Distribution Regression

Distribution regression tackles the problem of predicting a response variable when the input is a probability distribution, rather than a simple vector. Current research focuses on developing robust and efficient algorithms, including those based on deep generative models, kernel methods (especially those leveraging optimal transport metrics), and ensemble techniques like stacking. These advancements aim to improve prediction accuracy, particularly in extrapolation scenarios, and provide reliable uncertainty quantification, addressing challenges in diverse fields such as satellite precipitation prediction and actuarial modeling. The resulting models offer improved predictive power and interpretability compared to traditional regression methods.