Theoretical Foundations and Algorithms for Outlier Ensembles

Ensemble analysis has recently been studied in the context of the outlier detection problem. In this paper, we investigate the theoretical underpinnings of outlier ensemble analysis. In spite of the significant differences between the classification and the outlier analysis problems, we show that the theoretical underpinnings between the two problems are actually quite similar in terms of the bias-variance trade-off. We explain the existing algorithms within this traditional framework, and clarify misconceptions about the reasoning underpinning these methods. We propose more effective variants of subsampling and feature bagging. We also discuss the impact of the combination function and discuss the specific trade-offs of the average and maximization functions. We use these insights to propose new combination functions that are robust in many settings.