Multitask Gaussian Process with Hierarchical Latent Interactions

TL;DR

This paper introduces a novel hierarchical kernel for multitask Gaussian processes that captures complex latent interactions, enhancing expressiveness and interpretability for joint learning tasks.

Contribution

The paper proposes a new kernel representation modeling hierarchical interactions in MTGPs, improving their ability to learn complex task correlations.

Findings

Enhanced expressiveness and interpretability of MTGPs.

Improved knowledge transfer across tasks.

Outperforms state-of-the-art MTGP methods on datasets.

Abstract

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.