Research On Correlation Measurement Based On Copula And MI Theory And Its Application

The classical correlation coefficient can describe the monotonic dependence among variables.The emergence of Copula theory can not only effectively measure the correlation between variables,but also describe the correlation structure between variables.Mutual information measures the correlation between variables from the perspective of information theory.In this paper,the correlation measurement method based on Copula theory and MI theory is studied,and the correlation measurement method based on the correlation coefficient is compared.The difference and connection between the three correlation measurement methods are explored.Then the data of the education field are introduced to carry out an empirical analysis.The correlation between mathematics achievement and achievement of other disciplines are measured.There are several conclusions which are different from previous studies,and reasonable explanations and analysis are made,and corresponding suggestions are put forward.The main contents and research results of this paper are as follows:(1)The research status of classical correlation coefficient,Copula theory and mutual information theory is summarized,and the purpose and significance of comparing three kinds of correlation measurement methods are also expounded.(2)In the process of comparing three measurement correlation methods,we take the 5points of ideal statistics as the main line,and make a detailed comparison of three correlation measurement methods.On this basis,the differences and relations between the three methods of correlation measurement are analyzed,and the characteristics and applicable scope of all kinds of measurement methods are summarized.(3)With the introduction of the educational field data,the three correlation measurement methods studied in this paper are made an empirical analysis.Different results are obtained and analyzed accordingly.Finally,a comprehensive comparative analysis of different analytical results is made.(4)The results of empirical analysis show that there is a significant correlation between mathematics achievement and other academic achievements,and there is an obvious tail correlation,which shows that the learning of mathematics has a certain influence on the learning of other subjects.And corresponding suggestions are put forward on this influence,which will provide new ideas for the future teaching reform and the transformation of learning methods.(5)In the era of big data,the correlation measurement method based on Copula theory and mutual information theory is superior to the correlation measurement method based on classical correlation coefficients in describing the nonlinear correlation of complex variables.