Aggregating Correlated Estimations with (Almost) no Training

Abstract: Many decision problems cannot be solved exactly and use several estimation algorithms that assign scores to the different available options. The estimation errors can have various correlations, from low (e.g. between two very different approaches) to high (e.g. when using a given algorithm with different hyperparameters). Most aggregation rules would suffer from this diversity of correlations. In this article, we propose different aggregation rules that take correlations into account, and we compare them to naive rules in various experiments based on synthetic data. Our results show that when sufficient information is known about the correlations between errors, a maximum likelihood aggregation should be preferred. Otherwise, typically with limited training data, we recommend a method that we call Embedded Voting (EV).