ApproximateGP + MultivariateNormal + HeteroskedasticNoise

[olegmyrk]

📚 Documentation/Examples

I would like to understand how to model heteroscedastic multivariate normal likelihood in combination with Approximate GP and Variational Strategy?

I'm aware of this request about exact GPs: Way to model heteroskedastic noise? https://github.com/cornellius-gp/gpytorch/issues/982

[jacobrgardner]

Are there specific things about the existing likelihoods that handle heteroscedastic noise that do not work with ApproximateGP?

In addition to this, it's worth noting that variational GPs inherently allow for some degree of heteroscedasticity via the variational covariance matrix S. See e.g. this example notebook.

[CompRhys]

@jacobrgardner Do you have any suggested literature covering the insight here that;

variational GPs inherently allow for some degree of heteroscedasticity via the variational covariance matrix S.

This is something I haven't read before and would greatly appreciate hints to literature where I could dig deeper!