Multitask Gaussian Process with Hierarchical Latent Interactions
This work addresses a specific limitation in multitask learning for researchers in Gaussian processes, offering an incremental improvement over existing MTGP methods.
The authors tackled the inability of existing multitask Gaussian processes (MTGPs) to represent hierarchical latent interactions between latent functions, proposing a novel kernel representation that improves expressiveness and interpretability, and validated it on synthetic and real-world datasets.
Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its latent functions. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness and the interpretability of MTGP. Specifically, we express the interaction as a product of function interaction and coefficient interaction. The function interaction is modeled by using cross convolution of latent functions. The coefficient interaction between the LMCs is described as a cross coregionalization term. We validate that considering the interactions can promote knowledge transferring in MTGP and compare our approach with some state-of-the-art MTGPs on both synthetic- and real-world datasets.