Model Selection Of Graphical Model Based On Resampling Method With Missing Data

Graphical model is a statistical model associated with graphs that clearly reflects the conditional dependencies between variables and is widely used in various fields such as machine learning,psychology,biology and medicine.Graphical modelselection problem is a very important and challenging problem,in these application problems.For high-dimensional data,the popular method is penalizing the likelihood,but the method relies on the selection of penalty parameters.Especially for high-dimensional data with missing data,graphical model selection problem is more difficult.For example,using the EM algorithm with penalty the likelihood,it is often difficult to ensure that the algorithm converges to the global maximum.In this paper,we will combine the stability selection and multiple imputation to consider Gaussian graphical modelselection problemwith missing data.Our method has the following two characteristics.First,we deal with missing data by multiple imputation,it is an extension ofstability selection.Second,bootstrap with multiple imputation can achieve a more intenseperturbation and get more accurate results.In this paper,two implementation strategies are proposed.The first one is to resample the B self-sample sets,then multi-interpolate the B bootstrapdatasets,and finally use the stability selection to obtain the Gaussian graphical model.The second is the original sample is firstly interpolatedby multiple imputation,then the imputed datasetsare resampled to obtain the bootstrapdatasets,andfinally the Gaussian graphical model is estimated by stability selection.The first strategy is called GBISS and the second strategy is called GIBSS.We consider multiple imputation based on mice package and miceFast package.In this paper,we write the code of Rto simulatefour models,considerthe influence of parameterssuchasmultipleimputationtimesM,thenumberofadjustment parametersλn.lambda and the threshold parameterπ_thr.Then we compare our strategies with the MissGlasso method and GEMS method.The simulation results show that mcc obtained by our methodsis mostly higher than mcc obtained by MissGlasso method,only a small part of our mcc is smaller than mcc of MissGlasso method.Similarly,according to mcc,most of our results are also superior to the results of GEMS method.We also apply our strategies to the isoprenoid gene data for Gaussian graphical model.