Malgorzata Liszewska

Position preserving multi-output prediction

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.

Contour regression: A distribution-regularized regression framework for climate modeling

Regression methods are commonly used to learn the mapping from a set of predictor variables to a continuous-valued target variable such that their prediction errors are minimized. However, minimizing the errors alone may not be sufficient for some applications, such as climate modeling, which require the overall predicted distribution to resemble the actual observed distribution. On the other hand, histogram equalization methods, such as quantile mapping, are often used in climate modeling to alter the distribution of input data to fit the distribution of observed data, but they provide no guarantee of accurate predictions. This paper presents a flexible regression framework known as contour regression that simultaneously minimizes the prediction error and removes biases in the predicted distribution. The framework is applicable to linear, nonlinear, and conditional quantile models and can utilize data from heterogenous sources. We demonstrate the effectiveness of the framework in fitting the daily minimum and maximum temperatures as well as precipitation for 14 climate stations in Michigan. The framework showed marked improvement over standard regression methods in terms of minimizing their distribution bias.