  We consider the problem of detecting anomalies in a large dataset. We propose
a framework called Partial Identification which captures the intuition that
anomalies are easy to distinguish from the overwhelming majority of points by
relatively few attribute values. Formalizing this intuition, we propose a
geometric anomaly measure for a point that we call PIDScore, which measures the
minimum density of data points over all subcubes containing the point. We
present PIDForest: a random forest based algorithm that finds anomalies based
on this definition. We show that it performs favorably in comparison to several
popular anomaly detection methods, across a broad range of benchmarks.
PIDForest also provides a succinct explanation for why a point is labelled
anomalous, by providing a set of features and ranges for them which are
relatively uncommon in the dataset.
