  Outlier detection aims to identify unusual data instances that deviate from
expected patterns. The outlier detection is particularly challenging when
outliers are context dependent and when they are defined by unusual
combinations of multiple outcome variable values. In this paper, we develop and
study a new conditional outlier detection approach for multivariate outcome
spaces that works by (1) transforming the conditional detection to the outlier
detection problem in a new (unconditional) space and (2) defining outlier
scores by analyzing the data in the new space. Our approach relies on the
classifier chain decomposition of the multi-dimensional classification problem
that lets us transform the output space into a probability vector, one
probability for each dimension of the output space. Outlier scores applied to
these transformed vectors are then used to detect the outliers. Experiments on
multiple multi-dimensional classification problems with the different outlier
injection rates show that our methodology is robust and able to successfully
identify outliers when outliers are either sparse (manifested in one or very
few dimensions) or dense (affecting multiple dimensions).
