Sequential Ensemble Learning for Outlier Detection: A Bias-Variance Perspective

Ensemble methods for classification and clustering have been effectively used for decades, while ensemble learning for outlier detection has only been studied recently. In this work, we design a new ensemble approach for outlier detection in multi-dimensional point data, which provides improved accuracy by reducing error through both bias and variance. Although classification and outlier detection appear as different problems, their theoretical underpinnings are quite similar in terms of the bias-variance trade-off [1], where outlier detection is considered as a binary classification task with unobserved labels but a similar bias-variance decomposition of error. In this paper, we propose a sequential ensemble approach called CARE that employs a two-phase aggregation of the intermediate results in each iteration to reach the final outcome. Unlike existing outlier ensembles which solely incorporate a parallel framework by aggregating the outcomes of independent base detectors to reduce variance, our ensemble incorporates both the parallel and sequential building blocks to reduce bias as well as variance by ($i$) successively eliminating outliers from the original dataset to build a better data model on which outlierness is estimated (sequentially), and ($ii$) combining the results from individual base detectors and across iterations (parallelly). Through extensive experiments on sixteen real-world datasets mainly from the UCI machine learning repository [2], we show that CARE performs significantly better than or at least similar to the individual baselines. We also compare CARE with the state-of-the-art outlier ensembles where it also provides significant improvement when it is the winner and remains close otherwise.