text: A class of recent approaches for generating images, called Generative Adversarial Networks (GAN), have been used to generate impressively realistic images of objects, bedrooms, handwritten digits and a variety of other image modalities. However, typical GAN-based approaches require large amounts of training data to capture the diversity across the image modality. In this paper, we propose DeLiGAN -- a novel GAN-based architecture for diverse and limited training data scenarios. In our approach, we reparameterize the latent generative space as a mixture model and learn the mixture model's parameters along with those of GAN. This seemingly simple modification to the GAN framework is surprisingly effective and results in models which enable diversity in generated samples although trained with limited data. In our work, we show that DeLiGAN can generate images of handwritten digits, objects and hand-drawn sketches, all using limited amounts of data. To quantitatively characterize intra-class diversity of generated samples, we also introduce a modified version of "inception-score", a measure which has been found to correlate well with human assessment of generated samples.
  @cite_13: Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of variational approximations inspired by nonparametric kernel density estimation. The locations of these kernels and their bandwidth are treated as variational parameters and optimized to improve an approximate lower bound on the marginal likelihood of the data. Using multiple kernels allows the approximation to capture multiple modes of the posterior, unlike most other variational approximations. We demonstrate the efficacy of the nonparametric approximation with a hierarchical logistic regression model and a nonlinear matrix factorization model. We obtain predictive performance as good as or better than more specialized variational methods and sample-based approximations. The method is easy to apply to more general graphical models for which standard variational methods are difficult to derive.
  @cite_22: 
  @cite_16: The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.
  @cite_10: The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed flow consists of a chain of invertible transformations, where each transformation is based on an autoregressive neural network. In experiments, we show that IAF significantly improves upon diagonal Gaussian approximate posteriors. In addition, we demonstrate that a novel type of variational autoencoder, coupled with IAF, is competitive with neural autoregressive models in terms of attained log-likelihood on natural images, while allowing significantly faster synthesis.
  @cite_17: This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simpified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally we return to the examples and demonstrate how variational algorithms can be formulated in each case.
summary: Our central idea -- utilizing a mixture model for latent space -- has been suggested in various papers, but mostly in the context of variational inference. For example, @cite_13 , @cite_17 and @cite_22 model the approximate posterior of the inferred latent distribution as a mixture model to represent more complicated distributions. More recently, @cite_16 and @cite_10 propose normalizing flows' to transform the latent probability density through a series of invertible mappings to construct a complex distribution. In the context of GANs, no such approaches exist, to the best of our knowledge.