Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimator
This work addresses the need for interpretable divergence measures in high-dimensional data for applications like binary classification and two-sample tests, though it appears incremental as it builds on existing MMD methods.
The paper tackles the problem of identifying statistically significant features that discriminate between two distributions by proposing a post selection inference framework using an incomplete maximum mean discrepancy estimator, and demonstrates its effectiveness in synthetic and real-world feature selection experiments.
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.