We examined the use of modern Generative Adversarial Nets to generate novel images of oil paintings using the Painter By Numbers dataset. We implemented Spectral Normalization GAN (SN-GAN) and Spectral Normalization GAN with Gradient Penalty, and compared their outputs to a Deep Convolutional GAN. Visually, and quantitatively according to the Sliced Wasserstein Distance metric, we determined that the SN-GAN produced paintings that were most comparable to our training dataset. We then performed a series of experiments to add supervised conditioning to SN-GAN, the culmination of which is what we believe to be a novel architecture that can generate face paintings with user-specified characteristics.
where @math is the real data distribution, @math is the generator's learned distribution, and @math is the classification by the discriminator. At the optimal value for D, this loss function can be rewritten to be in terms of the distance measure known as Jensen-Shannon (JS) divergence between the real and generated distributions @cite_2 .
@cite_2
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Traditional generative adversarial networks (GAN) and many of its variants are trained by minimizing the KL or JS-divergence loss that measures how close the generated data distribution is from the true data distribution. A recent advance called the WGAN based on Wasserstein distance can improve on the KL and JS-divergence based GANs, and alleviate the gradient vanishing, instability, and mode collapse issues that are common in the GAN training. In this work, we aim at improving on the WGAN by first generalizing its discriminator loss to a margin-based one, which leads to a better discriminator, and in turn a better generator, and then carrying out a progressive training paradigm involving multiple GANs to contribute to the maximum margin ranking loss so that the GAN at later stages will improve upon early stages. We call this method Gang of GANs (GoGAN). We have shown theoretically that the proposed GoGAN can reduce the gap between the true data distribution and the generated data distribution by at least half in an optimally trained WGAN. We have also proposed a new way of measuring GAN quality which is based on image completion tasks. We have evaluated our method on four visual datasets: CelebA, LSUN Bedroom, CIFAR-10, and 50K-SSFF, and have seen both visual and quantitative improvement over baseline WGAN. 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 propose in this paper a novel approach to tackle the problem of mode collapse encountered in generative adversarial network (GAN). Our idea is intuitive but proven to be very effective, especially in addressing some key limitations of GAN. In essence, it combines the Kullback-Leibler (KL) and reverse KL divergences into a unified objective function, thus it exploits the complementary statistical properties from these divergences to effectively diversify the estimated density in capturing multi-modes. We term our method dual discriminator generative adversarial nets (D2GAN) which, unlike GAN, has two discriminators; and together with a generator, it also has the analogy of a minimax game, wherein a discriminator rewards high scores for samples from data distribution whilst another discriminator, conversely, favoring data from the generator, and the generator produces data to fool both two discriminators. We develop theoretical analysis to show that, given the maximal discriminators, optimizing the generator of D2GAN reduces to minimizing both KL and reverse KL divergences between data distribution and the distribution induced from the data generated by the generator, hence effectively avoiding the mode collapsing problem. We conduct extensive experiments on synthetic and real-world large-scale datasets (MNIST, CIFAR-10, STL-10, ImageNet), where we have made our best effort to compare our D2GAN with the latest state-of-the-art GAN's variants in comprehensive qualitative and quantitative evaluations. The experimental results demonstrate the competitive and superior performance of our approach in generating good quality and diverse samples over baselines, and the capability of our method to scale up to ImageNet database. In most algorithmic applications which compare two distributions, information theoretic distances are more natural than standard l p norms. In this paper we design streaming and sublinear time property testing algorithms for entropy and various information theoretic distances. posed the problem of property testing with respect to the Jensen-Shannon distance. We present optimal algorithms for estimating bounded, symmetric f-divergences (including the Jensen-Shannon divergence and the Hellinger distance) between distributions in various property testing frameworks. Along the way, we close a (log n) H gap between the upper and lower bounds for estimating entropy H, yielding an optimal algorithm over all values of the entropy. In a data stream setting (sublinear space), we give the first algorithm for estimating the entropy of a distribution. Our algorithm runs in polylogarithmic space and yields an asymptotic constant factor approximation scheme. An integral part of the algorithm is an interesting use of an F 0 (the number of distinct elements in a set) estimation algorithm; we also provide other results along the space time approximation tradeoff curve.Our results have interesting structural implications that connect sublinear time and space constrained algorithms. The mediating model is the random order streaming model, which assumes the input is a random permutation of a multiset and was first considered by Munro and Paterson in 1980. We show that any property testing algorithm in the combined oracle model for calculating a permutation invariant functions can be simulated in the random order model in a single pass. This addresses a question raised by regarding the relationship between property testing and stream algorithms. Further, we give a polylog-space PTAS for estimating the entropy of a one pass random order stream. This bound cannot be achieved in the combined oracle (generalized property testing) model.