GP wth latent variable

[Ruglio]

I am trying to work with a GP with latent variable (n.b. not a GP latent variable model). I would like to add some latent variables to each input feature in order to increase flexibility in a similar fashion as explained in Salimbeni or in the following notes. This "upgraded" model seems to perform way better compared to the standard GP and DGP
However, it looks like there is no way forward. Is there any way to implement it? Is it possible to model it using Pyro?

Thanks for any suggestion!

[gpleiss]

Would the Pyro integration work for you? It allows you to add latent variables to infer.

[Ruglio]

Yes, definitively it would. I have not much experience with Pyro, but as long as I can make it work, that's perfect.
Could one way be to use the gplvm example (https://pyro.ai/examples/gplvm.html) and concatenate the latent variable to my inputs?
How do you suggest proceeding?