We propose a novel statistical method for testing the results of anomaly
detection (AD) under domain adaptation (DA), which we call CAD-DA --
controllable AD under DA. The distinct advantage of the CAD-DA lies in its
ability to control the probability of misidentifying anomalies under a
pre-specified level $\alpha$ (e.g., 0.05). The challenge within this DA setting
is the necessity to account for the influence of DA to ensure the validity of
the inference results. Our solution to this challenge leverages the concept of
conditional Selective Inference to handle the impact of DA. To our knowledge,
this is the first work capable of conducting a valid statistical inference
within the context of DA. We evaluate the performance of the CAD-DA method on
both synthetic and real-world datasets.

我们提出了一种新颖的统计方法，用于在域适应（DA）下测试异常检测（AD）的结果，称为 CAD-DA -- 在 DA 下可控制的 AD。CAD-DA 的独特优势在于其能够控制在预先指定的水平 α（例如 0.05）下错误识别异常的概率。我们解决了在这个 DA 设置中需要考虑 DA 影响以确保推理结果有效性的挑战。我们的解决方案利用条件选择性推理的概念来处理 DA 的影响。据我们所知，这是第一个在 DA 背景下进行有效统计推理的工作。我们对 CAD-DA 方法在合成和真实数据集上的性能进行了评估。