Kernel selection for extrapolation/ Custom mean design

[pranav997]

Hi,
I am working with a regression problem that is dependent on two features (M,B). I want to perform regression by taking values of B up until 0.23 only(minima shifts to right) (basically extrapolate given half range of B) . I am able to interpolate all the curves using simple RBF if I use full range of B. My plan was to build composite kernels by maximzing BIC, which has worked for me in the past, but this dataset has an assymetry, and my composite kernels can't seem to learn this given restricted access to data. Can anyone suggest any other way of building kernels for this problem. I have tried Deep kernel learning, spectral mixture etc.

I also tried a double well custom mean function

class QuadraticMean(gpytorch.means.Mean):
      def __init__(self, batch_shape=torch.Size()):        
          super(QuadraticMean, self).__init__()
          self.register_parameter(name="weights", parameter=torch.nn.Parameter(torch.randn(6)))
 
    def forward(self, x):
        b=self.weights
        print(b)
        print(b.shape)
        parta = b[0]**2 / torch.sqrt((x - b[1])**2 + b[2]**2)
        partb = b[3]**2 / torch.sqrt((x - b[4])**2 + b[5]**2)
        return -parta - partb

But I get the following error

/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/mlls/exact_marginal_log_likelihood.py in forward(self, function_dist, target, *params)
     61 
     62         # Get the log prob of the marginal distribution
---> 63         output = self.likelihood(function_dist, *params)
     64         res = output.log_prob(target)
     65         res = self._add_other_terms(res, params)

~/opt/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/likelihoods/likelihood.py in __call__(self, input, *args, **kwargs)
     63         # Marginal
     64         elif isinstance(input, MultivariateNormal):
---> 65             return self.marginal(input, *args, **kwargs)
     66         # Error
     67         else:

~/opt/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/likelihoods/gaussian_likelihood.py in marginal(self, function_dist, *params, **kwargs)
     70         mean, covar = function_dist.mean, function_dist.lazy_covariance_matrix
     71         noise_covar = self._shaped_noise_covar(mean.shape, *params, **kwargs)
---> 72         full_covar = covar + noise_covar
     73         return function_dist.__class__(mean, full_covar)
     74 

~/opt/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/lazy/lazy_tensor.py in __add__(self, other)
   2165             return self
   2166         elif isinstance(other, DiagLazyTensor):
-> 2167             return AddedDiagLazyTensor(self, other)
   2168         elif isinstance(other, RootLazyTensor):
   2169             return self.add_low_rank(other.root)

~/opt/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/lazy/added_diag_lazy_tensor.py in __init__(self, preconditioner_override, *lazy_tensors)
     30             raise RuntimeError("An AddedDiagLazyTensor can only have two components")
     31 
---> 32         broadcasting._mul_broadcast_shape(lazy_tensors[0].shape, lazy_tensors[1].shape)
     33 
     34         if isinstance(lazy_tensors[0], DiagLazyTensor) and isinstance(lazy_tensors[1], DiagLazyTensor):

~/opt/anaconda3/envs/pyoffice/lib/python3.9/site-packages/gpytorch/utils/broadcasting.py in _mul_broadcast_shape(error_msg, *shapes)
     18             if any(size != non_singleton_sizes[0] for size in non_singleton_sizes):
     19                 if error_msg is None:
---> 20                     raise RuntimeError("Shapes are not broadcastable for mul operation")
     21                 else:
     22                     raise RuntimeError(error_msg)

RuntimeError: Shapes are not broadcastable for mul operation