Estimation Of Partial Linear Model Based On Gradient Descent Method

The rapid development of computer technology provides support for access to massive data,which contains a lot of information.While obtaining a lot of information from these data,the dimensions of the data are getting higher and higher,and the sparseness and complexity of the data structure have brought unprecedented challenges to the research of the data.While pursuing the accuracy and interpretability of model prediction,part of the linear model has become a hotspot in the study of modern regression models.How to realize the effective application of partial linear models in high-dimensional data is the problem to be studied in this paper.Gradient descent method is widely used in optimization problems because of its high speed,high accuracy,and easy operation.This article intends to solve the partially linear model under high-dimensional data by using the gradient descent method.In the estimation,the decision tree regression algorithm is used to extract the complex structure of the non-parametric part.In combination with the gradient descent algorithm,continuous training is performed based on the previous residuals to minimize the squared loss function.The estimation of the non-parametric part and the linear part is solved in order to realize the estimation of the parameters of the partial linear model.Non-parametric parts are estimated using a regression tree,which can solve problems such as poor fitting results due to the too high dimensions of the non-parametric parts and complex variable cross-relationships.For linear parts with higher dimensions,problems such as obvious multicollinearity and variable redundancy are easy to consider.Using ridge regression and LASSO methods for feature selection to reduce the data dimension,respectively.During the estimation of gradient descent method,the coefficient compression of variables is performed on the linear part,and the linear model and the non-parametric part of the part of the linear model are affected by too many variables and the model's estimation performance deteriorates.The traditional two-step estimation method and the gradient descent estimation method are compared by simulation values.The results show that the gradient descent method has good robustness for solving partial linear models.When the non-parametric part has high dimensions and the data has a complex structure,the gradient descent method is better than the two-step estimation method for the model.The gradient descent method to the estimation effect of the parameter part is better than the two-step estimation method.Finally,the part of the linear model was used in the study of passenger traffic of the civil aviation.The model was estimated using a gradient descent algorithm.The added value of the secondary industry,the mileage of scheduled airline routes,the number of civil airports,and passenger turnover,number of domestic residents,number of scheduled civil aviation routes,and other six variables have a greater impact on civil aviation passenger traffic.The results obtained are highly credible and highly practical.