Regression-based approaches are widely used in climate research to derive the statistical, spatial, and temporal relationships among climate variables. Despite its extensive literature, existing approaches are insufficient to address the unique challenges arising from the data characteristics and requirements of this domain. For example, climate variables such as precipitation have zero-inflated distributions, which render ineffective any linear regression models constructed from the data. In addition, whereas traditional regression-based approaches emphasize on minimizing the discrepancy between observed and predicted values, there is a growing demand for regression outputs that satisfy other domain-specific criteria. To address these challenges, this thesis presents multi-objective regression frameworks designed to extend current regression-based approaches to meet the needs of climate researchers. First, a framework called Integrated Classification and Regression (ICR) is developed to accurately capture the timing of rain events and the magnitude of rain amount in zero-inflated precipitation data. The second multi-objective regression framework focuses on modeling the extreme values of a distribution without degrading its overall accuracy in predicting non-extreme values. The third framework emphasizes on both minimizing the divergence between the regression output and observed data while maximizing the fit of their cumulative distribution functions. The fourth contribution extends this framework to a multi-output setting, to ensure that the joint distribution of the multiple regression outputs is realistic and consistent with true observations.
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