An Upper Bound for the Distribution Overlap Index and Its Applications

• URL: http://arxiv.org/abs/2212.08701v1
• Date: Fri, 16 Dec 2022 20:02:03 GMT
• Title: An Upper Bound for the Distribution Overlap Index and Its Applications
• Authors: Hao Fu, Prashanth Krishnamurthy, Siddharth Garg, Farshad Khorrami
• Abstract summary: This paper proposes an easy-to-compute upper bound for the overlap index between two probability distributions. The proposed bound shows its value in one-class classification and domain shift analysis. Our work shows significant promise toward broadening the applications of overlap-based metrics.
• Score: 18.481370450591317
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \textcolor{\colorname}{can be accurate with} only a small number of in-class samples and outperforms 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.

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