How to combine different kernels for Gaussian process in GPyTorch?

Question

I am trying to learn gaussian process by using GPyTorch to fit a Gaussian Process Regression model. However, I can't figure out a way to combine different kernels as shown in sklearn implementation of gaussian process. I am using GPyTorch as it is more flexible and have lot more kernels that one can play with compared to scikit-learn. Any help, particularly with code snippet would be very useful.

Thank you.

Answer 1

From official documentation: For example, to compose two kernels via addition, you can either add the kernel modules directly:

self.covar_module = ScaleKernel(RBFKernel() + WhiteNoiseKernel())

Or you can add the outputs of the kernel in the forward method:

covar_x = self.rbf_kernel_module(x) + self.white_noise_module(x)

The class for GPRegressionModel would then look like this:

class GPRegressionModel(gpytorch.models.ExactGP):
def __init__(self, train_x, train_y, likelihood):
    super(GPRegressionModel, self).__init__(train_x, train_y, likelihood)

    self.mean_module = gpytorch.means.ConstantMean()
    self.covar_module = ScaleKernel(RBFKernel() + WhiteNoiseKernel())

def forward(self, x):
    mean_x = self.mean_module(x)
    covar_x = self.covar_module(x)
    return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)