There is a growing demand for multiple output prediction methods capable of both minimizing residual errors and capturing the joint distribution of the response variables in a realistic and consistent fashion. Unfortunately, current methods are designed to optimize one of the two criteria, but not both. This paper presents a framework for multiple output regression that preserves the relationships among the response variables (including possible non-linear associations) while minimizing the residual errors of prediction by coupling regression methods with geometric quantile mapping. We demonstrate the effectiveness of the framework in modeling daily temperature and precipitation for climate stations in the Great Lakes region. We showed that, in all climate stations evaluated, the proposed framework achieves low residual errors comparable to standard regression methods while preserving the joint distribution of the response variables.
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