  We present a new subspace-based method to construct probabilistic models for
high-dimensional data and highlight its use in anomaly detection. The approach
is based on a statistical estimation of probability density using densities of
random subspaces combined with geometric averaging. In selecting random
subspaces, equal representation of each attribute is used to ensure correct
statistical limits. Gaussian mixture models (GMMs) are used to create the
probability densities for each subspace with techniques included to mitigate
singularities allowing for the ability to handle both numerical and categorial
attributes. The number of components for each GMM is determined automatically
through Bayesian information criterion to prevent overfitting. The proposed
algorithm attains competitive AUC scores compared with prominent algorithms
against benchmark anomaly detection datasets with the added benefits of being
simple, scalable, and interpretable.
