  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.
