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Ensemble methods for classification and clustering have been effectively usedfor decades, while ensemble learning for outlier detection has only beenstudied recently. In this work, we design a new ensemble approach for outlierdetection in multi-dimensional point data, which provides improved accuracy byreducing error through both bias and variance. Although classification andoutlier detection appear as different problems, their theoretical underpinningsare quite similar in terms of the bias-variance trade-off [1], where outlierdetection is considered as a binary classification task with unobserved labelsbut a similar bias-variance decomposition of error.  In this paper, we propose a sequential ensemble approach called CARE thatemploys a two-phase aggregation of the intermediate results in each iterationto reach the final outcome. Unlike existing outlier ensembles which solelyincorporate a parallel framework by aggregating the outcomes of independentbase detectors to reduce variance, our ensemble incorporates both the paralleland sequential building blocks to reduce bias as well as variance by ($i$)successively eliminating outliers from the original dataset to build a betterdata 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 datasetsmainly from the UCI machine learning repository [2], we show that CARE performssignificantly better than or at least similar to the individual baselines. Wealso compare CARE with the state-of-the-art outlier ensembles where it alsoprovides significant improvement when it is the winner and remains closeotherwise.

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