The Research Of Model Selection Method With A Class Of L₀ Shrinkage Exponential Prior

With the rapid development of information technology,the data dimension and the number of samples have greatly increased,and a large number of irrelevant and redundant data features are hidden in it,which brings great challenges to the application of data mining and machine learning algorithms.Therefore,Selecting important features from many features is an important task in data processing.In the past linear model research,when the noise of the data is low,the exponential weight method(EW)has more prominent results in variable selection,estimation and prediction errors.However,the EW often cannot correctly identify the real model in the case of low Signal-to-Noise Ratio(SNR)data.By discussing the size of the model hypothesis space,this thesis constructs a suitable prior to the model space,and then construct the prior distribution of the support set about the coefficient vector in the same subspace.We call the method for solving parameter estimation under the constructed prior distribution as the Extended Exponential Weights method(EEW).From the perspective of theoretical analysis,this thesis establishes the Oracle inequality of the chosen model under this sparse prior distribution.Secondly,it is proved that under the condition of identifiability,as long as the non-zero elements of the coefficient vector are large enough,the support that maximizes the posterior probability converges in probability to the support of the true coefficient vector.Furthermore,the error boundaries of the Bayesian estimation of the coefficient vector under three different measures are established,which shows that the parameter estimates obtained under the method in this thesis are consistent,i.e.,when the sample size tends to infinity,the obtained Bayesian estimation converges in probability to the true coefficient vector.Finally,this thesis confirms through numerical simulation that under the condition of low SNR,the method in this thesis can obtain coefficient estimation with lower estimation error and higher non-zero coefficient support recovery rate.And under the condition of high SNR,compared with other variable selection methods,our method also performs well.