The Research On High Dimension Variable Selection Based On Non-convex Function Penalty Factor

In recent years,a large amount of high dimensional data was generated in the fields of biological information,image processing and financial management.high dimensional data make the traditional variable selection methods insufficient in calculation and stability.Therefore,it is urgent to find more efficient methods to select variables form high dimensional variables.The penalty factor method is a popular method that can handle the problem.It can estimate the coefficients as well as selecting variables.In other words,variable selection can be achieved by compressing coefficients to zero in the process of parameters estimation.Due to the most of existing penalty factors are convex functions,some issues are caused.For example,a large amount of redundant data is difficult to remove and the position of sparse dimension is indistinguishable.To overcome these deficiencies,this paper mainly studies on high dimensional variable selection methods based on non-convex functions penalty factor,the main research contents are as follows:(1)A new high dimensional variable selection method is studied,which uses non-convex function-the fractional function as the penalty factor.First,we proved the equivalence between the regularized model and the original model,then studied the first and second order optimal conditions and the upper and lower bounds of the absolute value of the nonzero element of the optimal solution that solves the regularization model.Second,based on the threshold representation theory,FP thresholding algorithm is designed for the regularization model.(2)A new high dimensional variable selection method based on non-convex function penalty factor is given.By constructing a shrinkage operator and using the theory of proximal operators,a non-convex penalty factor is obtained.Then we applied the forward-backward splitting method to solve the corresponding model and got the iterative fractional thresholding algorithm(IFTA),then proved convergence of the algorithm.(3)An improved high-dimensional variable selection method.Improved the deficiency of converging slowly of the Iteration Soft Thresholding Algorithm(ISTA)which solves LASSO,so that when calculating the next iteration point,it depends on the first two iteration points simultaneously,then SFIST algorithm is obtained.Experimental results show that SFISTA tends to be faster than ISTA to the optimal solution,and the optimal solution obtained is more sparse.