We propose two neural network based mixture models in this article. The proposed mixture models are explicit in nature. The explicit models have analytical forms with the advantages of computing likelihood and efficiency of generating samples. Computation of likelihood is an important aspect of our models. Expectation-maximization based algorithms are developed for learning parameters of the proposed models. We provide sufficient conditions to realize the expectation-maximization based learning. The main requirements are invertibility of neural networks that are used as generators and Jacobian computation of functional form of the neural networks. The requirements are practically realized using a flow-based neural network. In our first mixture model, we use multiple flow-based neural networks as generators. Naturally the model is complex. A single latent variable is used as the common input to all the neural networks. The second mixture model uses a single flow-based neural network as a generator to reduce complexity. The single generator has a latent variable input that follows a Gaussian mixture distribution. We demonstrate efficiency of proposed mixture models through extensive experiments for generating samples and maximum likelihood based classification.
While GANs have high success in many applications, they are known to suffer in a mode dropping problem where a generator of a GAN is unable to capture all modes of an underlying probability distribution of data @cite_13 . To address diversity in data and model multiple modes in a distribution, variants of generative models have been developed and usage of multiple generators has been considered. For instance, methods of minibatch discrimination @cite_27 and feature representation @cite_10 are used to construct new discriminators of GANs which encourage the GANs to generate samples with diversity. Multiple Wasserstein GANs @cite_18 are used in @cite_13 with appropriate mutual information based regularization to encourage the diversity of samples generated by different GANs. A mixture GAN approach is proposed in @cite_26 using multiple generators and multi-classification solution to encourage diversity of samples. Multi-agent diverse GAN @cite_12 similarly employs @math generators, but uses a @math -class discriminator instead of a typical binary discriminator to increase the diversity of generated samples. These works are implicit probability distribution modeling and thus prior distribution of generators can not be inferred when multiple generators are used.
@cite_13 @cite_18 @cite_26 @cite_27 @cite_10 @cite_12
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Real images often lie on a union of disjoint manifolds rather than one globally connected manifold, and this can cause several difficulties for the training of common Generative Adversarial Networks (GANs). In this work, we first show that single generator GANs are unable to correctly model a distribution supported on a disconnected manifold, and investigate how sample quality, mode collapse and local convergence are affected by this. Next, we show how using a collection of generators can address this problem, providing new insights into the success of such multi-generator GANs. Finally, we explain the serious issues caused by considering a fixed prior over the collection of generators and propose a novel approach for learning the prior and inferring the necessary number of generators without any supervision. Our proposed modifications can be applied on top of any other GAN model to enable learning of distributions supported on disconnected manifolds. We conduct several experiments to illustrate the aforementioned shortcoming of GANs, its consequences in practice, and the effectiveness of our proposed modifications in alleviating these issues. We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. We present a variety of new architectural features and training procedures that we apply to the generative adversarial networks (GANs) framework. Using our new techniques, we achieve state-of-the-art results in semi-supervised classification on MNIST, CIFAR-10 and SVHN. The generated images are of high quality as confirmed by a visual Turing test: our model generates MNIST samples that humans cannot distinguish from real data, and CIFAR-10 samples that yield a human error rate of 21.3 . We also present ImageNet samples with unprecedented resolution and show that our methods enable the model to learn recognizable features of ImageNet classes. Despite of the success of Generative Adversarial Networks (GANs) for image generation tasks, the trade-off between image diversity and visual quality are an well-known issue. Conventional techniques achieve either visual quality or image diversity; the improvement in one side is often the result of sacrificing the degradation in the other side. In this paper, we aim to achieve both simultaneously by improving the stability of training GANs. A key idea of the proposed approach is to implicitly regularizing the discriminator using a representative feature. For that, this representative feature is extracted from the data distribution, and then transferred to the discriminator for enforcing slow updates of the gradient. Consequently, the entire training process is stabilized because the learning curve of discriminator varies slowly. Based on extensive evaluation, we demonstrate that our approach improves the visual quality and diversity of state-of-the art GANs. This paper describes an intuitive generalization to the Generative Adversarial Networks (GANs) to generate samples while capturing diverse modes of the true data distribution. Firstly, we propose a very simple and intuitive multi-agent GAN architecture that incorporates multiple generators capable of generating samples from high probability modes. Secondly, in order to enforce different generators to generate samples from diverse modes, we propose two extensions to the standard GAN objective function. (1) We augment the generator specific GAN objective function with a diversity enforcing term that encourage different generators to generate diverse samples using a user-defined similarity based function. (2) We modify the discriminator objective function where along with finding the real and fake samples, the discriminator has to predict the generator which generated the given fake sample. Intuitively, in order to succeed in this task, the discriminator must learn to push different generators towards different identifiable modes. Our framework is generalizable in the sense that it can be easily combined with other existing variants of GANs to produce diverse samples. Experimentally we show that our framework is able to produce high quality diverse samples for the challenging tasks such as image face generation and image-to-image translation. We also show that it is capable of learning a better feature representation in an unsupervised setting.