  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.
