Research On Relationship Among Courses By Mixed Graphical Models

A graphical model is a family of probability distributions related to a graph,which is used to describe conditional independent relationships among variables.A Bayesian network is a directed acyclic graph of a graphical model that is often used to represent causality between variables.This paper,we use three graphical models to study the mixed modeling of students' scores in higher education courses,explore the relationships among courses by three different graphical models,where those in hundred-mark system(e.g.,mathematical analysis,advanced algebra,etc.)are treated as continuous variables and those in graded system(e.g.,mathematical modeling,subject introduction,etc.)as categorical variables.Through exploratory analysis,intuitively draw the correlation between courses.The specific work is as follows:First,we analyze course relationships by Gaussian-Multinomial mixed models that is a special case based on mixed graphical models via exponential families.It is found that there are close correlations between different courses,highlighting the necessity of comprehensive analysis.Second,strongly decomposable graphical models and strongly decomposable forest models are used to explore the interrelationships among the scores of course.Strongly decomposable graphical model can describe more intricate course relationships.Third,according to the order of semester,we determine the sequence of some variables without limiting that continuous variables cannot be used as the parents of categorical variables.We propose to use linear regression and ordered multinomial probit regression to learn a Bayesian network structure,inferring the mutual influence between courses can be seen intuitively.In summary,starting from the course scores,three graphical models are used to analyze the relationship between courses,to clarify the relationship between courses,and to highlight the important and difficult points of the courses in the teaching process and to optimize the teaching design.