The GP kernels need to be set up to be invariant in case such constraints are present.
For Permutation Invariance:
Any base kernel k can be taken and an invariant one can be constructed by adding: k_actual(p1,p2) = k(p1,p2) + k(p2,p1). This can be done also for more than 2 affected parameters but requires more and more terms in the sum, so an upper limit of affected parameter needs to be implemented or a warning should be displayed.
For Dependency Invariance:
Not yet clear how to solve this
The GP kernels need to be set up to be invariant in case such constraints are present.
For Permutation Invariance:
Any base kernel
kcan be taken and an invariant one can be constructed by adding:k_actual(p1,p2) = k(p1,p2) + k(p2,p1). This can be done also for more than 2 affected parameters but requires more and more terms in the sum, so an upper limit of affected parameter needs to be implemented or a warning should be displayed.For Dependency Invariance:
Not yet clear how to solve this