  Multi-task regression attempts to exploit the task similarity in order to
achieve knowledge transfer across related tasks for performance improvement.
The application of Gaussian process (GP) in this scenario yields the
non-parametric yet informative Bayesian multi-task regression paradigm.
Multi-task GP (MTGP) provides not only the prediction mean but also the
associated prediction variance to quantify uncertainty, thus gaining popularity
in various scenarios. The linear model of coregionalization (LMC) is a
well-known MTGP paradigm which exploits the dependency of tasks through linear
combination of several independent and diverse GPs. The LMC however suffers
from high model complexity and limited model capability when handling
complicated multi-task cases. To this end, we develop the neural embedding of
coregionalization that transforms the latent GPs into a high-dimensional latent
space to induce rich yet diverse behaviors. Furthermore, we use advanced
variational inference as well as sparse approximation to devise a tight and
compact evidence lower bound (ELBO) for higher quality of scalable model
inference. Extensive numerical experiments have been conducted to verify the
higher prediction quality and better generalization of our model, named NSVLMC,
on various real-world multi-task datasets and the cross-fluid modeling of
unsteady fluidized bed.
