UC San Diego

Deep probabilistic forecasting is gaining attention across numerous applications. From weather prognosis, electricity consumption estimation, traffic flow prediction, to autonomous vehicle trajectory prediction. However, existing approaches focus on improving on average metrics without addressing the long-tailed distribution of errors. This thesis identifies long tail behavior in the error distribution of state-of-the-art deep learning methods for probabilistic forecasting. We analyze potential sources and explanations for this behavior. Further, we present two loss augmentation methods to mitigate tailedness pf error distributions: Pareto Loss and Kurtosis Loss. Both methods modify the loss using the concept of moments to penalize higher loss samples. Kurtosis Loss uses a symmetric measure, the fourth moment, while Pareto Loss uses an asymmetric measure of right-tailedness and models loss using a Generalized Pareto Distribution (GPD). We demonstrate the performance of our methods on several real-world datasets, including time series and spatiotemporal trajectories, achieving significant improvements on tail error metrics, while maintaining and even improving upon average error metrics.