[Feature Request] Recovering latent GP in LMC MOGP

[mrlj-hash]

🚀 Feature Request

Per "recovering latent GP in LMC MOGP #2182" (https://github.com/cornellius-gp/gpytorch/discussions/2182), request that the ability to recover the outputs of the latent functions in LMC MOGPs be implemented.

Motivation

For use of a model outside of the Python environment used for training, using analytic predictive mean and variance formulas is desirable as part of the calculation can be pre-computed. However, this requires having saved out some predictions made (e.g. in variational methods, on the inducing points) in Python. For LMC multi-output models, this requires having the latent function values on the inducing points associated with them.