This paper initiates the study of active learning for exact recovery of partitions exclusively through access to a same-cluster oracle in the presence of bounded adversarial error. We first highlight a novel connection between learning partitions and correlation clustering. Then we use this connection to build a R\'enyi-Ulam style analytical framework for this problem, and prove upper and lower bounds on its worst-case query complexity. Further, we bound the expected performance of a relevant randomized algorithm. Finally, we study the relationship between adaptivity and query complexity for this problem and related variants.

翻译：本文首次研究了在有限对抗误差环境下，仅通过同簇查询（same-cluster oracle）实现划分精确恢复的主动学习问题。我们首先揭示了划分学习与关联聚类（correlation clustering）之间的新颖联系，进而利用该联系构建了针对该问题的Rényi-Ulam分析框架，证明了其最坏情况查询复杂度的上界与下界。此外，我们界定了相关随机算法的期望性能，并探讨了自适应性与查询复杂度在该问题及其变体中的关系。