 Edgeworth expansion for semi-hard triplet lossMasanari Kimura Statistics & Probability Letters, 2025, vol. 224, issue C Abstract: We develop a higher-order asymptotic analysis for the semi-hard triplet loss using the Edgeworth expansion. It is known that this loss function enforces that embeddings of similar samples are close while those of dissimilar samples are separated by a specified margin. By refining the classical central limit theorem, our approach quantifies the impact of the margin parameter and the skewness of the underlying data distribution on the loss behavior. In particular, we derive explicit Edgeworth expansions that reveal first-order corrections in terms of the third cumulant, thereby characterizing non-Gaussian effects present in the distribution of distance differences between anchor-positive and anchor-negative pairs. Our findings provide detailed insight into the sensitivity of the semi-hard triplet loss to its parameters and offer guidance for choosing the margin to ensure training stability. Keywords: Metric learning; Triplet loss; Asymptotic analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225000860 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2025.110441 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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