Dynamic Transfer Gaussian Process Regression

Pengfei Wei, Xinghua Qu, Wen Song, Zejun Ma

Abstract: In this paper, we work on a challenging dynamic transfer regression problem where domains come in a streaming manner. At each time stage, a new domain emerges and is taken as the target domain while all the domains in previous time stages are taken as source domains. We propose a transfer Gaussian process model GPdk with a novel dynamic transfer kernel DyTK to handle the dynamic transfer regression problem. Specifically, DyTK is with a sequential form to fit the domain stream. To adaptively control the knowledge transfer strength, DyTK is designed to be capable of modeling the inter-domain relatedness of every inter-domain pair. A theorem that ensures DyTK to be positive semi-definite is then proposed. We also theoretically analyze the transfer performance of GPdk by deriving its generalization error bounds. The error bounds further motivate us to propose a parameter reuse strategy to alleviate the scalability issue of GPdk along time. Extensive experiments on both synthetic and real-world datasets show the effectiveness of GPdk in handling dynamic transfer regression problems.