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Generative Adversarial Networks (GANs) have achieved great success in unsupervised learning. Despite the remarkable empirical performance, there are limited theoretical understandings on the statistical properties of GANs. This paper provides statistical guarantees of GANs for the estimation of data distributions which have densities in a H{o}lder space. Our main result shows that, if the generator and discriminator network architectures are properly chosen (universally for all distributions with H{o}lder densities), GANs are consistent estimators of the data distributions under strong discrepancy metrics, such as the Wasserstein distance. To our best knowledge, this is the first statistical theory of GANs for H{o}lder densities. In comparison with existing works, our theory requires minimum assumptions on data distributions. Our generator and discriminator networks utilize general weight matrices and the non-invertible ReLU activation function, while many existing works only apply to invertible weight matrices and invertible activation functions. In our analysis, we decompose the error into a statistical error and an approximation error by a new oracle inequality, which may be of independent interest.
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A Triangle Generative Adversarial Network ($Delta$-GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. $Delta$-GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach.
Conditional Generative Adversarial Networks (cGANs) are generative models that can produce data samples ($x$) conditioned on both latent variables ($z$) and known auxiliary information ($c$). We propose the Bidirectional cGAN (BiCoGAN), which effectively disentangles $z$ and $c$ in the generation process and provides an encoder that learns inverse mappings from $x$ to both $z$ and $c$, trained jointly with the generator and the discriminator. We present crucial techniques for training BiCoGANs, which involve an extrinsic factor loss along with an associated dynamically-tuned importance weight. As compared to other encoder-based cGANs, BiCoGANs encode $c$ more accurately, and utilize $z$ and $c$ more effectively and in a more disentangled way to generate samples.
Generative models are undoubtedly a hot topic in Artificial Intelligence, among which the most common type is Generative Adversarial Networks (GANs). These architectures let one synthesise artificial datasets by implicitly modelling the underlying probability distribution of a real-world training dataset. With the introduction of Conditional GANs and their variants, these methods were extended to generating samples conditioned on ancillary information available for each sample within the dataset. From a practical standpoint, however, one might desire to generate data conditioned on partial information. That is, only a subset of the ancillary conditioning variables might be of interest when synthesising data. In this work, we argue that standard Conditional GANs are not suitable for such a task and propose a new Adversarial Network architecture and training strategy to deal with the ensuing problems. Experiments illustrating the value of the proposed approach in digit and face image synthesis under partial conditioning information are presented, showing that the proposed method can effectively outperform the standard approach under these circumstances.
Ultra-wideband (UWB) radar systems nowadays typical operate in the low frequency spectrum to achieve penetration capability. However, this spectrum is also shared by many others communication systems, which causes missing information in the frequency bands. To recover this missing spectral information, we propose a generative adversarial network, called SARGAN, that learns the relationship between original and missing band signals by observing these training pairs in a clever way. Initial results shows that this approach is promising in tackling this challenging missing band problem.
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the models decision to bounded perturbations. Given a compact subset of the input space $Tsubseteq mathbb{R}^d$, a point $x^*$ and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in $T$. We develop a branch-and-bound scheme to refine the bounds and show, for any $epsilon > 0$, that our algorithm is guaranteed to converge to values $epsilon$-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark datasets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation.
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