Taming the Long Tail of Deep Probabilistic Forecasting

TL;DR

This paper addresses the challenge of improving deep probabilistic forecasting on rare and difficult cases by introducing moment-based tailness measures and loss functions, leading to better performance on tail examples.

Contribution

It proposes Pareto Loss and Kurtosis Loss to specifically enhance deep probabilistic forecasting on tail cases, a previously under-addressed aspect.

Findings

Significant improvements on tail examples across multiple datasets.

Introduction of Pareto Loss and Kurtosis Loss for tail-focused training.

Enhanced robustness of deep probabilistic models in rare event scenarios.

Abstract

Deep probabilistic forecasting is gaining attention in numerous applications ranging from weather prognosis, through electricity consumption estimation, to autonomous vehicle trajectory prediction. However, existing approaches focus on improvements on the most common scenarios without addressing the performance on rare and difficult cases. In this work, we identify a long tail behavior in the performance of state-of-the-art deep learning methods on probabilistic forecasting. We present two moment-based tailedness measurement concepts to improve performance on the difficult tail examples: Pareto Loss and Kurtosis Loss. Kurtosis loss is a symmetric measurement as the fourth moment about the mean of the loss distribution. Pareto loss is asymmetric measuring right tailedness, modeling the loss using a generalized Pareto distribution (GPD). We demonstrate the performance of our approach on several real-world datasets including time series and spatiotemporal trajectories, achieving significant improvements on the tail examples.