Sparse Research Group Lasso Lp Regularization Based Adaptive

With the development of science and technology and the ability to collect massive amount of data are growing. people are facing with the demand to han-dle high dimensional and massive amount of data. This demand exist in diverse fields of science,engineering, human genomics, economics, finance and so on. A major feature of the high dimentional and massive amount of data is taht they have a large number of redundant information, Studying how to extract useful information from the redundant variables effectively is very important. There-fore, variable selection is important issues in high-dimensional data analysising. Similarly, another feature of high-dimensional data is that they have Structural features, analysising structure of data will help us better discover rule.The main works of this paper are following:Firstly, we review existing M-estimators theory in high dimension, Dis-coursing the current research of non-convex loss function and non-convex penalty function, further, study the high-dimensional statistical property of group selec-tion methods with MCP penalty. Secondly, we study the model of adaptive sparse group lasso based on the Lp regularizer, Analysing the properties of loss function and penalty function, then the bounds of any solution and a unknown parameter are derived. In the end, we summarize the content and remark the main results.