Gaussian Regression with Measurement Uncertainties

[hsilver]

I have a vector X of input variables, and a vector Y of observations, with a vector SD of standard deviations. For the moment we can assume that the uncertainties on the observations Y are Gaussian. The standard deviations are different for each Y value. I want to perform Gaussian Process regression on this data set. How should I do this in gpytorch?

This seems like a very basic question but I've spent the afternoon digging through the GPyTorch documentation, and just found myself going around in circles with nothing working. In SciKit-Learn it can be done out-of-the-box like so: gp = GaussianProcessRegressor(kernel=kernel, alpha = SD**2, n_restarts_optimizer=10)

[jacobrgardner]

@hsilver Currently, the WhiteNoiseKernel will let you add a diagonal component to the train-train covariance matrix, e.g.:

self.covar_module = ScaleKernel(RBFKernel()) + WhiteNoiseKernel(SD**2)

The plan for 0.3.0 (ETA early April) is to move this functionality to a new likelihood rather than a kernel, because the noise model of a GP really is the likelihood more than a kernel choice. However for the moment the above should work.

[hsilver]

Fantastic, thanks!