Bayesian Nonparametric Learning using the Maximum Mean Discrepancy Measure for Synthetic Data Generation

We introduce a Bayesian estimator for maximum mean discrepancy (MMD), enabling a novel approach to measure-based data generation. To demonstrate the adaptability of our method, we embed this estimator within a generative adversarial network (GAN) framework. This integration offers a powerful avenue for Bayesian nonparametric (BNP) learning, showcasing the estimator's broad applicability. Our BNP-driven GAN not only enhances sample diversity but also improves inferential accuracy, surpassing the performance of traditional methods. Further theoretical properties, proofs, and experiments are given by the Appendix.