How to improve Gaussian Process Regression fit: reducing oscillations and narrowing confidence interval I’m trying to fit a model y=f(x1, x2) to some measurements using GPR. For each instance (x1i, x2i) there are two measurements of y. I’m using the following kernel:
WhiteKernel + ConstantKernel * RBF
The result is adequate but not quite right yet, there are mainly two problems:

*

*The average predicted value does pass through the measured values but there is some “oscillations” overshoot/undershoot between some points. This is shown with the red arrow in the images below.


*The 90% confidence intervals increase too much between some  measurement points. This is shown with the black arrows in the images below.


How should I specify the kernel to get better results? Do you have any tips for me?

For the over/undershoot issue I recommend trying the Matern kernel, it can be seen as a generalization of a RBF with an extra parameter that controls smoothness. This extra parameter very often helps in such issues.
