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Register a new userAn error analysis of generative adversarial networks for learning distributions
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Yunfei Yang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through Holder classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have Holder densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.
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Generative Adversarial Networks (GANs) based semi-supervised learning (SSL) approaches are shown to improve classification performance by utilizing a large number of unlabeled samples in conjunction with limited labeled samples. However, their performance still lags behind the state-of-the-art non-GAN based SSL approaches. We identify that the main reason for this is the lack of consistency in class probability predictions on the same image under local perturbations. Following the general literature, we address this issue via label consistency regularization, which enforces the class probability predictions for an input image to be unchanged under various semantic-preserving perturbations. In this work, we introduce consistency regularization into the vanilla semi-GAN to address this critical limitation. In particular, we present a new composite consistency regularization method which, in spirit, leverages both local consistency and interpolation consistency. We demonstrate the efficacy of our approach on two SSL image classification benchmark datasets, SVHN and CIFAR-10. Our experiments show that this new composite consistency regularization based semi-GAN significantly improves its performance and achieves new state-of-the-art performance among GAN-based SSL approaches.
We propose a unified game-theoretical framework to perform classification and conditional image generation given limited supervision. It is formulated as a three-player minimax game consisting of a generator, a classifier and a discriminator, and therefore is referred to as Triple Generative Adversarial Network (Triple-GAN). The generator and the classifier characterize the conditional distributions between images and labels to perform conditional generation and classification, respectively. The discriminator solely focuses on identifying fake image-label pairs. Under a nonparametric assumption, we prove the unique equilibrium of the game is that the distributions characterized by the generator and the classifier converge to the data distribution. As a byproduct of the three-player mechanism, Triple-GAN is flexible to incorporate different semi-supervised classifiers and GAN architectures. We evaluate Triple-GAN in two challenging settings, namely, semi-supervised learning and the extreme low data regime. In both settings, Triple-GAN can achieve excellent classification results and generate meaningful samples in a specific class simultaneously. In particular, using a commonly adopted 13-layer CNN classifier, Triple-GAN outperforms extensive semi-supervised learning methods substantially on more than 10 benchmarks no matter data augmentation is applied or not.
Generative Adversarial Networks (GANs) are performant generative methods yielding high-quality samples. However, under certain circumstances, the training of GANs can lead to mode collapse or mode dropping, i.e. the generative models not being able to sample from the entire probability distribution. To address this problem, we use the last layer of the discriminator as a feature map to study the distribution of the real and the fake data. During training, we propose to match the real batch diversity to the fake batch diversity by using the Bures distance between covariance matrices in feature space. The computation of the Bures distance can be conveniently done in either feature space or kernel space in terms of the covariance and kernel matrix respectively. We observe that diversity matching reduces mode collapse substantially and has a positive effect on the sample quality. On the practical side, a very simple training procedure, that does not require additional hyperparameter tuning, is proposed and assessed on several datasets.
This paper explores a simple regularizer for reinforcement learning by proposing Generative Adversarial Self-Imitation Learning (GASIL), which encourages the agent to imitate past good trajectories via generative adversarial imitation learning framework. Instead of directly maximizing rewards, GASIL focuses on reproducing past good trajectories, which can potentially make long-term credit assignment easier when rewards are sparse and delayed. GASIL can be easily combined with any policy gradient objective by using GASIL as a learned shaped reward function. Our experimental results show that GASIL improves the performance of proximal policy optimization on 2D Point Mass and MuJoCo environments with delayed reward and stochastic dynamics.
The standard practice in Generative Adversarial Networks (GANs) discards the discriminator during sampling. However, this sampling method loses valuable information learned by the discriminator regarding the data distribution. In this work, we propose a collaborative sampling scheme between the generator and the discriminator for improved data generation. Guided by the discriminator, our approach refines the generated samples through gradient-based updates at a particular layer of the generator, shifting the generator distribution closer to the real data distribution. Additionally, we present a practical discriminator shaping method that can smoothen the loss landscape provided by the discriminator for effective sample refinement. Through extensive experiments on synthetic and image datasets, we demonstrate that our proposed method can improve generated samples both quantitatively and qualitatively, offering a new degree of freedom in GAN sampling.
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