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.

翻译：在机器学习集成中，多个模型的预测结果被汇总。尽管集成方法在应用问题中被广泛使用且表现出色，但关于模型聚合的数学特性及其对安全、可解释地使用此类模型的相关影响，人们知之甚少。本文证明了一个定理，表明任何集成方法都将至少表现出以下一种形式的预测不稳定性：它要么会忽略所有底层模型之间的一致性，要么会在底层模型均未改变预测时改变其自身预测，要么会因包含或排除其实际上永远不会预测的选项而受到操纵。因此，集成聚合程序始终需要在信息利用的益处与这些预测不稳定性的风险之间进行权衡。此分析还阐明了特定集成算法（例如流行的树集成方法，如随机森林或xgboost）会违反哪些基本且直观的公平性属性。最后，我们证明在渐近条件下使用一致模型可以改善这一问题。