Hi osita,

Thanks for the question. By saying "predictions", I mean the function outputs given the inputs.

Kernel function is used to measure the similarity between predictions f() at different input locations. Say you have the input x1 and x2. Then, we can define a kernel function to describe how strongly f(x1) and f(x2) are correlated. Obviously, this correlation measure is a function of x1 and x2, therefore you will see a kernel function is written as K(x1, x2).

Best,

Shuai