We consider the problem of transfer learning in Neyman-Pearson classification, where the objective is to minimize the error w.r.t. a distribution $\mu_1$, subject to the constraint that the error w.r.t. a distribution $\mu_0$ remains below a prescribed threshold. While transfer learning has been extensively studied in traditional classification, transfer learning in imbalanced classification such as Neyman-Pearson classification has received much less attention. This setting poses unique challenges, as both types of errors must be simultaneously controlled. Existing works address only the case of distribution shift in $\mu_1$, whereas in many practical scenarios shifts may occur in both $\mu_0$ and $\mu_1$. We derive an adaptive procedure that not only guarantees improved Type-I and Type-II errors when the source is informative, but also automatically adapt to situations where the source is uninformative, thereby avoiding negative transfer. In addition to such statistical guarantees, the procedures is efficient, as shown via complementary computational guarantees.

翻译：本文研究Neyman-Pearson分类框架下的迁移学习问题，其目标是在确保分布$\mu_0$下的误差不超过预设阈值的前提下，最小化分布$\mu_1$下的分类误差。尽管迁移学习在传统分类任务中已得到广泛研究，但在Neyman-Pearson分类这类非平衡分类场景中的迁移学习却鲜有关注。该设定带来独特挑战，因为需要同时控制两类误差。现有研究仅处理$\mu_1$分布偏移的情况，然而在实际场景中$\mu_0$与$\mu_1$可能同时发生偏移。我们提出一种自适应方法，不仅能在源域信息有效时保证改进的I类与II类误差，还能在源域信息无效时自动调整以避免负迁移效应。除统计性能保证外，该方法通过计算复杂度分析证明其高效性。