, and the change of the Knowledge state is modeled by the change of the distributed vector or matrix at adjacent time steps. The model has the advantages of high prediction performance; the disadvantage is again that there is no gradual change in the state of knowledge modeled. The two models have good effects in practical application and are the solid foundation of follow-up research. However, the common defects are that the process of gradual evolution of the knowledge state of the learner is difficult to model, and a real learning scene cannot be restored.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides a knowledge tracking method and a knowledge tracking system based on learner knowledge state evolution representation, which generate a learner knowledge state representation-state matrix by counting learner answer sequence data, and model the whole change of the learner knowledge state by calculating the difference value of the state matrix at adjacent time steps; further introducing evolution weight for quantizing the influence of each state column in the state matrix in the overall change; further generating an evolution item for representing the accurate change of the knowledge state in the adjacent question answering process; and the evolution item is further incorporated into the loss function, so that the goal of restoring the gentle change process of the knowledge state is realized in the process of optimizing the loss function, and a real learning scene is modeled. The method can complete the knowledge tracking task, define the state matrix of the state matrix representing the knowledge state of the learner, and can further predict the future answering performance of the learner through the state matrix.
In order to achieve the above object, the present invention provides a knowledge tracking method based on learner knowledge state evolution representation, which comprises the following steps:
s1, acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
s2, generating knowledge state representation of the learner, and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of the long-term and short-term memory neural network and the input of the full-connection neural network are cognitive data sets, and the output of the long-term and short-term memory neural network and the full-connection neural network is a state matrix;
s3, generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner;
s4, generating an evolution item, and combining the evolution weight and the overall change of the knowledge state into the evolution item so as to represent the accurate change of the knowledge state of the learner in the adjacent answers;
and S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the learner's future answer performance and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set described in step S1 includes a plurality of time series, and a time series includes a plurality of time step data, and the plurality of time step data represent the answer condition of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
As a further improvement of the present invention, the input of the long-short term memory neural network described in step S2 is the acquired cognitive data set, and the output is the low-level feature representation of the knowledge state-distributed vector; the input of the fully-connected neural network is a distributed vector, the output is a high-level feature representation-state matrix of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner; the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
wherein, kstThe state matrix generated at the t-th time step, i belongs to {1,2, … … n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state line represents the knowledge state of the learner on the knowledge point i, and the i-th state line comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively: p is a radical ofi(Lt) E (0,1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical ofi(Tt) E (0,1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical ofi(Gt) E (0,1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical ofi(St)∈(0,1) The error parameter represents a probability value of a learner for error in learning the knowledge point i, a column in the state matrix ks is specifically defined as a state column, and the four state columns are respectively: l istInitial learning parameters representing all n knowledge points; t istA learning ability parameter representing n knowledge points; gtGuess parameters representing n knowledge points; stFault parameters representing n knowledge points.
As a further improvement of the present invention, in step S3, the state matrix is input into a Bayesian knowledge tracking algorithm to calculate a predicted value of the learner ' S future question answering performance, and the probability vector p (C) of the learner ' S correct prediction of the learner ' S answer at the current time step t is calculated for the t +1 th future time stept+1) The expression of (a) is:
p(Ct+1)=Lt*(1-St)+(1-Lt)*Gt
wherein the probability vector p (C)t+1) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C)t+1) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the present invention, in step S4, an evolutionary term is calculated to represent the exact change of the knowledge state of the learner in the adjacent answer, specifically: generating evolution weights by utilizing the established knowledge tracking model, combining the evolution weights and the integral change of the knowledge state into an evolution item by quantifying the action of each state column in the integral change in the state matrix, and generating the evolution item e at the current time step ttThe expression of (a) is:
wherein, wt=(w1,w2,w3,w4)∈(0,1)4Is the evolution weight, Δ kstThe overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
As a further improvement of the present invention, the step of defining the loss function in step S5 includes: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into an evolution item to obtain a loss function of the knowledge tracking model, and finding a global minimum value or a local minimum value by optimizing the loss function to realize the training target of the knowledge tracking model, and further minimizing the loss function by using a random gradient descent method commonly used in the field to make the knowledge tracking model reach an optimal state, wherein the loss function of a time sequence in the knowledge tracking model is as follows:
wherein f (-) is a cross entropy function,for the learner's predicted value of future answer performance, at+1Is the actual value of the learner's future answer performance, etIs an evolution term representing the accurate change of the knowledge state, E belongs to N*Is the total number of questions answered by the learner sequence, N*Is a natural number set.
The invention also provides a knowledge tracking system based on learner knowledge state evolution expression, which comprises:
the statistical cognitive data module is used for acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module generates knowledge state representation of learners and builds a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm;
the forecasting module is used for generating a forecasting value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the forecasting value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the overall change of the knowledge state of the learner in the adjacent answers;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set in the statistical cognitive data module includes a plurality of time series, one time series includes a plurality of time step data, and the plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
As a further improvement of the invention, the input of the long-short term memory neural network in the knowledge state representation module is the acquired cognitive data set, and the output is the low-level feature representation-distributed vector of the knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
As a further improvement of the present invention, in the evolution module, the difference value of the state matrix in the adjacent sequence is calculated to represent the overall change of the knowledge state of the learner in the adjacent answer, specifically: and generating evolution weights by using the established knowledge tracking model, quantifying the action of each state column in the state matrix in the overall change, and combining the evolution weights and the overall change of the knowledge state into an evolution item so as to express the accurate change of the knowledge state of the learner in the adjacent answers.
As a further improvement of the present invention, the step of defining the loss function in the optimization module comprises: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into the evolution item to obtain the loss function of the knowledge tracking model, and optimizing the loss function to enable the loss function to find the global minimum or the local minimum so as to realize the training target of the knowledge tracking model, and further using a random gradient descent method commonly used in the field to minimize the loss function, so that the knowledge tracking model reaches the optimal state.
As a further improvement of the invention, the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
wherein, kstThe state matrix generated at the t-th time step, i belongs to {1, 2.. the., n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state row represents the knowledge state of the learner on the knowledge point i, and the knowledge state comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively as follows: p is a radical ofi(Lt) E (0,1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical ofi(Tt) E (0,1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical ofi(Gt) E (0,1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical ofi(St) E (0,1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l istInitial learning parameters representing all n knowledge points; t istA learning ability parameter representing n knowledge points; gtGuess parameters representing n knowledge points; stRepresents n number of knownError parameters of point identification.
As a further improvement of the invention, the probability vector p (c) of correct prediction of answer of learner at current time step t and at t +1 time step in futuret+1) The expression of (a) is:
p(Ct+1)=Lt*(1-St)+(1-Lt)*Gt
wherein the probability vector p (C)t+1) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C)t+1) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the invention, at the current time step t, the evolution term etThe expression of (a) is:
wherein, wt=(w1,w2,w3,w4)∈(0,1)4Is the evolution weight, Δ kstThe overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
As a further improvement of the invention, in the knowledge tracking model, the loss function of a time series is as follows:
wherein f (-) is a cross entropy function,for the learner's predicted value of future answer performance, at+1Is the actual value of the learner's future answer performance, etIs an evolution term representing the accurate change of the knowledge state, E belongs to N*Is the total number of questions answered by the learner sequence, N*Is a natural number set.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein when the processor runs the computer program, the steps of the knowledge tracking method based on the learner knowledge state evolution representation are executed.
The present invention also provides a computer readable storage medium storing a computer program for causing a computer to perform the steps of the method for knowledge tracking based on an evolving representation of learner knowledge state as disclosed above.
Generally, compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a knowledge tracking method and system based on learner knowledge state evolution expression, which utilizes the 'memory' characteristic of a long-short term memory network neural network when processing time sequence data to generate a state matrix to inherit the characteristics implicit in a learner answer sequence, conforms to the learning rule of the learner when answering, more accurately expresses the knowledge state of the learner in the process of answering, and is more suitable for predicting the future answer expression of the learner.
The knowledge tracking method and the knowledge tracking system based on learner knowledge state evolution representation introduce the evolution item to specifically represent the accurate change of the knowledge state of a learner in the adjacent answering process, incorporate the evolution item into the loss function, reversely train the model to generate a more reasonable knowledge state of the learner, and finally achieve the aim of gradual change and gradual transition of the knowledge state of the learner. The method and the system solve the defects in the classical knowledge tracking model, restore the real learning process, are the key part for establishing the accurate knowledge tracking model, and can better assist the concrete teaching practice.
Drawings
FIG. 1 is a schematic diagram of a knowledge tracking method based on learner knowledge state evolution representation according to the present invention;
fig. 2 is a schematic structural diagram of an evolution item 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 further described in detail below with reference to fig. 1-2. 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. The present invention will be described in further detail with reference to specific embodiments.
FIG. 1 is a schematic diagram of a knowledge tracking method based on learner knowledge state evolution representation according to the present invention. As shown in fig. 1, the method comprises the steps of:
s1, acquiring a statistical cognitive data set of a plurality of learners for a plurality of knowledge point samples. The cognitive data set comprises a plurality of time sequences, one time sequence comprises a plurality of time step data, and the plurality of time step data represent the answering conditions of a learner on a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
For example: the cognitive data set comprises S time series, S belongs to N*Number of different learners in the data set, N*Is a natural number set; a time sequence comprises a plurality of time step data, which is the answering condition of a learner on a plurality of knowledge points; a time step data xt=(qt,at) Is a learner S belongs to [1, S ]]At a knowledge point i e [1, n ]]The answer situation of (1), wherein qtIs a vector representation of the current answering knowledge point, atIs the current answer result, at0 denotes a response error, at1 means correct response. t is an element of [1, E ∈],E∈N*Is the total number of questions answered by the learner, N*Is a natural number set, and n is the number of different knowledge points in the cognitive data set.
And S2, generating knowledge state representation of the learner and building a knowledge tracking model. In the established knowledge tracking model, the input of the long-term and short-term memory neural network and the fully-connected neural network is a cognitive data set, and the output is a state matrix;
the input of the long-short term memory neural network is an acquired cognitive data set, and the output is a low-level feature representation-distributed vector of a knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
At the t time step, the time step data xtInput into long-short term memory neural network, output is low-level feature representation of knowledge state of learner s-distributed vector ht∈(0,1)NWhere N is the number of hidden nodes. h istThe knowledge state of the learner s at the current time step t is shown, and the summary shows the knowledge state of the learner for n knowledge points, each of which has no specific meaning. Vector h to be distributedtInput to the whole neural network, and output is the state matrix ks, which is a high-level feature representation of the knowledge state of the learner st=|Lt,Tt,Gt,StL, the ith state row (p) thereini(Lt),pi(Tt),pi(Gt),pi(St))∈(0,1)4Are the four state parameters of knowledge point i, representing the knowledge state of learner s with respect to knowledge point i. State column LtRepresenting initial learning parameters of the learner s for all n knowledge points; t istThe learning ability parameter represents the learning ability of the learner s to the n knowledge points; gtRepresenting guess parameters of the learner s for the n knowledge points; stError parameters of the learner s for the n knowledge points are represented. At the t-th time step, kstThe knowledge state of the learner for each knowledge point is represented, and the expression is as follows:
and S3, generating a predicted value of the future answer expression of the learner. In the established knowledge tracking model, the input of the Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner.
At the t-th time step, the state matrix kstInputting the result into a Bayesian knowledge tracking algorithm, and calculating a prediction probability vector p (C) of a learner s with correct answer at the t +1 th time step in the future by using a prediction probability calculation formula in the algorithmt+1) The calculation formula is as follows:
p(Ct+1)=Lt*(1-St)+(1-Lt)*Gt
wherein the probability vector p (C)t+1) The ith dimension in (1) is the probability value of the knowledge point i that the learner s correctly answers at the t +1 th time step in the future.
Further, a probability vector p (C)t+1) Knowledge point vector q that will answer with the t +1 time stept+1Performing dot product operation to calculate the probability value of correct answer of learner s at next time step, and predicting answer result when the probability value is greater than or equal to 0.95When the probability value is less than 0.95, the predicted answer result
For example, learner s answers knowledge point j, p (C) at time step t +1t+1) And q ist+1The result of performing the dot product operation will be pj(Ct+1) The probability value of the knowledge point j correctly answered by the learner s at the t +1 th time step in the future. When p isj(Ct+1) Predicting that the learner s will answer correctly when the learner s is more than or equal to 0.95; when p isj(Ct+1) Below 0.95, it is predicted that learner s will respond correctly and incorrectly.
And S4, generating an evolution item, and combining the evolution weight and the integral change of the knowledge state into the evolution item so as to represent the accurate change of the knowledge state of the learner in the adjacent answers.
At the t-th time step, the overall change delta ks of the knowledge state between the t-th time step and the previous time step t-1 is calculatedtThe calculation formula is as follows:
then, the output evolution weight w of the fully-connected neural network is utilizedt=(w1,w2,w3,w4)∈(0,1)4。wtAnd generating according to the characteristics of the learner data, wherein each dimension of weight represents the action of each state column in the whole knowledge state change process. Then, the weight w is evolvedtGlobal change from knowledge state Δ kstCombining into evolution terms etE (0,1), and the calculation formula is as follows:
fig. 2 is a schematic diagram of an evolution term of an embodiment of the invention. The evolution item is used for representing the change of the accurate knowledge state in the adjacent question answering process, and each dimension weight represents the effect of each state column in the change of the overall knowledge state. The evolution item aims at modeling the accurate change of the knowledge state in the knowledge tracking model, and is specifically applied to the loss function of the knowledge tracking model to train the knowledge tracking model reversely, so that the knowledge state generated by the knowledge tracking model is more reasonable.
And S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the learner's future answer performance and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
There are two training goals for the model, one being to generate accurate learningThe second is to accurately model the gradual change of the knowledge state. Therefore, the loss function also comprises two parts, namely calculating the cross entropy between the real value and the predicted value of the future answer performance, and calculating the evolution item. The loss function is optimized using a commonly used stochastic gradient descent method such that it finds a global minimum or a local minimum, enabling two training objectives of the model. For the learner s, the total number of questions E belonging to N*The loss function is:
wherein f (-) is a cross entropy function,predicted value of answer performance for learner s at t +1 th time step in future, at+1Is the true value of the learner s' answer performance at the t +1 th time step in the future, etIs an evolution term representing the accurate change of the knowledge state, E belongs to N*Is the total number of questions answered by the learner sequence, N*Is a natural number set.
For all learners in the cognitive dataset, the loss function is:
wherein S is belonged to N*Number of different learners in the data set, N*Is a natural number set.
Table 1 shows the results of the knowledge tracking method of the present invention and the prior art method for predicting the future answer of the learner. As shown in table 1, experiments were performed on three cognitive datasets, ASSIST2009, ASSIST2015, Statics2011, respectively. The prior art method for comparison comprises a classic Bayesian knowledge tracking method and a depth knowledge tracking method, and the measurement index of the experimental result is Area Under Cut (AUC). As can be seen from the table, the prediction result of the technical scheme of the embodiment of the present invention is superior to that of the prior art.
Table 1 shows the results of the knowledge tracking method of the present invention and the prediction of the learner's answer state by the prior art method
In order to make the knowledge tracking method based on learner knowledge state evolution expression more clear, taking a learner as an example, the knowledge tracking method based on learner knowledge state evolution expression of the learner in a time sequence is introduced:
(1) the cognitive data set comprises a plurality of time sequences, and the answer sequence of each learner is a time sequence. If a learner answers 5 times in total (3 different knowledge points in total), the answer data is input once per time step, and the length of the time series is 5. In table 2, the practice data of the learner is shown, and the first line is the total number of the questions practiced by the learner, and 5 practice questions are made in total; the second line is the label of the knowledge point that the learner answered, such as the 1 st practice question that the first learner answered is about knowledge point 3, and the 2 nd practice question about knowledge point 1; the third line is the result of the learner's answer, 0 for wrong answer, 1 for correct answer, such as wrong answer for the first learner to answer the 1 st question, wrong answer for the 2 nd question, etc.
TABLE 2 data Format
(2) At the 1 st time step, the input data is x1=(q1,a1)=(0,0,1,0)TWherein q is1=(0,0,1)TIs a one-hot vector representation of the current knowledge point to answer, and represents that the student answers the third knowledge point. a is10 is the current answer result, indicating an error.
(3) Long-short term memory neural network according to x in knowledge tracking model1Generating a low-level feature representation of a knowledge state-a distributed vector h1∈(0.1,0.4,0.2,0.1)TWhere it is assumed that the number of hidden nodes of the neural network is 4, and thus the vector dimension is 4.
(4) All neural network basis h in knowledge tracking model1The state matrix ks, an advanced feature representation of the knowledge state, is generated1=|L1,T1,G1,S1L is as follows:
where the first line is the learner's knowledge state for knowledge point 1, the second line is the learner's knowledge state for knowledge point 2, and the third line is the learner's knowledge state for knowledge point 3. The first column is the learner's initial learning parameters for 3 knowledge points; the second column is the learner's learning ability parameters for 3 knowledge points; the third column is the learner's guess parameters for 3 knowledge points and the fourth column is the learner's miss parameters for 3 knowledge points.
(5) Bayesian knowledge tracking algorithm in knowledge tracking model according to ks1And calculating the predicted value of the 2 nd answer performance of the learner.
p(C2)=L1*(1-S1)+(1-L1)*G1
=(0.3,0.1,0.15)*(0.9,0.95,0.85)T+(0.7,0.9,0.85)*(0.1,0.05,0.15)T
=0.735
Since 0.735 < 0.95, the learner is predicted to have the wrong answer for the second time.
(6) Fully connected neural network generation evolution weight w in knowledge tracking model1=(0.2,0.3,0.1,0.4)TChange it by Δ ks from the whole1=(||L1-L0||,||T1-T0||,||G1-G0||,||S1-S0Group I)Combining into evolution terms
(7) Incorporating evolutionary terms into a loss functionAnd training the knowledge tracking model reversely to be optimal. Where f (-) is a commonly used cross entropy loss function.
(8) Time step 2 … … (loop through steps 2-7 above).
The invention also provides a knowledge tracking system based on learner knowledge state evolution expression, which comprises:
the statistical cognitive data module is used for acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module generates knowledge state representation of learners and builds a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm;
the forecasting module is used for generating a forecasting value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the forecasting value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the overall change of the knowledge state of the learner in the adjacent answers;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
As a further improvement of the present invention, the cognitive data set in the statistical cognitive data module includes a plurality of time series, one time series includes a plurality of time step data, and the plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
As a further improvement of the invention, the input of the long-short term memory neural network in the knowledge state representation module is the acquired cognitive data set, and the output is the low-level feature representation-distributed vector of the knowledge state; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is a high-level feature representation of the knowledge state, and the state matrix is a representation method of the knowledge state of the learner.
As a further improvement of the present invention, in the evolution module, the difference value of the state matrix in the adjacent sequence is calculated to represent the overall change of the knowledge state of the learner in the adjacent answer, specifically: and generating evolution weights by using the established knowledge tracking model, quantifying the action of each state column in the state matrix in the overall change, and combining the evolution weights and the overall change of the knowledge state into an evolution item so as to express the accurate change of the knowledge state of the learner in the adjacent answers.
As a further improvement of the present invention, the step of defining the loss function in the optimization module comprises: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into the evolution item to obtain the loss function of the knowledge tracking model, and optimizing the loss function to enable the loss function to find the global minimum or the local minimum so as to realize the training target of the knowledge tracking model, and further using a random gradient descent method commonly used in the field to minimize the loss function, so that the knowledge tracking model reaches the optimal state.
As a further improvement of the invention, the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
wherein, kstThe state matrix generated at the t-th time step, i belongs to {1, 2.. the., n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state row represents the knowledge state of the learner on the knowledge point i, and the knowledge state comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively as follows: p is a radical ofi(Lt) E (0,1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical ofi(Tt) E (0,1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical ofi(Gt) E (0,1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical ofi(St) E (0,1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l istInitial learning parameters representing all n knowledge points; t istA learning ability parameter representing n knowledge points; gtGuess parameters representing n knowledge points; stFault parameters representing n knowledge points.
As a further improvement of the invention, the probability vector p (C) of correct prediction of answer of the learner at the current time step t and at the t +1 th time step in the futuret+1) The expression of (a) is:
p(Ct+1)=Lt*(1-St)+(1-Lt)*Gt
wherein the probability vector p (C)t+1) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C)t+1) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
As a further improvement of the inventionEvolution term e at the current time step ttThe expression of (a) is:
wherein, wt=(w1,w2,w3,w4)∈(0,1)4Is the evolution weight, Δ kstThe overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
As a further improvement of the invention, in the knowledge tracking model, the loss function of a time series is as follows:
wherein f (-) is a cross entropy function,for the learner's predicted value of future answer performance, at+1Is the actual value of the learner's future answer performance, etIs an evolution term representing the accurate change of the knowledge state, E belongs to N*Is the total number of questions answered by the learner sequence, N*Is a natural number set.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein when the processor runs the computer program, the steps of the knowledge tracking method based on the learner knowledge state evolution representation are executed.
The present invention also provides a computer readable storage medium storing a computer program for causing a computer to perform the steps of the method for knowledge tracking based on an evolving representation of learner knowledge state as disclosed above.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the embodiment of the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (9)
1. A knowledge tracking method based on learner knowledge state evolution representation is characterized by comprising the following steps:
s1, acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
s2, generating knowledge state representation of the learner, and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of the long-term and short-term memory neural network and the input of the full-connection neural network are cognitive data sets, and the output of the long-term and short-term memory neural network and the full-connection neural network is a state matrix;
s3, generating a predicted value of the future answer expression of the learner, wherein in the established knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the predicted value of the future answer expression of the learner;
s4, generating an evolution item, and combining the evolution weight and the overall change of the knowledge state into the evolution item so as to represent the accurate change of the knowledge state of the learner in the adjacent answers;
and S5, incorporating the evolution item into a loss function and optimizing, wherein the training target of the knowledge tracking model is to generate an accurate predicted value of the learner's future answer performance and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
2. The knowledge tracking method based on the learner knowledge state evolution representation as claimed in claim 1, wherein the cognitive data set in step S1 includes a plurality of time series, a time series includes a plurality of time step data, a plurality of time step data represent the answering situation of a learner at a plurality of knowledge points; a time step data is a learner's answer at a knowledge point.
3. The knowledge tracking method based on learner knowledge state evolution representation as claimed in claim 1, wherein the input of the long-short term memory neural network in step S2 is the acquired cognitive data set, and the output is the low-level feature representation of knowledge state-distributed vector; the input of the fully-connected neural network is a distributed vector, the output is a state matrix which is high-level characteristic representation of knowledge state, and the state matrix is a representation method of the knowledge state of the learner; the rows in the state matrix ks are specifically defined as state rows, which are the overall knowledge states of a learner for a knowledge point; the columns in the state matrix ks are specifically defined as state columns, which are a knowledge state of a learner for all knowledge points in the cognitive dataset, and the state matrix ks is expressed as:
wherein, kstThe state matrix generated at the t-th time step, i belongs to {1,2, … … n } is the knowledge point being answered at the t-th time step, n is the total number of knowledge points in the cognitive data set, the i-th state line represents the knowledge state of the learner on the knowledge point i, and the i-th state line comprises four state parameters corresponding to the knowledge point i, and the four state parameters are respectively: p is a radical ofi(Lt) E (0,1) is an initial learning parameter and represents the probability value of learning the knowledge point i before the learner answers; p is a radical ofi(Tt) E (0,1) is a learning ability parameter and represents a probability value of the learner from the unknown to the learned knowledge point i; p is a radical ofi(Gt) E (0,1) is a guess parameter and represents a guess probability value when the learner does not learn the knowledge point i; p is a radical ofi(St) E (0,1) is a fault parameter and represents the probability value of the fault answering of the learner at the learned knowledge point i, the columns in the state matrix ks are specifically defined as state columns, and the four state columns are respectively: l istInitial learning parameters representing all n knowledge points; t istA learning ability parameter representing n knowledge points; gtGuess parameters representing n knowledge points; srFault parameters representing n knowledge points.
4. The knowledge tracking method according to claim 1, wherein the state matrix is inputted into a Bayesian knowledge tracking algorithm in step S3 to calculate the predicted value of the learner 'S future answer performance, and the probability vector p (C) of the learner' S correct prediction of the answer at the current time step t is calculated for the t +1 th time stept+1) The expression of (a) is:
p(Ct+1)=Lt*(1-St)+(1-Lt)*Gt
wherein the probability vector p (C)t+1) The ith dimension in (b) is the probability value of the learner to correctly answer the knowledge point i at the t +1 th time step in the future, and the probability vector p (C)t+1) Performing dot product operation with the knowledge point vector answered at the t +1 th time step to calculate the probability value of correct answer at the next time step of the learner, and predicting that the learner will correctly answer when the probability value is more than or equal to 0.95; when the probability value is less than 0.95, the learner is predicted to respond incorrectly.
5. The knowledge tracking method of claim 1, wherein the step S4 is to calculate evolution terms to represent the exact change of the learner' S knowledge state in the adjacent answer, specifically: generating evolution weights by utilizing the established knowledge tracking model, combining the evolution weights and the integral change of the knowledge state into an evolution item by quantifying the action of each state column in the integral change in the state matrix, and generating the evolution item e at the current time step ttThe expression of (a) is:
wherein, wt=(w1,w2,w3,w4)∈(0,1)4Is the evolution weight, Δ kstThe overall change of the knowledge state at t time steps and t-1 time steps is the difference value of the state matrix of the adjacent time steps, namely the difference value of the state columns of the adjacent time steps, the influence of different state columns on the overall change of the knowledge state is different, and the specific action of each state column is accurately modeled by the evolution weight.
6. The knowledge tracking method based on the learner knowledge state evolution representation as claimed in claim 1, wherein the step of defining the loss function in step S5 comprises: calculating the cross entropy between the true value and the predicted value of the future answer performance, and incorporating into an evolution item to obtain a loss function of the knowledge tracking model, and finding a global minimum value or a local minimum value by optimizing the loss function to realize the training target of the knowledge tracking model, and further minimizing the loss function by using a random gradient descent method commonly used in the field to make the knowledge tracking model reach an optimal state, wherein the loss function of a time sequence in the knowledge tracking model is as follows:
wherein f (-) is a cross entropy function,for the learner's predicted value of future answer performance, at+1Is the actual value of the learner's future answer performance, etIs an evolution term representing the accurate change of the knowledge state, E belongs to N*Is the total number of questions answered by the learner sequence, N*Is a natural number set.
7. A knowledge tracking system based on an evolving representation of a learner's knowledge state, the system comprising:
the statistical cognitive data module is used for acquiring statistical cognitive data sets of a plurality of learners on a plurality of knowledge point samples;
the knowledge state representation module generates knowledge state representation of learners and builds a knowledge tracking model on the basis of a long-short term memory neural network, a full-connection neural network and a Bayesian knowledge tracking algorithm;
the forecasting module is used for generating a forecasting value of the future answer expression of the learner and building a knowledge tracking model, wherein in the built knowledge tracking model, the input of a Bayesian knowledge tracking algorithm is a state matrix, and the output is the forecasting value of the future answer expression of the learner;
the evolution module is used for generating evolution items and calculating the difference value of the state matrixes in the adjacent sequences so as to represent the overall change of the knowledge state of the learner in the adjacent answers;
and the optimization module is used for incorporating the evolution item into the loss function and optimizing the evolution item, the training target of the knowledge tracking model is to generate an accurate predicted value of the future answer performance of the learner and accurately model the gradual change of the knowledge state, and the target is customized by defining the loss function.
8. An electronic device, characterized in that: comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the computer program to perform the steps of a knowledge tracking method based on an evolving representation of a learner's knowledge state as set forth in any one of claims 1 to 7.
9. A computer-readable storage medium storing a computer program for causing a computer to perform the steps of a knowledge tracking method based on an evolving representation of a learner's knowledge state as claimed in any one of claims 1 to 7.
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