On Negative Transfer and Structure of Latent Functions in Multioutput Gaussian Processes

摘要

The multioutput Gaussian process (MGP) is based on the assumption that outputs share commonalities; however, if this assumption does not hold, negative transfer will lead to decreased performance relative to learning outputs independently or in subsets. In this article, we first define negative transfer in the context of MGP and then derive necessary conditions for an MGP model to avoid negative transfer. Specifically, under the convolution construction, we show that avoiding negative transfer is mainly dependent on having a sufficient number of latent functions Q regardless of the flexibility of the kernel or inference procedure used. However, a slight increase in Q leads to a large increase in the number of parameters to be estimated. To this end, we propose two latent structures which can scale to arbitrarily large datasets, can avoid negative transfer, and allow any kernel or sparse approximations to be used within. We also show that these structures allow regularization which can provide automatic selection of related outputs.