Gpytorch: [Bug] Typo in doc - Matern Kernel

[dhruvbalwada]

🐛 Bug

Should the documentation here https://docs.gpytorch.ai/en/v1.1.1/kernels.html#maternkernel have $ \Theta^{-2}$ in the definition of d like the other kernels (example RBF)?

[KeAWang]

That does seem like a typo: https://github.com/cornellius-gp/gpytorch/blob/169b3ad9d85a6e4dfd4a0456dcaefc27c004384c/gpytorch/kernels/matern_kernel.py#L100

[dhruvbalwada]

Is d defined a different way then? Maybe it should be $d=\sqrt( (x_1 - x_2)^T (x_1-x_2))$ when $\theta=1$. Otherwise the units don't seem to add up.
Also, I think that equation you are pointing to seems to suggest that when I take that x1_ and (x2_) and put it in the formula for d in the doc, then there would be a lengthscale^2 in the denominator.

[KeAWang]

d should be the distance after rescaling, so $d = \sqrt((x_1-x_2)^\top \Theta^{-2} (x_1 - x_2))$