  Non-parametric and distribution-free two-sample tests have been the
foundation of many change point detection algorithms. However, randomness in
the test statistic as a function of time makes them susceptible to false
positives and localization ambiguity. We address these issues by deriving and
applying filters matched to the expected temporal signatures of a change for
various sliding window, two-sample tests under IID assumptions on the data.
These filters are derived asymptotically with respect to the window size for
the Wasserstein quantile test, the Wasserstein-1 distance test, Maximum Mean
Discrepancy squared (MMD^2), and the Kolmogorov-Smirnov (KS) test. The matched
filters are shown to have two important properties. First, they are
distribution-free, and thus can be applied without prior knowledge of the
underlying data distributions. Second, they are peak-preserving, which allows
the filtered signal produced by our methods to maintain expected statistical
significance. Through experiments on synthetic data as well as activity
recognition benchmarks, we demonstrate the utility of this approach for
mitigating false positives and improving the test precision. Our method allows
for the localization of change points without the use of ad-hoc post-processing
to remove redundant detections common to current methods. We further highlight
the performance of statistical tests based on the Quantile-Quantile (Q-Q)
function and show how the invariance property of the Q-Q function to
order-preserving transformations allows these tests to detect change points of
different scales with a single threshold within the same dataset.
