A teaching quality prediction method integrating volatility information combination model

Abstract

The present invention discloses a teaching quality prediction method integrating a volatility information combination model, through data collection: collecting data corresponding to secondary indicators affecting teaching factors; data cleaning: cleaning the data corresponding to the collected secondary indicators according to preset data cleaning rules; feature data reconstruction: determining the feature data model order and reconstructing the feature sequence of the features of the collected data corresponding to the secondary indicators; fusion volatility information Ridge prediction: integrating the volatility information in the reconstructed feature data into the Ridge regression algorithm; prediction results of each feature: obtaining the prediction results of each feature in the data corresponding to the secondary indicators according to the Ridge regression algorithm integrating volatility information; teaching quality prediction: predicting the teaching quality according to the prediction results of each feature in the data corresponding to the secondary indicators. The present invention improves the accuracy and efficiency of teaching quality prediction.

Description

Technical Field

[0001] The invention relates to the field of artificial intelligence technology, and in particular discloses a teaching quality prediction method integrating a volatility information combination model. Background Art

[0002] Education and teaching evaluation is the baton for the development of higher education and plays a vital role in ensuring the quality of talent training. In the era of intelligent technology, the evaluation of higher education teaching quality can only better meet the requirements of the current new development stage if it combines reality, conforms to the requirements of the development of the times, innovates evaluation tools, and makes full use of modern information technologies such as the Internet, big data, and artificial intelligence to improve the evaluation mechanism.

[0003] At present, the research on teaching quality prediction has made some progress. Xu Kangtai et al. "Application of analytic hierarchy process and grey correlation method in evaluation of teachers' teaching quality" uses grey correlation analysis and analytic hierarchy process to analyze teaching quality. Its disadvantages are high proportion of subjective information judgment, many uncertain factors, linear relationship between required indicators and results, and easy distortion of results. KAYMAZ et al. "Sustainable development goals assessment of Erzurum province with SWOT-AHP analysis" proposed an adaptive feedforward machine learning network algorithm with the advantages of strong robustness, high fault tolerance, and ability to effectively handle any complex nonlinear problems. The descent learning method used by the neural network is local search, which has the disadvantages of weak generalization ability, poor prediction accuracy, and slow convergence speed. Fang Qianru et al. "Construction of ideological and political teaching quality evaluation system for higher vocational colleges based on AHP-FCE" proposed the use of analytic hierarchy process (AHP) and fuzzy comprehensive evaluation (FCE) theory to construct an evaluation model, calculate the weight and score of comprehensive indicators. This evaluation system makes up for the subjective defects of qualitative evaluation, transforms qualitative into quantitative analysis, and provides a reference for the effective evaluation of course teaching quality. However, there may be limitations in terms of operational complexity, data dependency, and the need for regular updates to adapt to changes in the educational environment. Cao Shuxia et al., "Research on Classroom Teaching Quality Evaluation System Based on AHP - Taking Probability Theory and Mathematical Statistics Courses as an Example", provides a new and scientific teaching quality evaluation method for probability theory and mathematical statistics courses by constructing a classroom teaching quality evaluation system based on AHP, which helps to improve teaching effectiveness and students' learning experience. However, there may be a lack of extensive empirical research to verify its applicability and effectiveness in different teaching environments and different disciplines. Summary of the invention

[0004] The present invention provides a teaching quality prediction method integrating a volatility information combination model, aiming to solve at least one defect in the current teaching quality prediction method.

[0005] The present invention relates to a teaching quality prediction method integrating a volatility information combination model, comprising the following steps:

[0006] Data collection: According to the determination of the indicators affecting teaching factors in the teaching quality evaluation indicator confirmation module, collect the data corresponding to the secondary indicators affecting teaching factors, and then form a 15-dimensional feature as the input of the combined model;

[0007] Data cleaning: Clean the collected data corresponding to the secondary indicators of the factors affecting teaching according to the preset data cleaning rules;

[0008] Feature data reconstruction: The feature data model is determined and the feature sequence is reconstructed for the features of the collected data corresponding to the secondary indicators of the factors affecting teaching;

[0009] Ridge prediction with integrated volatility information: The volatility information in the reconstructed feature data is integrated into the Ridge regression algorithm, that is, the volatility information is included in the Ridge regression algorithm as part of the penalty term to adjust the degree of shrinkage of the coefficients in the combined model.

[0010] Prediction results of each feature: Based on the Ridge regression algorithm that integrates volatility information, the prediction results of each feature in the data corresponding to the secondary indicators that affect teaching factors are obtained;

[0011] Teaching quality prediction: The teaching quality is predicted based on the prediction results of each feature in the data corresponding to the secondary indicators of the factors affecting teaching.

[0012] Furthermore, the data cleaning step includes:

[0013] QPSO-SVM prediction: Construct a QPSO-SVM model and introduce quantum behavior into the QPSO-SVM algorithm.

[0014] Furthermore, in the data collection step, the formula corresponding to the teaching quality sample set D is:

[0015]

[0016] Among them, D is the teaching quality sample set, is a 15-dimensional teaching quality feature vector, is the number of samples;

[0017] The mathematical formula corresponding to teaching quality is:

[0018]

[0019] For teaching quality, For sample The corresponding target value, is the number of samples.

[0020] Furthermore, in the feature data reconstruction step, it is assumed that a multi-input single-output regression model has N samples, one dependent variable, and g-1 independent variables. Ridge regression is used to perform leave-one-out test from low order to high order, and the expansion order is determined based on the minimum RMSE standard. The judgment formula is:

[0021]

[0022] in, is the mean square error of Ridge(n), is the mean square error of Ridge(n+1), ridge(n) is the model after order determination;

[0023] Use the judgment formula to determine the order of each feature of the data corresponding to the secondary indicators of the factors affecting teaching. Finally, the order of each feature model will be obtained. The corresponding mathematical formula is:

[0024]

[0025] in, For the The order of a characteristic model is determined; is the number of features; A collection that determines the order of the feature model.

[0026] Furthermore, in the feature data reconstruction step, for the feature data sequence According to the determined ridge embedding dimension w, the input sample is converted into a w-column matrix, and the output sample is a 1-column matrix. The input and output matrices are merged, with the first w columns as features and the last column as the target. The sequence reconstruction matrix is ​​obtained as follows:

[0027]

[0028] in, is the matrix reconstructed from features of order w; w is the order of the model, and N is the number of samples; is the jth value corresponding to the feature;

[0029] Combined with the model order determination The set of features is obtained by reconstructing the matrix of each feature. The mathematical formula is expressed as:

[0030]

[0031] in, A set of L feature reconstruction matrices; is the jth feature and the order is The reconstruction matrix.

[0032] Furthermore, the Ridge prediction step of integrating volatility information includes:

[0033] Step S41, estimating the volatility of each feature of the matrix;

[0034] Step S42, constructing a penalty term of the Ridge regression algorithm;

[0035] Step S43: Determine the problem to be optimized and find the coefficients that minimize the objective function ;

[0036] Step S44: Solve the objective function and use the coordinate descent method to minimize the objective function to obtain the adjusted coefficients. , and then build a Ridge model that integrates volatility information and predicts future values ;

[0037] Step S45: for each feature reconstructed matrix, loop steps S41 to S44 to obtain multiple Ridge models, and obtain the prediction result of each Ridge model.

[0038] Further, in step S42, the volatility It is added to the penalty term of the Ridge algorithm in the form of a reciprocal, as follows:

[0039]

[0040] in, is the regularization parameter, is the number of features, For volatility, To minimize the objective function The coefficient in front of each feature.

[0041] Furthermore, in step S43, the objective function includes a loss function and a penalty term, and the form is as follows:

[0042]

[0043] in, is the observed value; is the eigenvector, is the coefficient vector, is the regularization parameter, is the number of features, is the sample size.

[0044] Furthermore, in step S45, the form of the multiple Ridge models is as follows:

[0045]

[0046] in, is a collection of Ridge models that incorporate volatility information; To reconstruct the matrix The Ridge model constructed by integrating volatility information.

[0047] Furthermore, in step S45, the future prediction values ​​obtained by each Ridge model through prediction are in the following form:

[0048]

[0049] in, A collection of prediction results for each volatility-weighted Ridge model; For Model The predicted result vector.

[0050] The beneficial effects achieved by the present invention are:

[0051] The present invention provides a teaching quality prediction method integrating a volatility information combination model, through data collection: according to the determination of the indicators affecting the teaching factors in the teaching quality evaluation index confirmation module, the data corresponding to the secondary indicators affecting the teaching factors are collected, and then a 15-dimensional feature is formed as the input of the combination model; data cleaning: the collected data corresponding to the secondary indicators affecting the teaching factors are cleaned according to the preset data cleaning rules; feature data reconstruction: the features of the collected data corresponding to the secondary indicators affecting the teaching factors are subjected to feature data model order determination and feature sequence reconstruction; fusion volatility information Ridge prediction: the volatility information in the reconstructed feature data is integrated into the Ridge regression algorithm, that is, the volatility information is included in the Ridge regression algorithm as part of the penalty term to adjust the degree of contraction of the coefficient in the combination model; the prediction results of each feature: according to the Ridge regression algorithm integrating volatility information, the prediction results of each feature in the data corresponding to the secondary indicators affecting the teaching factors are obtained; teaching quality prediction: the teaching quality is predicted according to the prediction results of each feature in the data corresponding to the secondary indicators affecting the teaching factors. The teaching quality prediction method integrating a volatility information combination model provided by the present invention has the following beneficial effects:

[0052] 1. Improve the accuracy and efficiency of teaching quality prediction: By fusing volatility information and optimizing the support vector machine (SVM) model parameters using the quantum particle swarm optimization (QPSO) algorithm, this method can predict teaching quality more accurately.

[0053] 2. Comprehensive consideration of teaching quality factors: This method not only considers the key factors affecting teaching quality, such as teaching content, teaching attitude, teaching methods and teaching effects, but also integrates volatility information to make the prediction model more comprehensive.

[0054] 3. Enhance the robustness of the model: By incorporating volatility as part of the penalty term into the Ridge regression algorithm, the model can dynamically adjust the degree of coefficient shrinkage according to the volatility of the data, thereby improving the robustness of the model in the face of noise and outliers.

[0055] 4. Provide a reliable teaching quality prediction solution: The combined use of Ridge regression and QPSO-SVM models provides a more comprehensive and reliable teaching quality prediction solution, supporting teaching managers to make more accurate and timely scheduling decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of an embodiment of a teaching quality prediction method integrating a volatility information combination model according to the present invention;

[0057] Figure 2 A schematic diagram for determining the direction of the teaching quality indication in the present invention;

[0058] Figure 3 It is a schematic diagram of the process of the QPSO-SVM prediction step in the present invention;

[0059] Figure 4 It is a flow chart of the Ridge prediction step of integrating volatility information in the present invention;

[0060] Figure 5 It is a flowchart of the step of estimating the volatility of each feature of the matrix in the present invention. DETAILED DESCRIPTION

[0061] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0062] like Figure 1 and Figure 2 As shown, the first embodiment of the present invention proposes a teaching quality prediction method integrating a volatility information combination model, comprising the following steps:

[0063] Step S10, data collection: according to the determination of the indicators affecting teaching factors in the teaching quality evaluation indicator confirmation module, collect the data corresponding to the secondary indicators affecting teaching factors, and then form a 15-dimensional feature as the input of the combined model.

[0064] The confirmation of teaching quality evaluation indicators needs to be combined with the evaluation focus of two types of subjects, namely teachers and students. This embodiment sorts out and selects teaching quality evaluation indicators from four aspects: teaching attitude, teaching content, teaching methods, and teaching effect. Figure 2 shown.

[0065] (1) Teaching attitude

[0066] Teaching attitude mainly examines whether teachers have good professional qualities and teaching attitudes, whether they can carry out teaching work with a professional, responsible and enthusiastic attitude, so as to ensure the quality of teaching. The determination of its indicators mainly has four dimensions, as shown in Table 1. First, the appearance is generous and the spirit is full. The focus is on the external image and professional image of the teacher, and whether they can face the teaching work with a positive and full state, setting a good example for students. Second, there is no phenomenon of lateness, early departure and random skipping of classes. It is mainly to examine the teacher's time concept and sense of responsibility, whether they can abide by the teaching discipline, and ensure the punctuality and continuity of teaching activities. Third, teaching and tutoring are patient and positive. Examine the teacher's teaching attitude and care for students, whether they can patiently answer students' questions, actively tutor students, and help them understand and master knowledge. Fourth, teaching is serious and rigorous. In order to examine the degree of attention paid by teachers to teaching content and the scientific nature of teaching methods, whether they can prepare lessons carefully, teach rigorously, and ensure the quality of teaching.

[0067] Table 1 Determination of secondary indicators of teaching attitude

[0068]

[0069] (2) Teaching content

[0070] The teaching content is mainly to examine whether teachers have good teaching design ability, teaching content organization ability and teaching skills, and whether they can improve teaching quality through these abilities and help students learn and grow better. There are three main dimensions for determining its indicators, as shown in Table 2. First, clear teaching objectives and purposes. In order to examine whether teachers can clearly define the purpose and intention of teaching, whether they can set clear teaching objectives according to the syllabus and student needs, and whether they can design teaching around these objectives. Second, the content is substantial and scientific, highlighting the key points and explaining the difficulties. In order to examine the degree of mastery of the teaching content by teachers, whether they can organize the teaching content scientifically and reasonably, highlight the teaching key points, clearly explain the teaching difficulties, and ensure that students can understand and master the key knowledge points. Third, the lectures are clear, logical and innovative. In order to examine the teaching skills and teaching methods of teachers, whether they can clearly and logically express the teaching content, and whether they can use innovative teaching methods to stimulate students' interest in learning and improve teaching effectiveness.

[0071] Table 2 Determination of secondary indicators of teaching content

[0072]

[0073] (3) Teaching methods

[0074] Teaching methods are mainly to examine whether teachers can use modern teaching concepts and methods, conduct personalized teaching according to students' actual conditions, stimulate students' learning interest and innovation ability, and improve teaching quality and effect. There are four main dimensions for determining its indicators, as shown in Table 3. First, the rational use of rich teaching resources and means. Examine whether teachers can make full use of various teaching resources and teaching tools, such as multimedia, network resources, etc., and whether they can flexibly use different teaching methods and technologies to improve teaching effects. Second, heuristic teaching and active classroom atmosphere. Examine whether teachers can use heuristic teaching methods to stimulate students' thinking and participation, and whether they can create a positive and active classroom atmosphere to encourage students to actively learn and communicate. Third, teach students in accordance with their aptitude. Examine whether teachers can adopt personalized teaching strategies according to students' different characteristics and needs to help each student get learning opportunities and guidance suitable for themselves. Fourth, encourage innovation and focus on cultivating innovation ability. Examine whether teachers can encourage students to think and practice innovatively, and whether they focus on cultivating students' innovation ability to lay a foundation for students' all-round development and lifelong learning.

[0075] Table 3 Determination of secondary indicators of teaching methods

[0076]

[0077] (4) Teaching effectiveness

[0078] The purpose of teaching effectiveness is to examine whether teachers' teaching can promote students' knowledge mastery, ability improvement and interest cultivation, and whether teachers can reflect and adjust teaching according to students' learning effects to achieve teaching goals and improve teaching quality. There are four main dimensions for determining its indicators, as shown in Table 4. First, students understand and master the main content. This examines whether students can understand and master the core content and key knowledge points of the course, reflecting the effectiveness of teachers' teaching and the basic effectiveness of students' learning. Second, self-study ability and learning interest are improved. This examines whether students have improved their ability to learn independently under the guidance of teachers, and whether they have cultivated their interest and enthusiasm in learning content, which is related to students' lifelong learning ability. Third, attach importance to students' learning effect feedback. This examines whether teachers pay attention to students' learning feedback and whether they can adjust teaching strategies and methods according to students' feedback to better meet students' learning needs. Fourth, students' ability to analyze and solve problems is improved. This examines whether students have improved their ability to analyze and solve problems under the guidance of teachers. This is an important indicator for measuring students' comprehensive application of knowledge, critical thinking and innovative thinking.

[0079] Table 4 Determination of secondary indicators of teaching effectiveness

[0080]

[0081] Step S20, data cleaning: Clean the collected data corresponding to the secondary indicators of the factors affecting teaching according to the preset data cleaning rules.

[0082] Due to the complexity and diversity of the acquired data, it is not possible to fully meet the modeling conditions, so the acquired data needs to be cleaned. The data cleaning rules are as follows:

[0083] ①Fill or discard the obtained empty values.

[0084] ② De-duplicate the obtained duplicate data.

[0085] ③Clean the data with incorrect range.

[0086] ④ Carry out necessary verification on data that does not conform to the norm to ensure the reliability of the data.

[0087] Step S30, feature data reconstruction: feature data model order determination and feature sequence reconstruction are performed on the features of the collected data corresponding to the secondary indicators of the influencing teaching factors.

[0088] The goal of this embodiment is to predict the future teaching quality using SVM optimized by the vector weighted average algorithm (INFO). At this time, it is necessary to know the future prediction value corresponding to each feature, and the future value of each feature will be predicted by volatility-weighted Ridge regression. Therefore, each feature data needs to be reconstructed, which is specifically divided into two parts: one is the order determination of the feature data model; the other is the reconstruction of the feature sequence.

[0089] Step S40, integrating volatility information into Ridge prediction: integrating the volatility information in the reconstructed feature data into the Ridge regression algorithm, that is, incorporating the volatility information into the Ridge regression algorithm as part of the penalty term to adjust the degree of shrinkage of the coefficients in the combined model.

[0090] Based on the Ridge method, volatility information is integrated into the Ridge method, that is, volatility is used as a component of the penalty term to adjust the degree of shrinkage of the coefficients in the model. The principle is that when the data volatility is high, the penalty for the coefficient should be stricter, while when the volatility is low, it can be relatively loose. This can ensure that the model is more robust in the face of data fluctuations, while maintaining sensitivity to the data when volatility is low.

[0091] Step S50, prediction results of each feature: According to the Ridge regression algorithm integrating volatility information, the prediction results of each feature in the data corresponding to the secondary indicators affecting the teaching factors are obtained.

[0092] Step S60, prediction of teaching quality: predicting the teaching quality according to the prediction results of each feature in the data corresponding to the secondary indicators of the factors affecting the teaching.

[0093] Further, see Figure 1 and Figure 3 The teaching quality prediction method of the integrated volatility information combination model provided in this embodiment further includes after step S20:

[0094] Step S70, QPSO-SVM prediction: construct a QPSO-SVM model and introduce quantum behavior into the QPSO-SVM algorithm.

[0095] The QPSO-SVM algorithm is a hybrid intelligent algorithm that integrates quantum particle swarm optimization (QPSO) and support vector machine (SVM). The algorithm is mainly used for feature selection problems. In the classic PSO-SVM algorithm, the particle convergence speed is limited and implemented in the form of orbits, that is, the search space is limited, and it cannot be guaranteed that the entire space is searched, and the global optimal solution may not be obtained. The QPSO-SVM algorithm can search in the entire feasible solution space, which can find the global optimal solution faster and easier, and the form of the evolution equation is simpler, with fewer parameters and easier to control. This is because the QPSO algorithm introduces quantum behavior on the basis of PSO, so that the position and speed of particles in the search space are determined by the probability density function of the wave function, which helps the algorithm to jump out of the local optimal solution and improve the global search capability.

[0096] Preferably, see Figures 1 to 5 The teaching quality prediction method of the integrated volatility information combination model provided in this embodiment, step S70 includes:

[0097] Step S71, initialize the particle swarm. Randomly initialize the particle swarm position , where G is the number of particles and X(t) is the set of particle positions at time t.

[0098] Step S72: Establish an SVM model and calculate the fitness. The scikit-learn library is called to implement SVM modeling, and the fitness function is used. To judge the performance of the SVM model, the RMSE of the cross-validation method is selected as the fitness function, and the calculation formula is:

[0099] (1)

[0100] In formula (1), is the true value, is the predicted value, is the number of prediction samples.

[0101] Step S73, update the particle position, the particle position update formula is as follows:

[0102] (2)

[0103] In formula (2), It is a particle In time new location; It is a particle The individual optimal position (pbest); is the global optimal position; is the contraction-expansion coefficient; is a random number in the range [0,1].

[0104] Step S74: Calculate the learning tendency point (LIP). The calculation formula is:

[0105] (3)

[0106] In formula (3), is the individual optimal position of the particle in the dth dimension; is the dth dimension of the global optimal position; and is a random number in the range [0,1], and .

[0107] Step S75, update the individual optimal position (pbest). If the fitness value of the current particle is equal to its individual optimal value, update pbset. The judgment formula is:

[0108] (4)

[0109] In formula (4), It is Particles in time The fitness value of the corresponding position, It is The individual optimal fitness value of each particle is It is The individual optimal position of each particle, It is Particles in time location.

[0110] Step S76: Update the global optimal position (gbest). The formula for updating the global optimal position is:

[0111] (5)

[0112] In formula (5), gbest is the global optimal position, is the individual optimal fitness value of the i-th particle.

[0113] Step S77: Check the convergence condition. If the maximum number of iterations MAX_ITER is reached or the SVM model converges, the algorithm ends. Otherwise, go to step S72.

[0114] Furthermore, in the teaching quality prediction method integrating the volatility information combination model proposed in this embodiment, in step S10, the formula corresponding to the teaching quality sample set D is:

[0115] (6)

[0116] In formula (6), D is the teaching quality sample set, is a 15-dimensional teaching quality feature vector, is the number of samples.

[0117] The mathematical formula corresponding to teaching quality is:

[0118] (7)

[0119] In formula (7), For teaching quality, For sample The corresponding target value, is the number of samples.

[0120] Preferably, see Figures 1 to 5 In the teaching quality prediction method of integrating the volatility information combination model proposed in this embodiment, in step S30, each feature data needs to be reconstructed, which is specifically divided into two parts: one is the order determination of the feature data model; the other is the reconstruction of the feature sequence.

[0121] (1) Determining the order of the feature data model

[0122] The order of the model is called the embedding dimension. Generally, there are two methods for selecting it. One is to select it based on experience, and the other is to set other parameters of the model first, and then optimize the lag order according to certain standards. The first method relies too much on the level and experience of the researcher and cannot objectively select the best lag stage. The second method ignores an important issue: the influence of the lag order and other parameters on the quality of the model is mutual. If other parameters are set artificially to select the lag order, and then the lag order value is used to optimize the parameters, it is very likely that only the parameters under the lag order are optimal, not the global optimal. This embodiment optimizes the model order together with the Ridge model parameters. The specific operation is as follows:

[0123] Assume that a multi-input single-output regression model has N samples, one dependent variable, and g-1 independent variables. Ridge regression is used to perform leave-one-out test from low order to high order, and the expansion order is determined based on the minimum RMSE standard. The judgment formula is:

[0124] (8)

[0125] In formula (8), is the mean square error of Ridge(n), is the mean square error of Ridge(n+1), and ridge(n) is the model after order determination.

[0126] Use the judgment formula to determine the order of each characteristic data corresponding to the secondary indicators of the collected teaching factors, and finally get the order of each characteristic model. The corresponding mathematical formula is:

[0127] (9)

[0128] In formula (9), For the The order of a characteristic model is determined; is the number of features; A collection that determines the order of the feature model.

[0129] (2) Feature sequence reconstruction

[0130] The current value of each feature is significantly affected by the previous values. Assuming that the order of a feature is w, this means that the previous w values ​​are used as the input of the ridge to predict the current value. According to the determined ridge embedding dimension w, the input sample is converted into a w-column matrix, and the output sample is a 1-column matrix. The input and output matrices are merged, with the first w columns as features and the last column as the target. The sequence reconstruction matrix is ​​obtained as follows:

[0131] (10)

[0132] In formula (10), is the matrix reconstructed from features of order w; w is the order of the model, and N is the number of samples; is the jth value corresponding to the feature.

[0133] Similarly, according to the above method, combined with the model order determination to obtain The set of features is obtained by reconstructing the matrix of each feature. The mathematical formula is expressed as:

[0134] (11)

[0135] In formula (11), A set of L feature reconstruction matrices; is the jth feature and the order is The reconstruction matrix.

[0136] Further, see Figures 1 to 5 The teaching quality prediction method of the integrated volatility information combination model proposed in this embodiment, step S40 includes:

[0137] Step S41: Estimating the volatility of each feature of the matrix.

[0138] The GARCH (1, 1) model is used to estimate the volatility of each independent variable in the matrix.

[0139] Step S42: construct a penalty term for the Ridge regression algorithm.

[0140] The volatility It is added to the penalty term of the Ridge algorithm in the form of a reciprocal, as follows:

[0141] (12)

[0142] In formula (12), is the regularization parameter, is the number of features, For volatility, To minimize the objective function The coefficient in front of each feature.

[0143] Step S43: Determine the problem to be optimized and find the coefficients that minimize the objective function .

[0144] The objective function contains the loss function and the penalty term, and is in the following form:

[0145] (13)

[0146] In formula (13), is the observed value; is the eigenvector, is the coefficient vector, is the regularization parameter, is the number of features, is the sample size.

[0147] Step S44: Solve the objective function and use the coordinate descent method to minimize the objective function to obtain the adjusted coefficients. , and then build a Ridge model that integrates volatility information and predicts future values .

[0148] Use the coordinate descent method to solve the function of step S43 to obtain the adjusted coefficients .

[0149] Step S45: for each feature reconstructed matrix, loop steps S41 to S44 to obtain multiple Ridge models, and obtain the prediction result of each Ridge model.

[0150] The form of multiple Ridge models is as follows:

[0151] (14)

[0152] In formula (14), is a collection of Ridge models that incorporate volatility information; To reconstruct the matrix The Ridge model constructed by integrating volatility information.

[0153] The future prediction values ​​obtained by each Ridge model are as follows:

[0154] (15)

[0155] In formula (15), A collection of prediction results for each volatility-weighted Ridge model; For Model The predicted result vector.

[0156] Preferably, see Figure 4 The teaching quality prediction method of the integrated volatility information combination model proposed in this embodiment, step S41 includes:

[0157] Step S411: Model setting. Volatility The calculation formula is as follows:

[0158] (16)

[0159] (17)

[0160] (18)

[0161] In formulas (16) to (18), is a constant term, representing the base level of volatility; and are model parameters that measure past volatility and the impact of past volatility on current volatility, respectively; is the past error term; is the conditional variance, which represents the volatility at time t; is the mean; is the observed value of the time series at time t; are independent and identically distributed random error terms, usually assumed to follow a standard normal distribution.

[0162] Step S412: Parameter estimation. This embodiment uses the gradient descent method to estimate , and .

[0163] Step S413: Volatility prediction. Use the parameters obtained in step 2 to perform prediction in the following formula. The corresponding formula is:

[0164] (19)

[0165] In formula (19), is volatility, is a constant term, representing the base level of volatility; and are model parameters that measure past volatility and the impact of past volatility on current volatility, respectively; is the past error term; It's in time conditional variance.

[0166] Step S414, looping step S411-step S413, obtaining the volatility corresponding to each independent variable in the matrix.

[0167] Compared with the prior art, the teaching quality prediction method of the combined model integrating volatility information provided in the present embodiment includes the following steps: data collection: according to the determination of the indicators affecting the teaching factors in the teaching quality evaluation indicator confirmation module, data corresponding to the secondary indicators affecting the teaching factors are collected, and then a 15-dimensional feature is formed as the input of the combined model; data cleaning: the collected data corresponding to the secondary indicators affecting the teaching factors are cleaned according to the preset data cleaning rules; feature data reconstruction: the feature data model is determined and the feature sequence is reconstructed for the features of the collected data corresponding to the secondary indicators affecting the teaching factors; Ridge prediction integrating volatility information: the volatility information in the reconstructed feature data is integrated into the Ridge regression algorithm, that is, the volatility information is included in the Ridge regression algorithm as part of the penalty term to adjust the degree of contraction of the coefficients in the combined model; prediction results of each feature: the prediction results of each feature in the data corresponding to the secondary indicators affecting the teaching factors are obtained according to the Ridge regression algorithm integrating volatility information; teaching quality prediction: the teaching quality is predicted according to the prediction results of each feature in the data corresponding to the secondary indicators affecting the teaching factors. The beneficial effects achieved by the teaching quality prediction method integrating the volatility information combination model provided in this embodiment are as follows:

[0168] 1. Improve the accuracy and efficiency of teaching quality prediction: By fusing volatility information and optimizing the support vector machine (SVM) model parameters using the quantum particle swarm optimization (QPSO) algorithm, this method can predict teaching quality more accurately.

[0169] 2. Comprehensive consideration of teaching quality factors: This method not only considers the key factors affecting teaching quality, such as teaching content, teaching attitude, teaching methods and teaching effects, but also integrates volatility information to make the prediction model more comprehensive.

[0170] 3. Enhance the robustness of the model: By incorporating volatility as part of the penalty term into the Ridge regression algorithm, the model can dynamically adjust the degree of coefficient shrinkage according to the volatility of the data, thereby improving the robustness of the model in the face of noise and outliers.

[0171] 4. Provide a reliable teaching quality prediction solution: The combined use of Ridge regression and QPSO-SVM model provides a more comprehensive and reliable teaching quality prediction solution, supporting teaching managers to make more accurate and timely scheduling decisions.

[0172] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A teaching quality prediction method integrating a volatility information combination model, characterized in that: The following steps are involved: Data collection: According to the determination of the indicators affecting teaching factors in the teaching quality evaluation indicator confirmation module, collect the data corresponding to the secondary indicators affecting teaching factors, and then form a 15-dimensional feature as the input of the combined model; Data cleaning: Clean the collected data corresponding to the secondary indicators of the factors affecting teaching according to the preset data cleaning rules; Feature data reconstruction: The feature data model is determined and the feature sequence is reconstructed for the features of the collected data corresponding to the secondary indicators of the factors affecting teaching; include: Assume that a multi-input single-output regression model has N samples, one dependent variable, and g-1 independent variables. Ridge regression is used to perform leave-one-out test from low order to high order, and the expansion order is determined based on the minimum RMSE standard. The judgment formula is: in, is the mean square error of Ridge(n), is the mean square error of Ridge(n+1), ridge(n) is the model after order determination; Use the judgment formula to determine the order of each characteristic data corresponding to the secondary indicators of the collected teaching factors, and finally get the order of each characteristic model. The corresponding mathematical formula is: in, For the The order of a characteristic model is determined; is the number of features; A set of order determinations for feature models; For feature data series According to the determined ridge embedding dimension w, the input sample is converted into a w-column matrix, and the output sample is a 1-column matrix. The input and output matrices are merged, with the first w columns as features and the last column as the target. The sequence reconstruction matrix is ​​obtained as follows: in, is the matrix reconstructed from features of order w; w is the order of the model, and N is the number of samples; is the jth value corresponding to the feature; Combined with the model order determination The set of features is obtained by reconstructing the matrix of each feature. The mathematical formula is expressed as: in, A set of L feature reconstruction matrices; is the jth feature and the order is The reconstruction matrix of Ridge prediction with integrated volatility information: The volatility information in the reconstructed feature data is integrated into the Ridge regression algorithm, that is, the volatility information is included in the Ridge regression algorithm as part of the penalty term to adjust the degree of shrinkage of the coefficients in the combined model. include: Step S41, estimating the volatility of each feature of the matrix; Step S42, constructing a penalty term of the Ridge regression algorithm; Step S43: Determine the problem to be optimized and find the coefficients that minimize the objective function ; Step S44: Solve the objective function and use the coordinate descent method to minimize the objective function to obtain the adjusted coefficients. , and then build a Ridge model that integrates volatility information and predicts future values ; Step S45: for each feature reconstructed matrix, loop through steps S41 to S44 to obtain multiple Ridge models, and obtain the prediction results of each Ridge model. Prediction results of each feature: Based on the Ridge regression algorithm that integrates volatility information, the prediction results of each feature in the data corresponding to the secondary indicators that affect teaching factors are obtained; Teaching quality prediction: The teaching quality is predicted based on the prediction results of each feature in the data corresponding to the secondary indicators of the factors affecting teaching.

2. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 1 is characterized in that: The data cleaning step also includes: QPSO-SVM prediction: Construct a QPSO-SVM model and introduce quantum behavior into the QPSO-SVM algorithm.

3. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 1 is characterized in that: In the data collection step, the formula corresponding to the teaching quality sample set D is: Among them, D is the teaching quality sample set, is a 15-dimensional teaching quality feature vector, is the number of samples; The mathematical formula corresponding to teaching quality is: For teaching quality, For sample The corresponding target value, is the number of samples.

4. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 1 is characterized in that: In step S42, the volatility It is added to the penalty term of the Ridge algorithm in the form of a reciprocal, as follows: in, is the regularization parameter, is the number of features, For volatility, To minimize the objective function The coefficient in front of each feature.

5. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 4 is characterized in that: In step S43, the objective function includes a loss function and a penalty term, and is in the following form: in, is the observed value; is the eigenvector, is the coefficient vector, is the regularization parameter, is the number of features, is the sample size.

6. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 5 is characterized in that: In step S45, the form of the multiple Ridge models is as follows: in, is a collection of Ridge models that incorporate volatility information; To reconstruct the matrix The Ridge model constructed by integrating volatility information.

7. The teaching quality prediction method integrating the volatility information combination model as claimed in claim 6 is characterized in that: In step S45, the future prediction values ​​obtained by each Ridge model through prediction are in the following form: in, A collection of prediction results for each volatility-weighted Ridge model; For Model The predicted result vector.

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