Enhancing Time Series Predictors with Generalized Extreme Value Loss

Abstract

Time series prediction has wide applications in many safety-critical scenarios. According to previous studies, time series of recorded events usually contain a non-trivial proportion of extreme events, featured with extremely large/small values and may have huge societal consequences if overlooked by a predictive model (i.e., predictor). Despite its significance in time series, we however observe the conventional square loss in time series prediction would ignore the modeling of extreme events. Specifically, we prove the square loss as a learning objective of the predictor behaves equivalently as a Gaussian kernel density estimator (KDE) on the recorded events, which is light-tailed itself and unable to model the ground-truth event distribution, usually heavy-tailed due to the existence of extreme events. Considering the benefits of forecasting extreme events, we propose a unified loss form called Generalized Extreme Value Loss (GEVL), which bridges the misalignment between the tail parts of the estimation and the ground-truth via transformations on either the observed events or the estimator. Following the proposed framework, we present three heavy-tailed kernels and derive the corresponding GEVLs which show different levels of trade-off between modeling effectiveness and computational resources.Comprehensive experiments validate our novel loss form substantially enhances representative time series predictors in modeling extreme events.