Implementing Gaussian Process Regression with Hyperparameter Optimization

This implementation utilizes MATLAB software to perform Gaussian process regression for data fitting, achieving more accurate prediction results. During the Gaussian process regression procedure, hyperparameters are employed to select optimal covariance functions, thereby improving model precision and reliability. The implementation typically involves defining a covariance kernel function (such as squared exponential or Matern kernel) and optimizing hyperparameters through methods like maximum likelihood estimation or Bayesian optimization. Additionally, by analyzing data characteristics and trends, more refined model construction and parameter tuning can be performed through residual analysis and cross-validation techniques to obtain superior fitting results. Key MATLAB functions used in this process may include fitrgp for model fitting, predict for making predictions, and specialized optimization functions for hyperparameter tuning. In summary, Gaussian process regression serves as a highly effective data analysis tool applicable to various data fitting and prediction problems, with MATLAB providing comprehensive support through its Statistics and Machine Learning Toolbox.