Any way to use combination of multiple kernels ?

[pranav997]

Hi,
Thanks very much for this code implementation. I was wondering if there is any way to use combination of different kernels like (Krbf*Kmatern+Krbf) within the same code ??

[brunzema]

Hi,
The code is part of our paper, where we use a product kernel as k_RBF * k_Wiener, where only the RBF kernel is constrained; thus combinations of different kernels are possible, if the other kernels should not be constrained. Then you can simply define the self.covar_module as:

self.spatio_kernel = gpytorch.kernels.ScaleKernel(
RBFKernelForConvexityConstraints(constrained_dims=constrained_dims,
                                 ard_num_dims=self.spatio_dims,
                                 active_dims=range(self.spatio_dims),
                                 lengthscale_prior=lengthscale_hyperprior,
                                 lengthscale_constraint=lengthscale_constraint),
...
self.covar_module = self.spatio_kernel * MaternKernel(...) + RBFKernel(...)

This way, your first RBF kernel is constrained and the others are not. Unfortunately, all the derivatives of the kernels are all hardcoded. If you want a constrained Matern kernel you would have to do this as well...

[pranav997]

Thanks for your response. I was wondering if there is a way to put data dependent constraints on function. I have a four dimensional function x=[x1,x2,x3,x4]. I would want to put constraints such as f(x2)>f(x'2) for x2>x'2. I also want to put bound constraints which are data dependent such as f(x1)<x1 for different values of x1. Is there any way to do that with your code?

[brunzema]

No, unfortunately, monotonicity constraints as well as bounds on the predictions are currently not implemented. One can however extend the code to do this. I would suggest to first look at the repo of Agrell (2019) (here) and then reimplement the stacking of matricies using this code base. :)