Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization
This work addresses the problem of high complexity and limited capability in multi-task regression for researchers and practitioners in fields like fluid dynamics, offering an incremental improvement over existing LMC methods.
The paper tackles the limitations of linear model of coregionalization (LMC) in multi-task Gaussian processes by developing a neural embedding method to enhance model capability and using variational inference for scalable inference, resulting in improved prediction quality and generalization on real-world datasets, including cross-fluid modeling.
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.