Enforcing tail calibration when training probabilistic forecast models

TL;DR

This paper explores how modifying loss functions during training can enhance the calibration of probabilistic forecasts for extreme events, focusing on wind speed predictions.

Contribution

It introduces tailored loss functions based on weighted scoring rules and tail miscalibration measures to improve extreme event forecast calibration.

Findings

State-of-the-art models lack calibration for extreme wind speeds.

Loss function adaptations improve tail calibration.

Trade-off exists between extreme event and general forecast calibration.

Abstract

Probabilistic forecasts are typically obtained using state-of-the-art statistical and machine learning models, with model parameters estimated by optimizing a proper scoring rule over a set of training data. If the model class is not correctly specified, then the learned model will not necessarily issue forecasts that are calibrated. Calibrated forecasts allow users to appropriately balance risks in decision making, and it is particularly important that forecast models issue calibrated predictions for extreme events, since such outcomes often generate large socio-economic impacts. In this work, we study how the loss function used to train probabilistic forecast models can be adapted to improve the reliability of forecasts made for extreme events. We investigate loss functions based on weighted scoring rules, and additionally propose regularizing loss functions using a measure of tail miscalibration. We apply these approaches to a hierarchy of increasingly flexible forecast models for UK wind speeds, including simple parametric models, distributional regression networks, and conditional generative models. We demonstrate that state-of-the-art models do not issue calibrated forecasts for extreme wind speeds, and that the calibration of forecasts for extreme events can be improved by suitable adaptations to the loss function during model training. This introduces a trade-off between calibrated forecasts for extreme events and calibrated forecasts for more common outcomes.