Transductive Learning for Multi-Task Copula Processes

TL;DR

This paper introduces a transductive learning approach for multi-task copula processes, enabling better multivariable predictions in non-Gaussian spatial and temporal data scenarios by capturing complex dependence structures.

Contribution

It presents a novel transductive approximation method for multi-task copula processes with analytical derivations, improving prediction accuracy in non-Gaussian settings.

Findings

Outperforms Gaussian-based methods on artificial and real datasets.

Effectively models non-Gaussian dependence structures.

Enhances multivariable prediction accuracy in spatial-temporal problems.

Abstract

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.