  We study statistical inference on the similarity/distance between two
time-series under uncertain environment by considering a statistical hypothesis
test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The
sampling distribution of the DTW distance is too difficult to derive because it
is obtained based on the solution of the DTW algorithm, which is complicated.
To circumvent this difficulty, we propose to employ the conditional selective
inference framework, which enables us to derive a valid inference method on the
DTW distance. To our knowledge, this is the first method that can provide a
valid p-value to quantify the statistical significance of the DTW distance,
which is helpful for high-stake decision making such as abnormal time-series
detection problems. We evaluate the performance of the proposed inference
method on both synthetic and real-world datasets.
