  Despite tremendous progress in outlier detection research in recent years,
the majority of existing methods are designed only to detect unconditional
outliers that correspond to unusual data patterns expressed in the joint space
of all data attributes. Such methods are not applicable when we seek to detect
conditional outliers that reflect unusual responses associated with a given
context or condition. This work focuses on multivariate conditional outlier
detection, a special type of the conditional outlier detection problem, where
data instances consist of multi-dimensional input (context) and output
(responses) pairs. We present a novel outlier detection framework that
identifies abnormal input-output associations in data with the help of a
decomposable conditional probabilistic model that is learned from all data
instances. Since components of this model can vary in their quality, we combine
them with the help of weights reflecting their reliability in assessment of
outliers. We study two ways of calculating the component weights: global that
relies on all data, and local that relies only on instances similar to the
target instance. Experimental results on data from various domains demonstrate
the ability of our framework to successfully identify multivariate conditional
outliers.
