2019/01/10 by Raif M. Rustamov, Rustamov, Raif M. · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification #Methodology (stat.ME) #Model Reduction and Neural Networks #cs.LG #stat.ME #stat.ML
paper · pdf · doi:10.48550/arxiv.1901.03227
Main paper is considerably shortened by moving some of the material into Appendix
openalex publication_date 2019/01/10 · arxiv created 2020/06/02 · arxiv updated 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the Gaussian kernel based MMD between a given distribution and the standard multivariate normal distribution. This formula reveals a connection to the Baringhaus-Henze-Epps-Pulley (BHEP) statistic of the Henze-Zirkler test and provides further insights about the MMD. We introduce the standardized version of MMD as a penalty for the WAE training objective, allowing for a better interpretability of MMD values and more compatibility across different hyperparameter settings. Next, we propose using a version of batch normalization at the code layer; this has the benefits of making the kernel width selection easier, reducing the training effort, and preventing outliers in the aggregate code distribution. Our experiments on synthetic and real data show that the analytic formulation improves over the commonly used stochastic approximation of the MMD, and demonstrate that code normalization provides significant benefits when training WAEs.