To fix the same length scale for certain predictors in a Gaussian Process Regression (GPR) model using MATLAB's fitrgp, you can manually adjust the initial KernelParameters name-value argument of the function to specify the same value for the desired predictors. However, the fitrgp function doesn't directly allow setting fixed length scales during optimization. Instead, you can initialize them to the same value and then check if they remain similar after fitting.
Refer to the following documentation section which shows the steps for the same: https://www.mathworks.com/help/stats/fitrgp.html#buv_v2o-1
If you need to completely fix the length scales during optimization, you might need to implement a custom optimization routine outside of fitrgp, as fitrgp optimizes these hyperparameters by default.
