CN110297817A - A method of the structure of knowledge is constructed based on personalized Bayes's knowledge tracing model - Google Patents
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Abstract
The invention proposes a kind of methods based on personalized Bayes's knowledge tracing model building structure of knowledge, belong to educational information model construction techniques field.The method includes the steps one, establish observation matrix and state matrix；Step 2: establishing the parameter model of Bayes's knowledge tracing model；Step 3: establishing Parameter fusion model for learner's personalizing parameters to be fused in traditional Bayes's knowledge trace parameters model；Step 4: being defined using the computational problem that forwards algorithms and backward algorithm complete the parameter model that step 3 obtains；Step 5: being estimated using very big log-likelihood the parameter model to utilize the loss function undated parameter θ to obtain loss function；Then according to the loss function calculating parameter and weight parameter；It is obtained with this based on personalized Bayes's knowledge tracing model, is finally completed the building of the structure of knowledge.
Description
Technical field
The present invention relates to a kind of methods based on personalized Bayes's knowledge tracing model building structure of knowledge, belong to education
Information model constructing technology field.
Background technique
IT application in education sector enters new developing stage, switchs to from digital education with big data analysis, artificial intelligence
Etc. modern information technologies be support wisdom education.The development and realization of online education platform make diversified course types capsule
Miscellaneous mode of learning and knowledge point have been included, provides advantageous premise to construct the knowledge model of learner.Construct knowledge knot
On the one hand structure model can allow learner to recognize on the other hand the knowledge blind spot of itself, intensified learning can depict study
The study track of person and study are intended to, and realize the personalized recommendation of course.
M.Alavi and DE Leidner is provided in proposition information management in 2001 and its conceptual foundation for the structure of knowledge
Basis.Paulheim and Heiko indicates that they pass through to knowledge point it is proposed that constructing knowledge graph using test and knowledge assessment
It carries out questionnaire and then test carries out knowledge reasoning and assessment to judge whether learner grasps, but for online education platform
For, it is more convenient and conveniently that learner wishes to mostly, for questionnaire and tests and loses interest in, although therefore this mode
Accurately but it can not popularize.The questionnaire to learner and test are abandoned, that just needs to divide from learner in the data of platform
The know-how of analysis and assessment learner, Pavlik proposed that analyzing (PFA) Lai Shixian knowledge by Performance Factors chases after in 2009
Track improves existing educational data mining model (such as learning study analysis (LFA)) mainly according to the daily record data of learner,
The assessment to learners' knowledge state is realized in the test and achievement of associative learning person.Knowledge tracking can according to the time develop and
Learner's study schedule, dynamic regularized learning algorithm person are a kind of realizations of hidden Markov model for the Grasping level of knowledge point,
Based on this model, Bayes's knowledge tracing model (BKT) is applied to edX platform by Zachary A.Pardos, and is provided clear
Knowledge component model, allow the learning study except evaluation as parameter, the further perfect approach of knowledge acquisition.
The Wang Zhuo of Peking University and an inscription improve Bayes's knowledge tracing model, propose Aspect-BKT model and History-BKT
Model, improve to learners' knowledge estimation accuracy rate, but in view of to learner's priori knowledge importance ignore and
For the computational accuracy deficiency etc. of learner's learning rate, therefore the model is also required to improve.
Summary of the invention
The present invention is insufficient for the calculating Jiangdu for solving the problems, such as reckoner's learning rate in the prior art, proposes this
Method of the kind based on personalized Bayes's knowledge tracing model building structure of knowledge, the technical solution taken are as follows:
A method of the structure of knowledge is constructed based on personalized Bayes's knowledge tracing model, which comprises
Step 1: establishing observation matrix and state matrix；The observation matrix is O={ ot, t ∈ [1, M], the observation
Matrix is for describing learner to the answer result set of knowledge point；The state matrix is S={ si, i ∈ [1, T], for retouching
Learner is stated to the grasp state set of knowledge point wherein, M represents the number of the observed result of the topic in relation to the knowledge point；t
Indicate the serial number of observation；otIndicate t-th of state；siIndicate i-th of state；The serial number of i expression state；T represents shape
The number of state；
Step 2: establishing the parameter model of Bayes's knowledge tracing model, the parameter model is λ1={ PIk,Ak,Bk,
The parameter model describes the parameter that knowledge point is indicated in model；Wherein, matrixIndicate the first of knowledge point
Begin to grasp Probability pk(L0), wherein [1, N] i ∈, N represent the number of hidden state；MatrixIndicate the state of knowledge point
Transition probability pk(T), wherein i, j ∈ [1, N]；MatrixIndicate the rate p that hits it of knowledge pointk(G) and accidentally error rate pk
(S), wherein [1, N] j ∈, m ∈ [1, M], M indicate the number of observed result；
It is tracked Step 3: establishing Parameter fusion model for learner's personalizing parameters to be fused to traditional Bayes's knowledge
In parameter model, the Parameter fusion model are as follows:
Wherein, μ, η, ε are weight parameters, and fused parameter model is defined as λ={ PI, A, B }, wherein PI is Ye Si
The probability matrix of knowledge tracing model, A are state transition probability matrixs, and B is observation probability matrix；At this point, new pattra leaves
This knowledge tracking parameter model in altogether include λ, μ, η, ε parameter, defined parameters form θ={ λ, μ, η, ε } indicate Bayes know
Know the parameter model of tracing model；
Step 4: being defined using the computational problem that forwards algorithms and backward algorithm complete the parameter model that step 3 obtains；
Step 5: being estimated using very big log-likelihood the parameter model to utilize the loss to obtain loss function
Function undated parameter θ；Then according to loss function the calculating parameter PI, A, B and weight parameter μ, η, ε；It is based on this
Personalized Bayes's knowledge tracing model, is finally completed the building of the structure of knowledge.
Further, the process that computational problem defines is obtained described in step 4 includes:
A series of given parameters θ={ λ, μ, η, ε } and observation sequence O={ ot, it calculates and observes what O occurred at model θ
Probability p (O | θ), wherein solving computational problem using forwards algorithms, steps are as follows:
The first step, for model θ, definition is to the status switch of t moment being initially o1,o2,…,otAnd state is qi's
Probability is preceding to probability, is denoted as:
αt(i)=P (o1,o2,…,ot,si=qi|θ)
To probability α before second step, solutiont(i) and p (O | θ), specific solution procedure are as follows: definition original state is α1(i)=
πibi(o1), wherein πiIndicate i-th of initial grasp probability matrix；biIndicate i-th hit it rate and accidentally error rate hybrid matrix；
Third step determines the transfer formula from state t to state t+1 according to original state:
4th step calculates the forward direction probability that O is observed at model θ, calculation formula are as follows:
Solving computational problem using backward algorithm, steps are as follows:
Step 1, for model θ, being defined on t moment state is qiUnder the premise of, the observation sequence from t+1 to T is ot+1,
ot+2,…,oTProbability be backward probability, be denoted as: βt(i)=P (ot+1,ot+2,…,oT|si=qi,θ)
Step 2 passes through Recursive Solution backward probability βt(i) and p (O | θ)；Wherein, original state may be defined as: β1(i)=1
Step 3, the determining transfer formula from state t+1 to state T:
Step 4 calculates the backward probability that O is observed at model θ, calculation formula are as follows:
Further, acquisition described in step 5 is finally completed the structure of knowledge based on personalized Bayes's knowledge tracing model
The process of building include:
Step 1 defines problem concerning study: given parameters θ and observation O and adjusting parameter θ obtain maximized p (O | θ)
The method for obtaining maximized p (O | θ), the method includes the estimation of very big log-likelihood, EM algorithms etc..
Step 2 described is estimated using very big log-likelihood based on personalized Bayes's knowledge tracing model to determine loss
Function, the loss function are as follows:
Step 3, the more new formula that parameter θ is obtained using the loss function:
Wherein, parameter τ indicates the step-length that model extends；
Step 4, according to loss function calculating parameter PI, A, B；
Step 5 calculates weight parameter μ, η, ε using loss function are as follows:
It is based on personalized Bayes's knowledge tracing model by obtaining above-mentioned each gain of parameter, the structure of knowledge can be completed
Building.
The invention has the advantages that:
For knowledge structure models, this project constructs 4 kinds of Bayes's knowledge tracing models altogether:
1. Bayes's knowledge tracing model of standard
2. the individualized knowledge tracing model with PI
3. having PI, the individualized knowledge tracing model of A
4. the PI having, A, B individualized knowledge tracing model
Personalized knowledge tracing model is embodied in the personalization of the parameter for learner, the individualized knowledge with PI
Tracing model is that only the probability parameter of the initial grasp knowledge point of learner is added in model, has PI, and the personalization of A is known
Knowing tracing model is that the probability parameter of the initial grasp knowledge point of learner and learning rate parameter are added in model, is had
PI, A, B individualized knowledge tracing model is rate and accidentally wrong that the initial grasp probability of learner, learning rate, answer are hit it
In the parameters such as rate addition all models.
When constructing model, the value of our restricted models all conjectures and sliding parameter, to prevent model degradation
Phenomenon.It is 0.5 that priori knowledge probability is initialized in this experiment, learning rate 0.4, and accidentally error rate and rate of hitting it are respectively 0.2,
0.2.All models are all made of 5 times of cross validations, to increase the training precision of model, for each cross validation results,
Calculate log-likelihood estimation (LL), akaike information criterion (AIC), Bayesian Information amount (BIC), root-mean-square error (RMSE)
It is the criterion of the quality for evaluation model with accurate (Acc) of model.The parameter index of four kinds of models is as shown in table 1 below:
Table 1
By the comparison of model 1 and model 2 it can be found that in view of adding the priori knowledge probability of each learner
Into personalized Bayes's knowledge tracing model, max log possibility predication has greatly improved, and root-mean-square error from
0.359333 is reduced to 0.34782, and accuracy also improves one percentage point, illustrates that algorithm model has and is obviously improved.
It is compared from modular concept by model 2 and model 3, it can be found that model 3 is relative to model 2 again by the study of learner
Rate probability, that is, state transition probability are added in training pattern, it can be found that max log possibility predication from result
LL, which has, significantly to be increased, and accuracy does not change substantially, but root-mean-square error RMSE is obviously increased, and AIC and BIC are also big
Amplitude increases, this indicates that model parameter becomes more complicated, this improvement for not being for training pattern, certainly, from standard
Exactness is it is also seen that model optimization structure is undesirable.
Model 4 is that will have PI, the individualized knowledge tracing model of A, B, contains the priori knowledge probability of learner, learns
It practises rate, rate of hitting it and misses error rate, the special parameter of user is added in training pattern, affecting for high degree is greatly right
Number possibility predications as a result, as can be seen from the table, model 4 is higher than majority compared to preceding 3 models, max log possibility predication LL
Model, model complexity assess parameter AIC and BIC also below average, it is often more important that root-mean-square error RMSE has significantly
It reduces, illustrates that model error is smaller, accuracy has also been increased to 89.22%.Judging from the experimental results, model 4 have PI,
The individualized knowledge tracing model of A, B, training effect is best, also illustrates the reasonability and effectively of personalized knowledge tracing model
Property.
Detailed description of the invention
Fig. 1 is the algorithm flow chart of individualized knowledge Bayes knowledge tracing model.
Specific embodiment
The present invention will be further described combined with specific embodiments below, but the present invention should not be limited by the examples.
Embodiment 1:
A method of the structure of knowledge is constructed based on personalized Bayes's knowledge tracing model, which comprises
Step 1: establishing observation matrix and state matrix；The observation matrix is O={ ot, t ∈ [1, M], the observation
Matrix is for describing learner to the answer result set of knowledge point；The state matrix is S={ si, i ∈ [1, T], for retouching
Learner is stated to the grasp state set of knowledge point wherein, M represents the number of the observed result of the topic in relation to the knowledge point；t
Indicate the serial number of observation；otIndicate t-th of state；siIndicate i-th of state；The serial number of i expression state；T represents of state
Number；
Step 2: establishing the parameter model of Bayes's knowledge tracing model, the parameter model is λ1={ PIk,Ak,Bk,
The parameter model describes the parameter that knowledge point is indicated in model；Wherein, matrixIndicate the first of knowledge point
Begin to grasp Probability pk(L0), wherein [1, N] i ∈, N represent the number of hidden state；MatrixIndicate the state of knowledge point
Transition probability pk(T), wherein i, j ∈ [1, N]；MatrixIndicate the rate p that hits it of knowledge pointk(G) and accidentally error rate pk
(S), wherein [1, N] j ∈, m ∈ [1, M], M indicate the number of observed result；
It is tracked Step 3: establishing Parameter fusion model for learner's personalizing parameters to be fused to traditional Bayes's knowledge
In parameter model, the Parameter fusion model are as follows:
Wherein, μ, η, ε are weight parameters, and fused parameter model is defined as λ={ PI, A, B }, wherein PI is pattra leaves
The probability matrix of this knowledge tracing model, A are state transition probability matrixs, and B is observation probability matrix；At this point, new shellfish
It altogether include λ, μ, η, ε parameter, defined parameters form θ={ λ, μ, η, ε } expression Bayes in the parameter model of this knowledge of leaf tracking
The parameter model of knowledge tracing model；
Step 4: being defined using the computational problem that forwards algorithms and backward algorithm complete the parameter model that step 3 obtains；
Step 5: being estimated using very big log-likelihood the parameter model to utilize the loss to obtain loss function
Function undated parameter θ；Then according to loss function the calculating parameter PI, A, B and weight parameter μ, η, ε；It is based on this
Personalized Bayes's knowledge tracing model, is finally completed the building of the structure of knowledge.
In the present embodiment, the process that acquisition computational problem defines described in step 4 includes:
A series of given parameters θ={ λ, μ, η, ε } and observation sequence O={ ot, it calculates and observes what O occurred at model θ
Probability p (O | θ), wherein solving computational problem using forwards algorithms, steps are as follows:
The first step, for model θ, definition is to the status switch of t moment being initially o1,o2,…,otAnd state is qi's
Probability is preceding to probability, is denoted as:
αt(i)=P (o1,o2,…,ot,si=qi|θ)
To probability α before second step, solutiont(i) and p (O | θ), specific solution procedure are as follows: definition original state is α1(i)=
πibi(o1), wherein πiIndicate i-th of initial grasp probability matrix；biIndicate i-th hit it rate and accidentally error rate hybrid matrix；
Third step determines the transfer formula from state t to state t+1 according to original state:
4th step calculates the forward direction probability that O is observed at model θ, calculation formula are as follows:
Solving computational problem using backward algorithm, steps are as follows:
Step 1, for model θ, being defined on t moment state is qiUnder the premise of, the observation sequence from t+1 to T is ot+1,
ot+2,…,oTProbability be backward probability, be denoted as: βt(i)=P (ot+1,ot+2,…,oT|si=qi,θ)
Step 2 passes through Recursive Solution backward probability βt(i) and p (O | θ)；Wherein, original state may be defined as: β1(i)=1
Step 3, the determining transfer formula from state t+1 to state T:
Step 4 calculates the backward probability that O is observed at model θ, calculation formula are as follows:
In the present embodiment, acquisition described in step 5 is finally completed knowledge knot based on personalized Bayes's knowledge tracing model
The process of the building of structure includes:
Step 1 defines problem concerning study: given parameters θ and observation O and adjusting parameter θ obtain maximized p (O | θ)
The method for obtaining maximized p (O | θ), the method includes the estimation of very big log-likelihood, EM algorithms etc..
Step 2 described is estimated using very big log-likelihood based on personalized Bayes's knowledge tracing model to determine loss
Function, the loss function are as follows:
Step 3, the more new formula that parameter θ is obtained using the loss function:
Wherein, parameter τ indicates the step-length that model extends；
Step 4, according to loss function calculating parameter PI, A, B；
Step 5 calculates weight parameter μ, η, ε using loss function are as follows:
It is based on personalized Bayes's knowledge tracing model by obtaining above-mentioned each gain of parameter, the structure of knowledge can be completed
Building.
Method flow such as Fig. 1 institute based on personalized Bayes's knowledge tracing model building structure of knowledge described in the present embodiment
It states, the pseudocode of the method is as shown in table 2:
Table 2
Although the present invention has been disclosed in the preferred embodiment as above, it is not intended to limit the invention, any to be familiar with this
The people of technology can do various changes and modification, therefore protection of the invention without departing from the spirit and scope of the present invention
Range should subject to the definition of the claims.
Claims (3)
1. a kind of method based on personalized Bayes's knowledge tracing model building structure of knowledge, which is characterized in that the method
Include:
Step 1: establishing observation matrix and state matrix；The observation matrix is O={ ot, t ∈ [1, M], the observation matrix
For describing learner to the answer result set of knowledge point；The state matrix is S={ si, i ∈ [1, T] is learned for describing
Wherein to the grasp state set of knowledge point, M represents the number of the observed result of the topic in relation to the knowledge point to habit person；T is indicated
The serial number of observation；otIndicate t-th of state；siIndicate i-th of state；The serial number of i expression state；T represents the number of state；
Step 2: establishing the parameter model of Bayes's knowledge tracing model, the parameter model is λ1={ PIk,Ak,Bk, it is described
Parameter model describes the parameter that knowledge point is indicated in model；Wherein, matrixIndicate the initial palm of knowledge point
Hold Probability pk(L0), wherein [1, N] i ∈, N represent the number of hidden state；MatrixIndicate the state transfer of knowledge point
Probability pk(T), wherein i, j ∈ [1, N]；MatrixIndicate the rate p that hits it of knowledge pointk(G) and accidentally error rate pk(S),
Wherein [1, N] j ∈, m ∈ [1, M], M indicate the number of observed result；
Step 3: establishing Parameter fusion model for learner's personalizing parameters to be fused to traditional Bayes's knowledge trace parameters
In model, the Parameter fusion model are as follows:
Wherein, μ, η, ε are weight parameters, and fused parameter model is defined as λ={ PI, A, B }, wherein PI is that Bayes knows
Know the probability matrix of tracing model, A is state transition probability matrix, and B is observation probability matrix；At this point, new Bayes
It altogether include λ, μ, η, ε parameter, defined parameters form θ={ λ, μ, η, ε } expression Bayes's knowledge in the parameter model of knowledge tracking
The parameter model of tracing model；
Step 4: being defined using the computational problem that forwards algorithms and backward algorithm complete the parameter model that step 3 obtains；
Step 5: being estimated using very big log-likelihood the parameter model to utilize the loss function to obtain loss function
Undated parameter θ；Then according to loss function the calculating parameter PI, A, B and weight parameter μ, η, ε；It is obtained with this based on individual character
Change Bayes's knowledge tracing model, is finally completed the building of the structure of knowledge.
2. construction method according to claim 1, which is characterized in that the process packet that acquisition computational problem defines described in step 4
It includes: a series of given parameters θ={ λ, μ, η, ε } and observation sequence O={ ot, it calculates and observes the Probability p that O occurs at model θ
(O | θ), wherein solving computational problem using forwards algorithms, steps are as follows:
The first step, for model θ, definition is to the status switch of t moment being initially o1,o2,…,otAnd state is qiProbability be
Forward direction probability, is denoted as:
αt(i)=P (o1,o2,…,ot,si=qi|θ)
To probability α before second step, solutiont(i) and p (O | θ), specific solution procedure are as follows: definition original state is α1(i)=πibi
(o1), wherein πiIndicate i-th of initial grasp probability matrix；biIndicate i-th hit it rate and accidentally error rate hybrid matrix；
Third step determines the transfer formula from state t to state t+1 according to original state:
4th step calculates the forward direction probability that O is observed at model θ, calculation formula are as follows:
Solving computational problem using backward algorithm, steps are as follows:
Step 1, for model θ, being defined on t moment state is qiUnder the premise of, the observation sequence from t+1 to T is ot+1,ot+2,…,
oTProbability be backward probability, be denoted as: βt(i)=P (ot+1,ot+2,…,oT|si=qi,θ)
Step 2 passes through Recursive Solution backward probability βt(i) and p (O | θ)；Wherein, original state may be defined as: β1(i)=1
Step 3, the determining transfer formula from state t+1 to state T:
Step 4 calculates the backward probability that O is observed at model θ, calculation formula are as follows:
。
3. construction method according to claim 1, which is characterized in that acquisition described in step 5 is based on personalized Bayes's knowledge
Tracing model, the process for being finally completed the building of the structure of knowledge include:
Step 1 defines problem concerning study: given parameters θ and observation O and adjusting parameter θ show that maximized p (O | θ) is obtained
The method of maximized p (O | θ), the method includes the estimation of very big log-likelihood and EM algorithms.
Step 2, it is described estimated using very big log-likelihood based on personalized Bayes's knowledge tracing model to determine loss function,
The loss function are as follows:
Step 3, the more new formula that parameter θ is obtained using the loss function:
Wherein, parameter τ indicates the step-length that model extends；
Step 4, according to loss function calculating parameter matrix PI, A, B；
Step 5 calculates weight parameter μ, η, ε using loss function are as follows:
It is based on personalized Bayes's knowledge tracing model by obtaining above-mentioned each gain of parameter, the structure of the structure of knowledge can be completed
It builds.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113495943A (en) * | 2020-04-02 | 2021-10-12 | 山东大学 | Knowledge tracking and transferring-based man-machine conversation method |
| CN113495943B (en) * | 2020-04-02 | 2023-07-14 | 山东大学 | Man-machine dialogue method based on knowledge tracking and transferring |
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