Adaptive Regression Model And Application Of Multivariate Smoothing Splines

In 1991, the famous American statistician Jerome Friedman first proposed multivariate adaptive regression splines, the MARS. MARS uses spline functions tensor product as its basic functions. It needs three steps to build the MARS model, forward process, pruning process and model selection. The advantage of MARS is its ability to deal with large volumes data with high dimensional variables.Based on the theory of general regression and spline, systematically we study about the modeling process of MARS and put forward the idea of introducing Bernstein basis functions to MARS model. In the view of metallurgical industry, we analyze a class of data to solve its components optimization problem and build a model to forecast with MARS. Forward process is the procedure of dividing data by adaptively selecting nodes. A new note comes with two new basic functions. At the end of forward process; it will create an over-fitting model. The pruning process is the procedure of removing basis functions from the over-fitting model which have little contribution to the model and also it can ensure the accuracy of the model. Finally it selects an optimal model as the regression model. During the study procedure, we preprocess original data by eliminating negative difference, excluding abnormal data, and data standardization, then compare MARS model with linear model, nonlinear model and neural network model. Due to its limitations, the linear model has lower precision and it is not inconsistent with the actual experience. To some elements, neural network can give more accurate description than liner model but it can not give the appropriate expression. Considering the interaction of elements, the MARS model can describe the problem more accurately. It can visualize the two variables and give an explicit expression.As the background of data science, this paper is a problem-driven application mathematics research. It does not only explore the theory of MARS but also provide a theoretical basis of data analysis and optimization on industrial areas.