Distributional Uncertainty

Distributional uncertainty, the inherent variability in data-generating processes, poses a significant challenge for machine learning and statistical inference. Current research focuses on developing robust methods that account for this uncertainty, employing techniques like Bayesian nonparametrics (e.g., Dirichlet processes), distributionally robust optimization (DRO) with various distance metrics (e.g., Wasserstein, Sinkhorn), and regularization methods. These approaches aim to improve model generalization, prediction accuracy, and the reliability of uncertainty quantification, impacting fields ranging from hypothesis testing and optimal control to explainable AI and risk-sensitive applications.