support for non-stationary GP

[torabin]

Hi GPytorch developers,

I was wondering whether GPytorch can be used with a custom Kernel where new hyper-parameters are introduced to the kernel? To be more specific, I want to extend my common RBF kernel with a temporal kernel (to support non-stationary latent function). So my new kernel would be in a form of G^|t - t'| * K(x, x') 0 < G <= 1 where G is a new hyper-parameter (t, t' are the time stamp related to x and x'). So, I would like to know whether it is possible to use GPytorch for this case or not. Thanks in advance

[Balandat]

This should be pretty straightforward to do. You wouldn't necessarily define this as a new compound kernel but define the single-dimensional G^|t - t'| kernel, and then in the model's forward method multiply the kernels. So unlike what's done in https://github.com/cornellius-gp/gpytorch/blob/master/examples/01_Exact_GPs/Simple_GP_Regression.ipynb you'd do something like

   def forward(self, x, t):
       mean = self.mean_module(x)
       covar = self.base_covar_module(x) * self.temporal_covar_module(t)
       return gpytorch.distributions.MultivariateNormal(mean, covar)

and you'll need to make sure that your train inputs are tuples of tensors (x, t). Here temporal_covar_module would be the new kernel you define (this could be modeled on ScaleKernel but have the multiplicative factor depend on the intput t.

[ginward]

This should be pretty straightforward to do. You wouldn't necessarily define this as a new compound kernel but define the single-dimensional G^|t - t'| kernel, and then in the model's forward method multiply the kernels. So unlike what's done in https://github.com/cornellius-gp/gpytorch/blob/master/examples/01_Exact_GPs/Simple_GP_Regression.ipynb you'd do something like

   def forward(self, x, t):
       mean = self.mean_module(x)
       covar = self.base_covar_module(x) * self.temporal_covar_module(t)
       return gpytorch.distributions.MultivariateNormal(mean, covar)

and you'll need to make sure that your train inputs are tuples of tensors (x, t). Here temporal_covar_module would be the new kernel you define (this could be modeled on ScaleKernel but have the multiplicative factor depend on the intput t.

Is there any example of temporal_covar_module (i.e. how to define a kernel dependent on t)? @torabin @Balandat

[gpleiss]

@ginward look at these docs on implementing custom kernels: https://docs.gpytorch.ai/en/latest/examples/00_Basic_Usage/Implementing_a_custom_Kernel.html

[sanaamouzahir]

Hi GPytorch developers,

I was wondering whether GPytorch can be used with a custom Kernel where new hyper-parameters are introduced to the kernel? To be more specific, I want to extend my common RBF kernel with a temporal kernel (to support non-stationary latent function). So my new kernel would be in a form of G^|t - t'| * K(x, x') 0 < G <= 1 where G is a new hyper-parameter (t, t' are the time stamp related to x and x'). So, I would like to know whether it is possible to use GPytorch for this case or not. Thanks in advance

Did you end up doing this?