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We introduce an online outlier detection algorithm to detect outliers in asequentially observed data stream. For this purpose, we use a two-stagefiltering and hedging approach. In the first stage, we construct a multi-modalprobability density function to model the normal samples. In the second stage,given a new observation, we label it as an anomaly if the value ofaforementioned density function is below a specified threshold at the newlyobserved point. In order to construct our multi-modal density function, we usean incremental decision tree to construct a set of subspaces of the observationspace. We train a single component density function of the exponential familyusing the observations, which fall inside each subspace represented on thetree. These single component density functions are then adaptively combined toproduce our multi-modal density function, which is shown to achieve theperformance of the best convex combination of the density functions defined onthe subspaces. As we observe more samples, our tree grows and produces moresubspaces. As a result, our modeling power increases in time, while mitigatingoverfitting issues. In order to choose our threshold level to label theobservations, we use an adaptive thresholding scheme. We show that our adaptivethreshold level achieves the performance of the optimal pre-fixed thresholdlevel, which knows the observation labels in hindsight. Our algorithm providessignificant performance improvements over the state of the art in our wide setof experiments involving both synthetic as well as real data.

Sequential Outlier Detection based on Incremental Decision Trees