An Upper Bound for the Distribution Overlap Index and Its Applications

TL;DR

This paper introduces a computationally efficient upper bound for the overlap index between probability distributions, enabling improved one-class classification and domain shift detection with minimal data and no distribution knowledge.

Contribution

It presents a novel, easy-to-compute upper bound for the overlap index, facilitating new applications in classification and domain analysis without requiring distribution models or extensive training.

Findings

The bound is computationally efficient and requires only finite samples.

The proposed classifier achieves high accuracy with few in-class samples.

The theorem effectively detects domain shifts and infers data information.

Abstract

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.