Hello, all. This is my first time within the PyTorch ecosystem (having switched over because of GpyTorch’s seemingly excellent GP modelling capabilities), and I would appreciate help getting through my first model.

Following the first example in the docs, I want to run a very simple model, but I encounter an error at the `loss = -mll(output, y_torch)`

step:

```
## Generating data for regression
# First, regular sine wave + normal noise
x = np.linspace(0,40, num=300)
noise1 = np.random.normal(0,0.3,300)
y = np.sin(x) + noise1
# Second, an upward trending starting halfway, with its own normal noise
temp = x[150:]
noise2 = 0.004*temp**2 + np.random.normal(0,0.1,150)
y[150:] = y[150:] + noise2
x_torch = torch.from_numpy(x)
y_torch = torch.from_numpy(y)
# initialize likelihood and model
class ExactGPModel(gpytorch.models.ExactGP):
def __init__(self, train_x, train_y, likelihood):
super(ExactGPModel, self).__init__(train_x, train_y, likelihood)
self.mean_module = gpytorch.means.ConstantMean()
self.covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())
def forward(self, x):
mean_x = self.mean_module(x)
covar_x = self.covar_module(x)
return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
likelihood = gpytorch.likelihoods.GaussianLikelihood()
model = ExactGPModel(x_torch, y_torch, likelihood)
# Find optimal model hyperparameters
model.train()
likelihood.train()
# Use the adam optimizer
optimizer = torch.optim.Adam([
{'params': model.parameters()}, # Includes GaussianLikelihood parameters
], lr=0.1)
# "Loss" for GPs - the marginal log likelihood
mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
training_iter = 50
for i in range(training_iter):
# Zero gradients from previous iteration
optimizer.zero_grad()
# Output from model
output = model(x_torch)
# Calc loss and backprop gradients
loss = -mll(output, y_torch)
loss.backward()
print('Iter %d/%d - Loss: %.3f lengthscale: %.3f noise: %.3f' % (
i + 1, training_iter, loss.item(),
model.covar_module.base_kernel.lengthscale.item(),
model.likelihood.noise.item()
))
optimizer.step()
```

At that line, I get a `RuntimeError: expected backend CPU and dtype Double but got backend CPU and dtype Float`

error. Having looked around, this seems like a common problem, but always has to do with CPU/CUDA errors, with the answers being vague, and I just want to run my model first on my CPU.

I would appreciate any help on the matter.