High-Dimensional Kernel Regression: A Guide for Practitioners

2015 ◽  
pp. 309-332
Keyword(s):  
Kernel Regression ◽  
High Dimensional

scholarly journals Forecasting of Steam Coal Price Based on Robust Regularized Kernel Regression and Empirical Mode Decomposition

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiangwan Fu ◽  
Mingzhu Tang ◽  
Dongqun Xu ◽  
Jun Yang ◽  
Donglin Chen ◽  
...  
Keyword(s):  
Empirical Mode Decomposition ◽  
Kernel Function ◽  
Dimensional Space ◽  
Kernel Regression ◽  
Model Performance ◽  
Feature Space ◽  
Evaluation Index ◽  
High Dimensional ◽  
Polynomial Kernel ◽  
Mode Decomposition

Aiming at the problem of difficulties in modeling the nonlinear relation in the steam coal dataset, this article proposes a forecasting method for the price of steam coal based on robust regularized kernel regression and empirical mode decomposition. By selecting the polynomial kernel function, the robust loss function and L2 regular term to construct a robust regularized kernel regression model are used. The polynomial kernel function does not depend on the kernel parameters and can mine the global rules in the dataset so that improves the forecasting stability of the kernel model. This method maps the features to the high-dimensional space by using the polynomial kernel function to transform the nonlinear law in the original feature space into linear law in the high-dimensional space and helps learn the linear law in the high-dimensional feature space by using the linear model. The Huber loss function is selected to reduce the influence of abnormal noise in the dataset on the model performance, and the L2 regular term is used to reduce the risk of model overfitting. We use the combined model based on empirical mode decomposition (EMD) and auto regressive integrated moving average (ARIMA) model to compensate for the error of robust regularized kernel regression model, thus making up for the limitations of the single forecasting model. Finally, we use the steam coal dataset to verify the proposed model and such model has an optimal evaluation index value compared to other contrast models after the model performance is evaluated as per the evaluation index such as RMSE, MAE, and mean absolute percentage error.

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