Research And Application Of Markov Boundary Discovery Based On Regularized Linear Models

Observing the data to find the causal relationship between variables,explaining how events occur and predicting their future development trends,have been studied and applied in almost all disciplines.For example,the fields of medicine,biology,economics,physics,and social sciences all use causality as the basis for the explanation,prediction,and decision-making.In the field of information science,the Markov blanket(boundary)in Bayesian networks can be used to represent causality in the real world.In recent years,some scholars have used the discovery of Markov boundary based on regularized linear models to study the causal correlation between events from observation data,and theoretically revealed the relationship between feature variables based on regularized linear models and Markov boundary.To deeply understand the discovery performance of Markov boundary of the regularized linear model and the influence of the permutation test on the discovery performance,this dissertation adopts the method of combining the regularized linear models with the permutation test to carry out relevant research.The specific content includes the following four aspects:1.Dissected the discovery process of Markov boundary in the existing modified ridge regression model(MRRLM-P)and its inapplicability to the data sets with collinear variables,studied the relationship between variable collinearity and covariance singularity and proposed a new variant ridge regularized linear models(NVRRPLM-P).2.Continue to focus on the deficiency of MRRLM-P,combine three kinds of classical regularized linear models(ridge regression model,LASSO model,and elastic network model)with the permutation test,and investigate their discovery performance of Markov boundary on the low-dimensional data sets in an empirical way and compare it with MRRLM-P.3.Based on reviewing the hypothesis test of the multiple regression model,three different implementation methods of the permutation test are discussed and their manifestations and application effects in the regularized linear model are analyzed.Among them,two implementation methods are used for the first time to discover Markov boundary for the regularized linear model,which extends the application scope of the permutation test.4.With a specific application example of soil near-infrared spectroscopy,the spectral matrix of soil organic matter and ergosterol was "dimensionless" by Markov blanket(boundary)theory,and the correction model was established by LS-SVM and LASSO-P.Conclusion:the new variable ridge regularized linear models can well solve the problem that MRRLM-P does not apply to the data sets with collinear variables.On the low-dimensional data sets,there is a classical regularized linear model with the discovery performance of Markov boundary similar to MRRLM-P.The two new implementation methods of the permutation test are slightly inferior to the previous ones.Markov blanket(boundary)theory can effectively perform "dimensionality reduction" operation on spectral information matrix,and both correction models can well reflect the dependence of detected objects on spectral information(correlation coefficient is greater than 0.90).