Prediction Instability in Machine Learning Ensembles
Jeremy Kedziora
TL;DR
This paper analyzes prediction stability in machine learning ensembles through an axiomatic framework that treats ensemble aggregation as a score-to-score mapping problem. It proves an ensemble aggregated--prediction instability theorem showing that for a label set with |Y|≥3, any nondegenerate aggregator using multiple high-capacity models will inevitably violate at least one stability property (insertion/deletion consistency, ensemble unanimity, or model choice reversal) in some scoring region, with the violation observable if the score function s(x) is surjective. The authors connect these instabilities to practical aggregators (hard/soft voting, RL-inspired voting, stacking) and explainability challenges, arguing that high model capacity exacerbates effects and that asymptotic consistency of models can restore stability, particularly for soft voting. They also discuss extensions and conjectures, such as the potential role of Borda-count-style aggregation in many-model limits and implications for bootstrap or cross-validation based model selection. Overall, the work highlights a fundamental finite-sample tradeoff between leveraging diverse models and maintaining stable, explainable predictions, suggesting design paths toward consistency as data or sample size grows.
Abstract
In machine learning ensembles predictions from multiple models are aggregated. Despite widespread use and strong performance of ensembles in applied problems little is known about the mathematical properties of aggregating models and associated consequences for safe, explainable use of such models. In this paper we prove a theorem that shows that any ensemble will exhibit at least one of the following forms of prediction instability. It will either ignore agreement among all underlying models, change its mind when none of the underlying models have done so, or be manipulable through inclusion or exclusion of options it would never actually predict. As a consequence, ensemble aggregation procedures will always need to balance the benefits of information use against the risk of these prediction instabilities. This analysis also sheds light on what specific forms of prediction instability to expect from particular ensemble algorithms; for example popular tree ensembles like random forest, or xgboost will violate basic, intuitive fairness properties. Finally, we show that this can be ameliorated by using consistent models in asymptotic conditions.