Transductive Learning for Multi-Task Copula Processes
This addresses the problem of handling non-Gaussian likelihoods in spatial and spatial-temporal processes for applications like pollution monitoring, though it appears incremental as it builds on existing copula process methods.
The paper tackles multi-task learning with copula processes to improve multivariable prediction in non-Gaussian settings, such as natural resource estimation and concrete slump prediction, by introducing a transductive approximation and showing competitive results on three datasets.
We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption is convenient from analytical and computational perspectives, nature is dominated by non-Gaussian likelihoods. Copula processes are an elegant and flexible solution to handle various non-Gaussian likelihoods by capturing the dependence structure of random variables with cumulative distribution functions rather than their marginals. We show how multi-task learning for copula processes can be used to improve multivariable prediction for problems where the simple Gaussianity prior assumption does not hold. Then, we present a transductive approximation for multi-task learning and derive analytical expressions for the copula process model. The approach is evaluated and compared to other techniques in one artificial dataset and two publicly available datasets for natural resource estimation and concrete slump prediction.