Is there code or research about Heteroscedastic Gaussian Process in GPflow?

Question

I'm now studying on GP models with heteroscedastic noise, and I want to know if there are codes or notes in GPflow community so I can learn about them. Thanks very much!

Answer 1

There is, indeed. Below are two notebooks from GPflow docs exemplifying it

Noise for each observation

https://gpflow.readthedocs.io/en/master/notebooks/advanced/varying_noise.html

This one considers the heteroscedasticity for each observation. The noise can be supplied as an input, or, alternatively, learned by optimization using the available data. The downside is that this model cannot be used to predict the noise of new observations.

Noise modeled by another GP

https://gpflow.readthedocs.io/en/develop/notebooks/advanced/heteroskedastic.html

This one uses a model with two latent GPs where one models the mean of the observations (as usual) and the other models the noise. It has the advantage of being able to predict noise of new observations, but it can be harder to train/optimize.

The notebook uses a "black box" implementation, computing the likelihood with Gauss-Hermite quadratures. There is also an open PR with analytical implementations of this likelihood.