We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erd\"{o}s-R\'{e}nyi uniform random hypergraph and the alternative hypothesis corresponds to a heterogeneous uniform random hypergraph that contains a dense subhypergraph. We establish detection boundaries when the edge probabilities are known and construct an asymptotically powerful test for distinguishing the hypotheses. We also construct an adaptive test which does not involve edge probabilities, and hence, is more practically useful.

翻译：我们研究测试多种族稠密次血压存在的问题。 无效假设相当于异种Erd\"{ o}s- R\' e}nyi uni unific 随机测高仪, 而替代假设则相当于异种统一的随机测高仪, 包含密密密次血压。 当边缘概率为人所知时, 我们设定探测界限, 并构建一个无症状的测试, 以区分假设。 我们还构建了一个适应性测试, 它不涉及边缘概率, 因此, 更实际有用 。