  Measuring divergence between two distributions is essential in machine
learning and statistics and has various applications including binary
classification, change point detection, and two-sample test. Furthermore, in
the era of big data, designing divergence measure that is interpretable and can
handle high-dimensional and complex data becomes extremely important. In the
paper, we propose a post selection inference (PSI) framework for divergence
measure, which can select a set of statistically significant features that
discriminate two distributions. Specifically, we employ an additive variant of
maximum mean discrepancy (MMD) for features and introduce a general hypothesis
test for PSI. A novel MMD estimator using the incomplete U-statistics, which
has an asymptotically Normal distribution (under mild assumptions) and gives
high detection power in PSI, is also proposed and analyzed theoretically.
Through synthetic and real-world feature selection experiments, we show that
the proposed framework can successfully detect statistically significant
features. Last, we propose a sample selection framework for analyzing different
members in the Generative Adversarial Networks (GANs) family.
