  This paper proposes an easy-to-compute upper bound for the overlap index
between two probability distributions without requiring any knowledge of the
distribution models. The computation of our bound is time-efficient and
memory-efficient and only requires finite samples. The proposed bound shows its
value in one-class classification and domain shift analysis. Specifically, in
one-class classification, we build a novel one-class classifier by converting
the bound into a confidence score function. Unlike most one-class classifiers,
the training process is not needed for our classifier. Additionally, the
experimental results show that our classifier can be accurate with only a small
number of in-class samples and outperform many state-of-the-art methods on
various datasets in different one-class classification scenarios. In domain
shift analysis, we propose a theorem based on our bound. The theorem is useful
in detecting the existence of domain shift and inferring data information. The
detection and inference processes are both computation-efficient and
memory-efficient. Our work shows significant promise toward broadening the
applications of overlap-based metrics.
