Beyond forecast leaderboards: Measuring individual model importance based on contribution to ensemble accuracy

TL;DR

This paper introduces two methods to evaluate the importance of individual models within an ensemble, enhancing understanding of each model's contribution to overall forecast accuracy, especially in collaborative settings like COVID-19 forecasting.

Contribution

It proposes leave-one-model-out and Shapley value-based algorithms to quantify individual model importance in ensembles, providing new insights beyond standard accuracy metrics.

Findings

The methods effectively measure individual model contributions.

Ensemble performance varies with model inclusion, influenced by error similarity.

Application to COVID-19 forecasts demonstrates practical utility.

Abstract

Ensemble forecasts often outperform forecasts from individual standalone models, and have been used to support decision-making and policy planning in various fields. As collaborative forecasting efforts to create effective ensembles grow, so does interest in understanding individual models' relative importance in the ensemble. To this end, we propose two practical methods that measure the difference between ensemble performance when a given model is or is not included in the ensemble: a leave-one-model-out algorithm and a leave-all-subsets-of-models-out algorithm, which is based on the Shapley value. We explore the relationship between these metrics, forecast accuracy, and the similarity of errors, both analytically and through simulations. We illustrate this measure of the value a component model adds to an ensemble in the presence of other models using US COVID-19 death probabilistic forecasts. This study offers valuable insight into individual models' unique features within an ensemble, which standard accuracy metrics alone cannot reveal.