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Outlier detection methods automatically identify instances that deviate from the majority of the data. In this paper, we propose a novel approach for unsupervised outlier detection, which re-formulates the outlier detection problem in numerical data as a set of supervised regression learning problems. For each attribute, we learn a predictive model which predicts the values of that attribute from the values of all other attributes, and compute the deviations between the predictions and the actual values. From those deviations, we derive both a weight for each attribute, and a final outlier score using those weights. The weights help separating the relevant attributes from the irrelevant ones, and thus make the approach well suitable for discovering outliers otherwise masked in high-dimensional data. An empirical evaluation shows that our approach outperforms existing algorithms, and is particularly robust in datasets with many irrelevant attributes. Furthermore, we show that if a symbolic machine learning method is used to solve the individual learning problems, the approach is also capable of generating concise explanations for the detected outliers

A decomposition of the outlier detection problem into a set of supervised learning problems