  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.
