Forough Fazeli-Asl

Forough Fazeli-Asl, Michael Minyi Zhang

We propose a novel generative model within the Bayesian non-parametric learning (BNPL) framework to address some notable failure modes in generative adversarial networks (GANs) and variational autoencoders (VAEs)--these being overfitting in the GAN case and noisy samples in the VAE case. We will demonstrate that the BNPL framework enhances training stability and provides robustness and accuracy guarantees when incorporating the Wasserstein distance and maximum mean discrepancy measure (WMMD) into our model's loss function. Moreover, we introduce a so-called ``triple model'' that combines the GAN, the VAE, and further incorporates a code-GAN (CGAN) to explore the latent space of the VAE. This triple model design generates high-quality, diverse samples, while the BNPL framework, leveraging the WMMD loss function, enhances training stability. Together, these components enable our model to achieve superior performance across various generative tasks. These claims are supported by both theoretical analyses and empirical validation on a wide variety of datasets.

Forough Fazeli-Asl, Michael Minyi Zhang, Lizhen Lin

A classic inferential statistical problem is the goodness-of-fit (GOF) test. Such a test can be challenging when the hypothesized parametric model has an intractable likelihood and its distributional form is not available. Bayesian methods for GOF can be appealing due to their ability to incorporate expert knowledge through prior distributions. However, standard Bayesian methods for this test often require strong distributional assumptions on the data and their relevant parameters. To address this issue, we propose a semi-Bayesian nonparametric (semi-BNP) procedure in the context of the maximum mean discrepancy (MMD) measure that can be applied to the GOF test. Our method introduces a novel Bayesian estimator for the MMD, enabling the development of a measure-based hypothesis test for intractable models. Through extensive experiments, we demonstrate that our proposed test outperforms frequentist MMD-based methods by achieving a lower false rejection and acceptance rate of the null hypothesis. Furthermore, we showcase the versatility of our approach by embedding the proposed estimator within a generative adversarial network (GAN) framework. It facilitates a robust BNP learning approach as another significant application of our method. With our BNP procedure, this new GAN approach can enhance sample diversity and improve inferential accuracy compared to traditional techniques.