A bayesian network-based mistake attribution method and system

Abstract

The application discloses a wrong question attribution method based on a Bayesian network, constructs a Bayesian network through a knowledge point structure diagram, and performs Bayesian network parameter learning and question mistake reason inference by using student question data. Each piece of input data is used to update the parameters of the Bayesian network, and when wrong question attribution is needed, the question mistake reason inference can be performed by using the data and the parameters of the current Bayesian network. The method can reveal the hierarchical relationship of the student question mistake reasons, and clarify the error reason chain in a fine granularity. In a large-scale scene, the method can realize efficient and accurate automatic wrong question attribution, assist teachers in targeted lesson preparation and student guidance, and help students realize personalized learning. Meanwhile, the method model is transparent, the process is interpretable, the result is reliable, and the method is suitable for the wrong question attribution scene in intelligent education. The application further discloses a wrong question attribution system based on the Bayesian network.

Description

Technical Field

[0001] This invention belongs to the field of intelligent education and relates to a method and system for attributing errors based on Bayesian networks. Background Technology

[0002] In the field of education, learning from mistakes is a necessary supplement to students' classroom learning and teachers' teaching. It can help students and teachers discover deficiencies in learning and teaching, and is very important for students to fill knowledge gaps and for teachers to prepare lessons.

[0003] In the traditional approach, attributing the causes of incorrect answers is usually done by teachers. This method requires teachers to conduct detailed analysis of each student's answers and each question, which is time-consuming, labor-intensive, and inefficient in large-scale scenarios. Furthermore, teachers sometimes have difficulty grasping the real-time cognitive status of all students and may not be able to make accurate judgments based on the students' current cognitive status.

[0004] Existing cognitive diagnostic algorithms focus on identifying students' cognitive states. Their main approach is to take a set of student problem-solving data and the knowledge points covered in the problems as input to the model and output the student's cognitive state. For example, item response theory can be used to model students' cognitive states. [1] (Item Response Theory, IRT); DINA, a classic discrete cognitive diagnostic model that models students using multidimensional cognitive state vectors. [2] (Deterministic Inputs, Noisy “And” gate model); FuzzyCDM, a continuous cognitive diagnostic model incorporating fuzzy logic. [3] (Fuzzy Cognitive Diagnosis Model); and NeuralCDM, which uses neural networks for modeling complex nonlinear interactions. [4] (Neura Cognitive Diagnosis Model). These methods alleviate the problem of low efficiency in teachers' attribution of errors in large-scale scenarios to some extent. Students can make appropriate adjustments based on their own cognitive situation. However, most of these models can only obtain the student's current cognitive state and cannot perform real-time attribution of errors based on each student's error. They are a coarse-grained cognitive diagnosis, and their output results are sometimes limited in terms of utilizing errors. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for attributing errors based on Bayesian networks, utilizing the Bayesian network model in machine learning to solve the problem of error attribution in the field of education.

[0006] This invention first constructs a Bayesian network using a knowledge point structure diagram. After obtaining the Bayesian network of knowledge point relationships, for each question a student answers, the student's knowledge point mastery map can be inferred and updated based on this Bayesian network. During inference, the parameters of the Bayesian network (i.e., the conditional probability table) are updated using input data and data sampled from the current network at a ratio of 1:n, where 1 represents the amount of input data and n represents the amount of data sampled from the current network. This ratio describes the magnitude of the influence of new input data on the current Bayesian network parameters, where the value of n is generally in the range of [5, 20]. By continuously updating the Bayesian network parameters according to this ratio and new input data (the student's latest question-answering data), the parameters can be made to match the student's current cognitive state, that is, the student's current mastery of each knowledge point. The student's mastery of each knowledge point is represented by the conditional probability table of each variable in the Bayesian network. When attributing errors, a Bayesian network that aligns with the student's current cognitive state is used to partially complete the student's problem-solving data. Then, subgraphs are extracted based on the knowledge points corresponding to the problem-solving data, and an attribution graph is constructed. The parameters of the attribution graph are learned using the problem-solving data and the sampled data from the Bayesian network, and the weights of the edges are calculated. After filtering out the edges with weights greater than the average, an attribution graph that matches the student's current cognitive state and the reasons for the student's errors is obtained. This provides assistance for students to identify and fill knowledge gaps in a personalized way and for teachers to prepare targeted lessons.

[0007] The method of this invention mainly includes two parts: parameter learning and error cause reasoning. Parameter learning includes steps 1-4, and error cause reasoning includes steps 5-9, specifically including the following steps:

[0008] Step 1: Construct a Bayesian network G based on the knowledge point structure diagram. k

[0009] Using a knowledge point structure diagram constructed by educational experts based on their experience as input, a Bayesian network G is constructed. k Among them, the Bayesian network G k The nodes are all the knowledge points contained in the knowledge point structure graph, and the Bayesian network G is a Bayesian network. k The structure is the same as the structure of the knowledge point structure diagram;

[0010] Step 2: Initialize the Bayesian network G k Conditional probability table

[0011] In order to subsequently learn the Bayesian network G based on students' problem-solving data k The parameters need to be set for G first. k The conditional probability table is initialized.

[0012] For Bayesian network G k The node with 0 parent nodes represents a root knowledge point without any prior knowledge. Its initial conditional probability table is shown in formula (1):

[0013]

[0014] Among them, V i Let Pa represent the i-th node. i Let represent the set of parent nodes of the i-th node. That is, when the set of parent nodes of the i-th node is empty, the probability that the i-th node has a value of 1 is 0.5, and similarly, the probability that it has a value of 0 is also 0.5.

[0015] For Bayesian network G k The nodes with a non-zero number of parent nodes represent nodes with prior knowledge points. Their conditional probability tables are initialized as shown in formula (2):

[0016]

[0017] Among them, Pa iK Represents node V i The Kth parent node, m represents node V i The total number of parent nodes. That is, when the set of parent nodes of the i-th node is not empty, the probability that the i-th node has a value of 1 is the number of parent nodes with a value of 1 divided by the total number of parent nodes;

[0018] Step 3: Based on the Bayesian network G k and its conditional probability table completion data D I

[0019] For each piece of input data D I The data includes student ID, question number, knowledge points covered in the question, whether the student scored points on each knowledge point, and whether the student answered the question correctly. Because data D... I This data may not include all the knowledge points, therefore, when updating G with this data... k Before the conditional probability table, G needs to be used. k and its conditional probability table for data D I Perform completion. For the node with the f-th missing value... Its posterior probability is calculated as shown in formula (3):

[0020]

[0021] Among them, V e V represents the set of nodes that have values. miss This represents the set of nodes with missing values. (Due to the nodes...) The represented random variable follows a Bernoulli distribution, therefore according to Bernoulli sampling and The posterior probability value for data D I All missing values, i.e., scores for knowledge points not included in the data DI, are filled in. The distribution is shown in formula (4):

[0022]

[0023] Where Ber represents the Bernoulli distribution;

[0024] Step 4: Update the Bayesian network G k Conditional probability table

[0025] From Bayesian network G k Medium sampling dataset D k This makes dataset D k The number of data entries and data D I The ratio is 9:1, with D k Compared with the data D completed in step 3 I Commonly used in Bayesian network G k Update of the conditional probability table, where learning G k The conditional probability table method uses maximum likelihood estimation. Maximum Likelihood Estimation (MLE) refers to using existing student test-taking samples to infer the parameter θ that is most likely to lead to that result, i.e., the θ that maximizes the likelihood function. If a student answers a question incorrectly, the error is attributed, and the process jumps to step 5; otherwise, no error attribution is performed, the next data entry is entered, and the process jumps to step 3.

[0026] Step 5: Based on data D I Knowledge point extraction subgraph G s

[0027] For data D I Extract all the preceding knowledge points contained therein, and then sort them according to G. k The structural composition subgraph G in s ;

[0028] Step 6: Based on subgraph G s Constructing Attribution Map G a

[0029] G s All leaf nodes are connected to the node "error" to form the attribution graph G. a ;

[0030] Step 7: Calculate the attribution map G a The weight W of the edge in i，j

[0031] From G k Medium sampling G s Data set D consists of all the knowledge points contained within it. aThe number of its items is related to D I The ratio is n:1, which describes the ratio from the current Bayesian network G k The data obtained from the sampling and the new student answer data DI were compared with the attribution graph G. a The weight W of the edge i，j The magnitude of the influence, where n typically ranges from [10, 30]. And for each data point, when all data points corresponding to G... s When the variable in a leaf node has a value of 1, the variable "wrong" added to that data entry has a value of 1; otherwise, it has a value of 0. This applies to dataset D. a and complete data D I Commonly used for Bayesian network attribution graph G a Learn the conditional probability table and calculate the edge weight W according to formula (5). i，j :

[0032] W i，j =P(V j =0|V i =0)×P(V i =0)

[0033] =P(V i =0, V j =0) (5)

[0034] The significance of weight is the probability of making a mistake at each stage of the knowledge point learning process. For the weight W... i，j That is, node V i and node V j The possibility of pointing to the wrong node is also present, namely node V. i Node V is not known j Not mastered or node V i Node V is not known j The probability of pointing to the wrong answer. That is, if there is an edge with a weight of 0.8 between knowledge point A and knowledge point B, it means that if knowledge point A is not mastered, the probability of answering the question incorrectly due to the lack of knowledge point B is also low.

[0035] Step 8: Obtain the attribution results

[0036] Attribution Map G a In the attribution graph G, all edges with weights less than the average weight are removed, and only edges with weights greater than the average weight are retained. a This is the final attribution result;

[0037] Step 9: Output Results

[0038] Output the attribution results obtained in step 8, and provide personalized suggestions to students based on the chain structure therein.

[0039] The present invention also proposes an error attribution system for implementing the above method, the system comprising: a user request module, a data loading module, a model training module, and an error attribution module.

[0040] The user request module is responsible for processing user-sent requests and the data contained in the request message body, such as specified dataset information.

[0041] The data loading module loads user-uploaded data into memory or loads data from the database into memory based on specified dataset information, and preprocesses the data, including filling in missing values ​​and deleting outliers.

[0042] The model training module constructs a Bayesian network based on the parameter learning process described in steps 1 to 4 of the present invention and the data loaded by the data loading module, and uses the data to learn the Bayesian network parameters to obtain model parameters that conform to the student's current cognitive state.

[0043] The error attribution module, according to the error attribution process described in steps 5 to 9 of the present invention, completes the construction of the attribution graph, weight calculation, and error cause inference and outputs the results through the Bayesian network obtained by the model training module and the students' error data.

[0044] The beneficial effects of this invention include: compared with traditional cognitive diagnostic methods, this invention has higher accuracy and stronger interpretability. Traditional cognitive diagnostic models such as DINA and FuzzyCDF analyze students' test-taking data to obtain their mastery of various knowledge points, thus transforming the cognitive diagnostic task into predicting whether students can answer the next question correctly. Compared with traditional cognitive diagnostic models such as DINA and FuzzyCDF, on the FrcSub, Math1, and Math2 datasets, the accuracy of student performance prediction is improved by 44.27%, 28.80%, 16.66%, 13.28%, 25.55%, and 34.35%, respectively. Compared with black-box models such as NeuralCDM, this invention has the characteristics of model transparency and strong interpretability. Furthermore, this invention can disclose the causal structure diagram between knowledge points that lead to errors based on students' problem-solving performance, achieving intelligent error attribution from the perspective of fine-grained cognitive diagnosis. It also enables efficient and accurate automatic intelligent error attribution in large-scale scenarios, helping students reveal the hierarchical relationship of error causes and clarify the error path. It is applicable to various error attribution scenarios. Attached Figure Description

[0045] Figure 1 This is a flowchart of the error attribution method of the present invention.

[0046] Figure 2 This is a schematic diagram of the interface of the error attribution system of the present invention.

[0047] Figure 3 This is a schematic diagram of the error attribution system of the present invention.

[0048] Figure 4 This is a complete Bayesian network diagram in an embodiment of the present invention.

[0049] Figure 5 This is an attribution graph used in an embodiment of the present invention.

[0050] Figure 6 Attribution graph G in this embodiment of the invention a This is the final attribution result. Detailed Implementation

[0051] The invention will be further described in detail below with reference to the specific embodiments and accompanying drawings. Except for the contents specifically mentioned below, the processes, conditions, and experimental methods for implementing the invention are all common knowledge and general knowledge in the art, and the invention does not have any particular limitations.

[0052] This invention proposes a Bayesian network-based error attribution method. It constructs a Bayesian network using a knowledge point structure graph and utilizes student problem-solving data to learn Bayesian network parameters and infer the reasons for errors. For each input data point, the parameters of the Bayesian network are updated. When error attribution is needed, the data point and the current Bayesian network parameters are used to infer the reasons for errors. This method can reveal the hierarchical relationships of students' error causes and clarify the error cause chain with fine granularity. In large-scale scenarios, it can achieve efficient and accurate automatic error attribution, assisting teachers in targeted lesson preparation and student tutoring, and helping students achieve personalized learning. Furthermore, the method's model is transparent, the process is interpretable, and the results are reliable, making it suitable for error attribution scenarios in intelligent education. This invention also proposes a system for implementing the aforementioned Bayesian network-based error attribution method.

[0053] This invention uses a knowledge point structure diagram, student problem-solving data, and the knowledge points contained in the problems as inputs to construct a Bayesian network. The conditional probability table of the Bayesian network is then continuously updated with input data to ensure it aligns with the student's current cognitive state. When attribution of incorrect answers is required, an attribution graph is constructed based on the knowledge points contained in the problems, and the weights on the attribution graph are calculated to output the attribution results.

[0054] The method of the present invention includes the following steps:

[0055] Step 1: Construct a Bayesian network G based on the knowledge point structure diagram. k ;

[0056] Step 2: Initialize the Bayesian network G k Conditional probability table;

[0057] Step 3: Based on the Bayesian network G k and its conditional probability table completion data D I ;

[0058] Step 4: Update the Bayesian network G k Conditional probability table;

[0059] Step 5: Based on data D I Knowledge point extraction subgraph G s ;

[0060] Step 6: Based on subgraph G s Constructing Attribution Map G a ;

[0061] Step 7: Calculate the attribution map G a The weight W of the edge in i，j ;

[0062] Step 8: Obtain the attribution results and output them.

[0063] Example

[0064] The following is a specific implementation of this method on a set of student problem-solving records containing 11 knowledge points and 70 problem-solving data, which further illustrates the present invention. The problem-solving records are taken from Math1 in the above dataset.

[0065] To implement error attribution based on Bayesian networks, follow these steps:

[0066] Step 1: Construct a Bayesian network G based on the knowledge point structure diagram. k

[0067] Using a knowledge point structure diagram constructed by educational experts based on their experience as input, a Bayesian network G is constructed. k This example includes 11 knowledge points and 14 edges. The knowledge points are "Sets", "Inequalities", "Trigonometric Functions", "Logarithms and Exponents", "Plane Vectors", "Properties of Functions", "Graphs of Functions", "Spatial Imagination", "Inductive Reasoning", "Reasoning and Proofing", and "Calculation". The complete Bayesian network is as follows: Figure 4 As shown;

[0068] Step 2: Initialize the Bayesian network G k Conditional probability table

[0069] For Bayesian network G k For nodes with zero parent nodes, such as nodes with no root knowledge points like "inequality", "set", and "plane vector", their conditional probability tables are initialized as shown in formula (1):

[0070]

[0071] Among them, V i Let Pa represent the i-th node. i This represents the set of parent nodes of the i-th node.

[0072] For Bayesian network G k For nodes with a non-zero number of parent nodes, such as nodes with prior knowledge points like "trigonometric functions", "function graphs", and "spatial imagination", their conditional probability tables are initialized as shown in formula (2):

[0073]

[0074] Among them, Pa iK Represents node V i The Kth parent node, m represents node V i The total number of parent nodes;

[0075] Step 3: Based on the Bayesian network G k and its conditional probability table completion data D I

[0076] For each piece of input data D I The data includes student ID, question number, the knowledge points covered in the question, whether the student scored on each knowledge point, and whether the student answered the question correctly. For example, a single data point might be [1, 1, null, 1, 1, null, null, 0, null, null, null, null, 0]. This data point represents student ID 1, question number 1, the student scored on the knowledge points "trigonometric functions" and "inequalities" (recorded as 1), scored no on "function properties" (recorded as 0), and null values ​​for the remaining knowledge points indicate that the question did not cover the corresponding knowledge point and the student answered the question incorrectly (recorded as 0). Since this data point may not include all knowledge points, it is used to update G. k Before the conditional probability table, G needs to be used. k and its conditional probability table for data D I Perform completion, that is, complete D. I =[1, 1, null, 1, 1, null, null, 0, null, null, null, null, null, 0] where null is missing. For the node with the f-th missing value... Its posterior probability is calculated as shown in formula (3):

[0077]

[0078] Among them, V e V represents the set of nodes that have values. miss This represents the set of nodes with missing values. (Due to the nodes...) The represented random variable follows a Bernoulli distribution, therefore according to Bernoulli sampling and The posterior probability value for data D I Complete all missing values. The distribution is shown in formula (4):

[0079]

[0080] Where Ber represents the Bernoulli distribution. Let D... I Taking the first missing data item in the middle: the score of the knowledge point "set" as an example, assuming its posterior probability P(V) is as shown in formula (3) 集合 =1|V 不等式 =1, V 三角函数 =1, V 函数性质 =0) =0.8, then V 集合 ~Ber(0.8), when the generated random number is less than or equal to 0.8, fill in the score of the missing knowledge point "set" with 1; otherwise, fill in 0. In this way, let the filled data in this example be [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0];

[0081] Step 4: Update the Bayesian network G k Conditional probability table

[0082] From Bayesian network G k Medium sampling dataset D k This makes dataset D k The number of data entries and data D I The ratio is 9:1, with D k Compared with the data D completed in step 3 I Commonly used in Bayesian network G k Update of the conditional probability table, where learning G k The conditional probability table method is maximum likelihood estimation. It then determines whether error attribution is needed based on the completed data D. I If the last item in the sequence [1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0] is 0, we know that the student did not answer the question correctly. Therefore, we need to attribute the error to the correct answer and jump to step 5. Otherwise, enter the next data and jump to step 3.

[0083] Step 5: Based on data D I Knowledge point extraction subgraph G s

[0084] For data D I The knowledge points included, their preceding knowledge points, namely D I Extract all parent nodes of the included knowledge points and sort them according to G. k The structural composition subgraph G in s The knowledge points extracted from this example are the prerequisite knowledge points of "trigonometric functions" ("sets") and the prerequisite knowledge points of "function properties" ("logarithms and exponents") and "inequalities";

[0085] Step 6: Based on subgraph G s Constructing Attribution Map G a

[0086] G s All leaf nodes are connected to the node "error" to form the attribution graph G. a ,like Figure 5 As shown;

[0087] Step 7: Calculate the attribution map G a The weight W of the edge in i，j

[0088] From G k Medium sampling G s Data set D consists of all the knowledge points contained within it. a The number of its items is related to D I The ratio is 9:1, and for each data point, when all data points correspond to G... s When the variable in a leaf node has a value of 1, the variable "wrong" added to that data entry has a value of 1; otherwise, it has a value of 0. This applies to dataset D. a and complete data D I Commonly used in Bayesian network G a Learn the conditional probability table and calculate the edge weight W according to formula (5). i，j :

[0089] W i，j =P(V j =0|V i =0)×P(V i =0)

[0090] =P(V i =0, V j =0) (5)

[0091] The significance of weights is the probability of making mistakes at each stage of the knowledge point learning process. In this example, the weights used are: "sets," "inequalities," "logarithms and exponents," "trigonometric functions," "function properties," and "mistakes." Figure 5 Taking the attribution diagram shown as an example, assume P(V) 函数性质=0)=0.6, P(V 错 =0|V 函数性质 =0) =0.9, then W 函数性质，错 =P(V 错 =0|V 函数性质 =0)×P(V 函数性质 =0) = 0.6 × 0.9 = 0.54, that is Figure 5 The weight of the edge from node "Functional Property" to node "Error" is 0.54.

[0092] Step 8: Obtain the attribution results

[0093] Attribution Map G a In the process, all edges with weights less than the average weight are removed, and only edges with weights greater than the average weight are retained, forming an array like this. Figure 6 Attribution diagram G shown a This is the final attribution result. In this example, the average weight of all edges is 0.30;

[0094] Step 9: Output Results

[0095] Output the attribution results obtained in step 8, and provide personalized suggestions to students based on the chain structure therein.

[0096] The attribution graph generated from the data used above ultimately includes the knowledge points "inequalities," "function properties," "logarithms and exponents," and "errors." "Sets" and "trigonometric functions" were removed because their weights were less than the average. The weight of the edge from "inequalities" to "function properties" in the attribution graph is 0.47, the weight of the edge from "logarithms and exponents" to "function properties" is 0.32, and the weight of the edge from "function properties" to "errors" is 0.54. Therefore, the student should strengthen their study of the knowledge point "function properties," followed by the knowledge points "inequalities" and "logarithms and exponents."

[0097] References

[0098] [1]Embretson SE, Reise S P.Item response theory[M].Psychology Press, 2013.

[0099] [2]De La Torre J.The generalized DINA model framework[J].Psychometrika, 2011, 76(2): 179-199.

[0100] [3]Wu R, Liu Q, Liu Y, et al.Cognitive modeling for predicting examineeperformance[C] / / Twenty-Fourth International Joint Conference on ArtificialIntelligence.2015, 1017-1024.

[0101] [4]Wang F, Liu Q, Chen E, et al.Neural cognitive diagnosis for intelligent education systems[C] / / Proceedings of the Thirty-Fourth AAAIConference on Artificial Intelligence.2020, 34(04): 6153-6161.

[0102] The scope of protection of this invention is not limited to the above embodiments. Any variations and advantages that can be conceived by those skilled in the art without departing from the spirit and scope of the inventive concept are included in this invention and are protected by the appended claims.

Claims

1. A method for error attribution based on Bayesian network, characterized in that, The method comprises the following steps: Step 1: Constructing Bayesian network G according to knowledge point structure diagram k ; Step 2: Initialize Bayesian network G k conditional probability tables; Step 3: Complete data D according to the Bayesian network G k and its conditional probability table I ; In step 3, for each input data D I The data includes student ID, question number, knowledge points covered in the question, whether the student scored points on each knowledge point, and whether the student answered the question correctly; data D is being used. I Update G k Before the conditional probability table, G needs to be used. k and its conditional probability table for data D I Perform completion; for the node with the f-th missing value. Its posterior probability is calculated as follows: wherein V e represents a set of nodes with values, Vm iss represents a set of nodes with missing values; nodes represent a random variable following a Bernoulli distribution, according to Bernoulli sampling and the posterior probability value of D I completes all missing values of D has a distribution as shown in the following formula: Wherein, Ber represents Bernoulli distribution; Step 4: Update the Bayesian network G k the conditional probability table of G; Step 5: According to data D I The knowledge point extraction subgraph G s ; Step 6: According to sub-diagram G s Constructing the attribution graph G a ; Step 7: Compute the attribution graph G a the weight W of the edge in G i,j ; Step 8: obtaining the attribution result and outputting the result, and giving personalized suggestions for the student according to the chain structure of the attribution result.

2. The Bayesian network-based mistake attribution method of claim 1, wherein, In step 1, a knowledge point structure diagram constructed by an education expert according to expert experience is taken as input to construct a Bayesian network G k ; wherein the nodes of the Bayesian network G k are all knowledge points contained in the knowledge point structure diagram, and the structure of the Bayesian network G k is the same as that of the knowledge point structure diagram; Step 2: Initialize the Bayesian network G k with conditional probability tables.

3. The Bayesian network-based mistake attribution method of claim 1, wherein, In step 2, for the Bayesian network G k For a node with 0 parent nodes, initialize its conditional probability table as follows: Wherein, V i represents the i-th node, Pa i represents the parent node set of the i-th node; the Bayesian network G k The node with the number of parent nodes being 0 in the Bayesian network G represents the node of the root knowledge point without prior knowledge. For Bayesian network G k For the nodes with parent number not equal to 0, initialize their conditional probability tables as follows: Pa iK represents the Kth parent node of the node V i , and m represents the total number of parent nodes of the node V i ; the number of nodes with a parent node number other than 0 in the Bayesian network G k is the node of the knowledge point with prior knowledge.

4. The Bayesian network-based mistake attribution method of claim 1, wherein, In step 4, the data set D is sampled from the Bayesian network G k k , so that the ratio of the number of data in D k to the data D I is 9:1, D k is used together with the completed data D I to update the conditional probability table of the Bayesian network G k , wherein the method for learning G k is maximum likelihood estimation, and the existing student sample results are used to inversely deduce θ capable of making the likelihood function take the maximum value; if the student makes a mistake, mistake attribution is performed, and a subgraph G I is extracted according to the knowledge points contained in the data D s , otherwise, mistake attribution is not performed, the next data is input, and the data D k is completed again according to the Bayesian network G I and the conditional probability table.​ 5. The Bayesian network-based mistake attribution method of claim 1, wherein, Step 5 for data D I The included knowledge points, all of its pre-knowledge points are extracted, and according to the structure of G k The structure of the subgraph G s ; Step 6 connects all the leaf nodes in G s To the node "wrong", constitute the attribution graph G a .

6. The Bayesian network-based mistake attribution method of claim 1, wherein, In step 7, from G k sample G s contains all the knowledge points in the data set D a , the number of which is proportional to D I n:1, and for each data, when all the variables corresponding to the leaf nodes of G s are 1, the value of the variable "error" added to the data is 1, otherwise it is 0; the data set D a and the complementary data D I are used together to learn the conditional probability table of the Bayesian network G a , and the weights W of the edges are calculated according to the following formula: i,j : W i,j = P(V j = 0 | V i = 0) x P(V i = 0) = P(V i = 0, V j = 0); The weight refers to the possibility of error in each link in the learning process of the knowledge point.

7. The Bayesian network-based mistake attribution method of claim 1, wherein, In step 8, the attribution graph G a In which all edges with weights less than the average weight are removed, and only edges with weights greater than the average weight are retained, to form an attribution graph G a is the final attribution result.

8. A problem attribution system for implementing the problem attribution method according to any one of claims 1 to 7, characterized in that, The system comprises a user request module, a data loading module, a model training module and a wrong question attribution module. The user request module is responsible for processing the request sent by the user and processing the data contained in the request message body. The data loading module loads the data uploaded by the user into the memory or loads the data into the memory from the database according to the specified data set information, and pre-processes the data. The model training module constructs a Bayesian network by using the parameter learning process and the data loaded by the data loading module, and learns the parameters of the Bayesian network by using the data, so as to obtain model parameters conforming to the current cognitive state of the student. The wrong question attribution module completes the construction of the attribution graph, the calculation of the weight and the cause and effect reasoning according to the cause and effect reasoning process, the Bayesian network obtained by the model training module and the wrong question data of the student, and outputs the result.

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