Neyman-Pearson Classification under Both Null and Alternative Distributions Shift
This addresses a gap in imbalanced classification for scenarios where both error types must be controlled under distribution shifts, which is incremental as it extends existing work from single-distribution shifts.
The paper tackles the problem of transfer learning in Neyman-Pearson classification under distribution shifts in both null and alternative distributions, deriving an adaptive procedure that guarantees improved Type-I and Type-II errors when the source is informative and avoids negative transfer when it is uninformative, with complementary computational guarantees.
We consider the problem of transfer learning in Neyman-Pearson classification, where the objective is to minimize the error w.r.t. a distribution $μ_1$, subject to the constraint that the error w.r.t. a distribution $μ_0$ 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 $μ_1$, whereas in many practical scenarios shifts may occur in both $μ_0$ and $μ_1$. 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.