Threshold Estimation And Robust Migration For High-Dimensional Generalized Linear Model

In recent years,due to the convenience of data acquisition,research on machine learning and statistical inference of high-dimensional data has been highly regarded.However,when the training data is insufficient,the parameter estimation and prediction performance of traditional machine learning and statistical methods may decline.Therefore,it is possible to improve traditional estimation methods or use the idea of transfer learning.Transfer learning achieves the purpose of borrowing data by finding data related to the target data.Although transfer learning has been widely used in the computer field in recent years,there are fewer studies combining transfer learning with statistical models.Therefore,this paper studies the threshold estimation and transfer learning of high-dimensional generalized linear models to explore the application prospects in this field.Firstly,based on the low-dimensional projection weighting method in logistic regression,a threshold estimator is proposed,and the theoretical properties of this estimation method are proved.Secondly,when the transferable domain is known,a new two-step transfer learning algorithm based on elastic net is proposed in this paper.This algorithm uses data with different but related distributions to solve the problem of parameter estimation of target domain data,and its theoretical properties are studied.The losses show that the proposed estimation method is convergent.Further,the extreme risk of estimation errors shows that the proposed algorithm is robust.When the transferable domain is unknown,based on the idea of stepwise regression,a data-driven transferable domain identification algorithm is proposed on the basis of the previous algorithm,which further improves the efficiency and application range of transfer learning.Simulation results show that the two proposed algorithms are superior to traditional parameter estimation methods and compared transfer learning methods.Finally,the two algorithms mentioned above are combined and applied to six actual datasets,and the results also show that the estimation method has better performance.