隐超图的多阶段学习
On Multistage Learning a Hidden Hypergraph
摘要：
学习一个隐藏超图是一个自然推广的经典组测试问题，包括在检测未知超图$H_{un}=H(V,E)$进行边缘检测测试。在给定的论文中，我们仅将注意力集中在特定的局部超图族$F(t,s,\ell)$上，其中顶点总数$|V| = t$、边数$|E|\le s$、$s\ll t$以及任何边的基数$|e|\le\ell$、$\ell\ll t$。我们的目标是通过使用最少数量的测试来识别$H_{un}\in F(t,s,\ell)$的所有边缘。我们开发了一个自适应算法，匹配的信息论界，即，最坏情况下算法的测试总数至多为$s\ell\log_2 t(1+o(1))$。我们还讨论了一个概率推广的问题。
英文摘要：
Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family $F(t,s,\ell)$ of localized hypergraphs for which the total number of vertices $|V| = t$, the number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge $|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in F(t,s,\ell)$ by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most $s\ell\log_2 t(1+o(1))$. We also discuss a probabilistic generalization of the problem.
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。
