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arXiv 2511.22014cs.LG
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基于距离的超树学习

Distance-based Learning of Hypertrees

Department of Mathematics and Statistics, University of Regina(Regina 大学数学与统计学系);Department of Computer Science, University of Regina(Regina 大学计算机科学系);Department of Computer Science, University of British Columbia(不列颠哥伦比亚大学计算机科学系);Department of Computer Science, Simon Fraser University(Simon Fraser 大学计算机科学系);Alberta Machine Intelligence Institute (Amii)(阿尔伯塔人工智能研究所)

Shaun Fallat, Kamyar Khodamoradi, David Kirkpatrick, Valerii Maliuk, S. Ahmad Mojallal, Sandra Zilles

AI总结:

本文提出了一种基于距离的超树学习方法,针对有序超树设计了可证明最优的在线和离线算法,并探讨了有界距离查询在学习一般超树中的应用。

摘要:

我们研究了使用最短路径查询(SP查询)学习超图的问题,并提出了首个可以证明最优的在线算法,用于一个广泛且自然的超树类,我们称之为有序超树。我们的在线算法可以转换为可以证明最优的离线算法。有序超树可以定位在acyclic超图的Fagin层次结构中(在数据库理论中已广泛研究),并且严格包含该层次结构中最宽的可学习类,其SP查询复杂度为次二次。认识到在某些情况下,例如进化树重建中,距离测量会随着距离增加而退化,我们还考虑了一种使用有界距离查询的学习模型。在此模型中,我们展示了学习一般超树的渐近紧复杂度界。

英文摘要:

We study the problem of learning hypergraphs with shortest-path queries (SP-queries), and present the first provably optimal online algorithm for a broad and natural class of hypertrees that we call orderly hypertrees. Our online algorithm can be transformed into a provably optimal offline algorithm. Orderly hypertrees can be positioned within the Fagin hierarchy of acyclic hypergraph (well-studied in database theory), and strictly encompass the broadest class in this hierarchy that is learnable with subquadratic SP-query complexity. Recognizing that in some contexts, such as evolutionary tree reconstruction, distance measurements can degrade with increased distance, we also consider a learning model that uses bounded distance queries. In this model, we demonstrate asymptotically tight complexity bounds for learning general hypertrees.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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