Research On Regularization Method With Log - Type Penalty Function

With the rapid development of science and technology,various fields have produced massive data. How to analyze high-dimensional massive data is one of the main problems in the current fields of statistics, financial economics, internet security and genomics.Regularization approach, as an effective way to extract information from high-dimensional massive data has been widely used. There are many learning algorithms for solving regularization problems. The iterative thresholding algo-rithm is one of the efficient and fast ways with high reconstruction accuracy for solving regularization problems, which has been used in the analysis of high dimensional massive data in recent years.Based on the theoretical framework of regularization approach, we study a sparse regularization approach with a Log type penalty function. A new strat-egy of nonconvex variable selection and compressive sensing is proposed with a fast alternative thresholding algorithm. Meanwihle, we use variable selection experiment and signal recovery experiment to prove the validity of the sparse regularization with Log type penalty. Further, we analyze the convergence of the algorithm, and show the sufficient condition under which the algorithm could converges to the sparse solution, what’s more, we proved that under this suffi-cient condition, the estimates error of the model could converge to zero with the exponential rate.The study of Log type penalty function is a further extension for the sparse regularization approach, it provides a favorable choice for high-dimensional mas-sive data analysis.