A Comparative Study On Algorithms For High-Dimensional Linear Regression

In the era of big data,high-dimensional data appears widely in the fields of bioin-formatics,financial economy and image processing.A common feature among them is the sparsity of the predictors.Selecting the most relevant predictors is one of the main research contents of high-dimensional data analysis,which has extremely important ap-plication value.Because of this,high-dimensional linear regression algorithms which can solve the problems of compressed sensing and variable selection have become the focus of scholars' research.Many fast and efficient algorithms have been proposed successively and bring lots of help to the problems of compressed sensing and variable selection,which are worth our in-depth discussion and careful study.In this paper,we compare and study the current popular high-dimensional linear regression algorithms in the perspective of solving different models in the problem of compressed sensing and variable selection.With the premise of summarizing the char-acteristics of previous algorithms,we focus on comparing deeply the precision and effi-ciency of the algorithms.Based on the existing Newton algorithm,we refine the frame and parameter selection of Newton algorithm to achieve a better numerical effect.At the same time,we propose an adaptive Newton algorithm with unknown sparsity.We compare the effect of the solution difference principle,residual-error difference prin-ciple and HBIC on sparsity selection.Lots of numerical experiments indicate that the precision and speed of the refined Newton algorithm in this paper are both better than those of the accepted algorithms in the fields of compressed sensing and variable selec-tion,and at the same time,the precision of the adaptive Newton algorithm proposed by this paper also exceeds the algorithms which are widely accepted in this field.Based on those,we develop a software package by MATLAB.