Post Selection Inference with Incomplete Maximum Mean Discrepancy Estimator

Abstract

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.

References in corpus (11)

• Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
• Spectral Normalization for Generative Adversarial Networks
• Improved Techniques for Training GANs
• BEGAN: Boundary Equilibrium Generative Adversarial Networks
• Change-Point Detection in Time-Series Data by Relative Density-Ratio Estimation
• Generative Moment Matching Networks
• The Cramer Distance as a Solution to Biased Wasserstein Gradients
• A Kernel Method for the Two-Sample Problem
• Mode Regularized Generative Adversarial Networks
• Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy
• Interpretable Distribution Features with Maximum Testing Power