Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, where (ideally) each network models a single mode. In this paper, we introduce a principled method for training an ensemble of GANs using semi-discrete optimal transport theory. In our approach, each generative network models the transportation map between a point mass (Dirac measure) and the restriction of the data distribution on a tile of a Voronoi tessellation that is defined by the location of the point masses. We iteratively train the generative networks and the point masses until convergence. The resulting k-GANs algorithm has strong theoretical connection with the k-medoids algorithm. In our experiments, we show that our ensemble method consistently outperforms baseline GANs.
Generative Adversarial Networks (GANs) are commonly used for modeling complex distributions of data. Both the generators and discriminators of GANs are often modeled by neural networks, posing a non-transparent optimization problem which is non-convex and non-concave over the generator and discriminator, respectively. Such networks are often heuristically optimized with gradient descent-ascent (GDA), but it is unclear whether the optimization problem contains any saddle points, or whether heuristic methods can find them in practice. In this work, we analyze the training of Wasserstein GANs wit…
The field of deep generative modeling is dominated by generative adversarial networks (GANs). However, the training of GANs often lacks stability, fails to converge, and suffers from model collapse. It takes an assortment of tricks to solve these problems, which may be difficult to understand for those seeking to apply generative modeling. Instead, we propose two novel generative autoencoders, AE-OTtrans and AE-OTgen, which rely on optimal transport instead of adversarial training. AE-OTtrans and AEOTgen, unlike VAE and WAE, preserve the manifold of the data; they do not force the latent distr…
Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine learning, in that they are best described as a two-player game between a discriminator and generator. This has yielded both unreliability in the training process, and a general lack of understanding as to how GANs converge, and if so, to what. The purpose of this dissertation is to provide an account of the theory of GANs suitable for the mathematician, high…
University of Maryland, College Park（马里兰大学帕克分校）；University of Pennsylvania（宾夕法尼亚大学）
Building on the success of deep learning, two modern approaches to learn a probability model from the data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohib…
University of Michigan（密歇根大学）；Chinese Academy of Sciences（中国科学院）；Nanyang Technological University（南洋理工大学）；University of Sydney（悉尼大学）；DiDi AI Labs（滴滴人工智能实验室）
Generative adversarial networks (GANs) are a hot research topic recently. GANs have been widely studied since 2014, and a large number of algorithms have been proposed. However, there is few comprehensive study explaining the connections among different GANs variants, and how they have evolved. In this paper, we attempt to provide a review on various GANs methods from the perspectives of algorithms, theory, and applications. Firstly, the motivations, mathematical representations, and structure of most GANs algorithms are introduced in details. Furthermore, GANs have been combined with other ma…
International Institute of Information Technology（国际信息技术学院）
In recent years, Generative Adversarial Networks (GANs) have received significant attention from the research community. With a straightforward implementation and outstanding results, GANs have been used for numerous applications. Despite the success, GANs lack a proper theoretical explanation. These models suffer from issues like mode collapse, non-convergence, and instability during training. To address these issues, researchers have proposed theoretically rigorous frameworks inspired by varied fields of Game theory, Statistical theory, Dynamical systems, etc. In this paper, we propose to gi…
We propose Unbalanced GANs, which pre-trains the generator of the generative adversarial network (GAN) using variational autoencoder (VAE). We guarantee the stable training of the generator by preventing the faster convergence of the discriminator at early epochs. Furthermore, we balance between the generator and the discriminator at early epochs and thus maintain the stabilized training of GANs. We apply Unbalanced GANs to well known public datasets and find that Unbalanced GANs reduce mode collapses. We also show that Unbalanced GANs outperform ordinary GANs in terms of stabilized learning, …
Google Research（谷歌研究院）；CIMS（库朗数学科学研究所）；New York University（纽约大学）
Generative adversarial networks (GANs) generate data based on minimizing a divergence between two distributions. The choice of that divergence is therefore critical. We argue that the divergence must take into account the hypothesis set and the loss function used in a subsequent learning task, where the data generated by a GAN serves for training. Taking that structural information into account is also important to derive generalization guarantees. Thus, we propose to use the discrepancy measure, which was originally introduced for the closely related problem of domain adaptation and which pre…
Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are easily available. However, in many applications, this assumption is violated. In this paper, we consider the observation setting when the samples from target distribution are given by the superposition of two structured components and leverage GANs for learning the structure of the components. We propose two novel frameworks: denoising-GAN and demixing-GAN.…
Singapore Management University（新加坡管理大学）；Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
Realistic fine-grained multi-agent simulation of real-world complex systems is crucial for many downstream tasks such as reinforcement learning. Recent work has used generative models (GANs in particular) for providing high-fidelity simulation of real-world systems. However, such generative models are often monolithic and miss out on modeling the interaction in multi-agent systems. In this work, we take a first step towards building multiple interacting generative models (GANs) that reflects the interaction in real world. We build and analyze a hierarchical set-up where a higher-level GAN is c…
Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distributions that have densities in a Hölder space. Our main result shows that, if the generator and discriminator network architectures are properly chosen, GANs are consistent estimators of data distributions under strong discrepancy metrics, such as the Wasserstein-1 distance. Furt…
A wide variety of deep generative models has been developed in the past decade. Yet, these models often struggle with simultaneously addressing three key requirements including: high sample quality, mode coverage, and fast sampling. We call the challenge imposed by these requirements the generative learning trilemma, as the existing models often trade some of them for others. Particularly, denoising diffusion models have shown impressive sample quality and diversity, but their expensive sampling does not yet allow them to be applied in many real-world applications. In this paper, we argue that…
Most current computer vision datasets are composed of disconnected sets, such as images from different classes. We prove that distributions of this type of data cannot be represented with a continuous generative network without error. They can be represented in two ways: With an ensemble of networks or with a single network with truncated latent space. We show that ensembles are more desirable than truncated distributions in practice. We construct a regularized optimization problem that establishes the relationship between a single continuous GAN, an ensemble of GANs, conditional GANs, and Gau…
A recent technical breakthrough in the domain of machine learning is the discovery and the multiple applications of Generative Adversarial Networks (GANs). Those generative models are computationally demanding, as a GAN is composed of two deep neural networks, and because it trains on large datasets. A GAN is generally trained on a single server. In this paper, we address the problem of distributing GANs so that they are able to train over datasets that are spread on multiple workers. MD-GAN is exposed as the first solution for this problem: we propose a novel learning procedure for GANs so th…
Generative Adversarial Networks (GANs) have been promising in the field of image generation, however, they have been hard to train for language generation. GANs were originally designed to output differentiable values, so discrete language generation is challenging for them which causes high levels of instability in training GANs. Consequently, past work has resorted to pre-training with maximum-likelihood or training GANs without pre-training with a WGAN objective with a gradient penalty. In this study, we present a comparison of those approaches. Furthermore, we present the results of some e…
The University of Adelaide（阿德莱德大学）；Queensland University of Technology（昆士兰科技大学）；CMU（卡内基梅隆大学）
Traditional GANs use a deterministic generator function (typically a neural network) to transform a random noise input $z$ to a sample $\mathbf{x}$ that the discriminator seeks to distinguish. We propose a new GAN called Bayesian Conditional Generative Adversarial Networks (BC-GANs) that use a random generator function to transform a deterministic input $y'$ to a sample $\mathbf{x}$. Our BC-GANs extend traditional GANs to a Bayesian framework, and naturally handle unsupervised learning, supervised learning, and semi-supervised learning problems. Experiments show that the proposed BC-GANs outpe…
Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distribu…
In this paper, we show that Generative Adversarial Networks (GANs) suffer from catastrophic forgetting even when they are trained to approximate a single target distribution. We show that GAN training is a continual learning problem in which the sequence of changing model distributions is the sequence of tasks to the discriminator. The level of mismatch between tasks in the sequence determines the level of forgetting. Catastrophic forgetting is interrelated to mode collapse and can make the training of GANs non-convergent. We investigate the landscape of the discriminator's output in different…
Generative adversarial networks (GANs) are a powerful framework for generative tasks. However, they are difficult to train and tend to miss modes of the true data generation process. Although GANs can learn a rich representation of the covered modes of the data in their latent space, the framework misses an inverse mapping from data to this latent space. We propose Invariant Encoding Generative Adversarial Networks (IVE-GANs), a novel GAN framework that introduces such a mapping for individual samples from the data by utilizing features in the data which are invariant to certain transformation…
Filtering out unrealistic images from trained generative adversarial networks (GANs) has attracted considerable attention recently. Two density ratio based subsampling methods---Discriminator Rejection Sampling (DRS) and Metropolis-Hastings GAN (MH-GAN)---were recently proposed, and their effectiveness in improving GANs was demonstrated on multiple datasets. However, DRS and MH-GAN are based on discriminator based density ratio estimation (DRE) methods, so they may not work well if the discriminator in the trained GAN is far from optimal. Moreover, they do not apply to some GANs (e.g., MMD-GAN…
Qian Xuesen Laboratory of Space Technology（钱学森空间技术实验室）；China Academy of Space Technology（中国空间技术研究院）
Generative adversarial networks (GANs) have attracted intense interest in the field of generative models. However, few investigations focusing either on the theoretical analysis or on algorithm design for the approximation ability of the generator of GANs have been reported. This paper will first theoretically analyze GANs' approximation property. Similar to the universal approximation property of the fully connected neural networks with one hidden layer, we prove that the generator with the input latent variable in GANs can universally approximate the potential data distribution given the inc…
University of Liverpool（利物浦大学）；Alibaba Group（阿里巴巴集团）
Generative adversarial networks (GANs) are powerful generative models, but usually suffer from instability and generalization problem which may lead to poor generations. Most existing works focus on stabilizing the training of the discriminator while ignoring the generalization properties. In this work, we aim to improve the generalization capability of GANs by promoting the local robustness within the small neighborhood of the training samples. We also prove that the robustness in small neighborhood of training sets can lead to better generalization. Particularly, we design a robust optimizat…
Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are compared and contrasted, explaining the premises behind each and how they are interrelated,…
MILA（蒙特利尔学习算法研究所）；University of Montréal（蒙特利尔大学）；IVADO（魁北克人工智能研究所）；MSR（微软研究院）；University of Waterloo（滑铁卢大学）；New York University（纽约大学）；CIFAR（加拿大高级研究所）
Generative adversarial networks (GANs) are a learning framework that rely on training a discriminator to estimate a measure of difference between a target and generated distributions. GANs, as normally formulated, rely on the generated samples being completely differentiable w.r.t. the generative parameters, and thus do not work for discrete data. We introduce a method for training GANs with discrete data that uses the estimated difference measure from the discriminator to compute importance weights for generated samples, thus providing a policy gradient for training the generator. The importa…
Generative Adversarial Networks (GANs) are one of the most popular tools for learning complex high dimensional distributions. However, generalization properties of GANs have not been well understood. In this paper, we analyze the generalization of GANs in practical settings. We show that discriminators trained on discrete datasets with the original GAN loss have poor generalization capability and do not approximate the theoretically optimal discriminator. We propose a zero-centered gradient penalty for improving the generalization of the discriminator by pushing it toward the optimal discrimin…
Generative Adversarial Networks (GANs) are a revolutionary class of Deep Neural Networks (DNNs) that have been successfully used to generate realistic images, music, text, and other data. However, GAN training presents many challenges, notably it can be very resource-intensive. A potential weakness in GANs is that it requires a lot of data for successful training and data collection can be an expensive process. Typically, the corrective feedback from discriminator DNNs to generator DNNs (namely, the discriminator's assessment of the generated example) is calculated using only one real-numbered…
Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection in GANs to cluster, we demonstrate that the cluster structure is not retained in the GAN latent space. In this paper, we propose ClusterGAN as a new mechanism for clustering using GANs. By sampling latent variables from a mixture of one-hot encoded variables and continuous latent variables, coupled with an inverse network (which projects the data to…
Generative Adversarial Networks are a new family of generative models, frequently used for generating photorealistic images. The theory promises for the GAN to eventually reach an equilibrium where generator produces pictures indistinguishable for the training set. In practice, however, a range of problems frequently prevents the system from reaching this equilibrium, with training not progressing ahead due to instabilities or mode collapse. This paper describes a series of experiments trying to identify patterns in regard to the effect of the training set on the dynamics and eventual outcome …
Building performance discrepancies between building design and operation are one of the causes that lead many new designs fail to achieve their goals and objectives. One of main factors contributing to the discrepancy is occupant behaviors. Occupants responding to a new design are influenced by several factors. Existing building performance models (BPMs) ignore or partially address those factors (called contextual factors) while developing BPMs. To potentially reduce the discrepancies and improve the prediction accuracy of BPMs, this paper proposes a computational framework for learning mixtur…
University of Copenhagen（哥本哈根大学）；IT University of Copenhagen（哥本哈根信息技术大学）
Generative Adversial Networks (GANs) have made a major impact in computer vision and machine learning as generative models. Wasserstein GANs (WGANs) brought Optimal Transport (OT) theory into GANs, by minimizing the $1$-Wasserstein distance between model and data distributions as their objective function. Since then, WGANs have gained considerable interest due to their stability and theoretical framework. We contribute to the WGAN literature by introducing the family of $(q,p)$-Wasserstein GANs, which allow the use of more general $p$-Wasserstein metrics for $p\geq 1$ in the GAN learning proce…
Generative Adversarial Networks (GANs) represent a promising class of generative networks that combine neural networks with game theory. From generating realistic images and videos to assisting musical creation, GANs are transforming many fields of arts and sciences. However, their application to healthcare has not been fully realized, more specifically in generating electronic health records (EHR) data. In this paper, we propose a framework for exploring the value of GANs in the context of continuous laboratory time series data. We devise an unsupervised evaluation method that measures the pr…
Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objective function through an adversarial game between a family of generators and a family of discriminators. In this paper, we offer a better theoretical understanding of GANs by analyzing some of their mathematical and statistical properties. We study the deep connection between the adversarial principle …
Hong Kong University of Science and Technology（香港科技大学）
Generative Adversarial Nets (GAN) have received considerable attention since the 2014 groundbreaking work by Goodfellow et al. Such attention has led to an explosion in new ideas, techniques and applications of GANs. To better understand GANs we need to understand the mathematical foundation behind them. This paper attempts to provide an overview of GANs from a mathematical point of view. Many students in mathematics may find the papers on GANs more difficulty to fully understand because most of them are written from computer science and engineer point of view. The aim of this paper is to give…
Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative model) and a discriminator (a teacher providing training signal) that each minimize their own cost. GANs are designed to reach a Nash equilibrium at which each player cannot reduce their cost without changing the other players' parameters. One useful approach for the theory of GANs is to show that a divergence between the training distribution and the model distr…
Generative adversarial networks are a novel method for statistical inference that have achieved much empirical success; however, the factors contributing to this success remain ill-understood. In this work, we attempt to analyze generative adversarial learning -- that is, statistical inference as the result of a game between a generator and a discriminator -- with the view of understanding how it differs from classical statistical inference solutions such as maximum likelihood inference and the method of moments. Specifically, we provide a theoretical characterization of the distribution infer…
Facebook AI Research（Facebook人工智能研究）；UC Berkeley（加州大学伯克利分校）
Unconditional image generation has recently been dominated by generative adversarial networks (GANs). GAN methods train a generator which regresses images from random noise vectors, as well as a discriminator that attempts to differentiate between the generated images and a training set of real images. GANs have shown amazing results at generating realistic looking images. Despite their success, GANs suffer from critical drawbacks including: unstable training and mode-dropping. The weaknesses in GANs have motivated research into alternatives including: variational auto-encoders (VAEs), latent …
Generative adversarial networks (GANs) are a class of deep generative models which aim to learn a target distribution in an unsupervised fashion. While they were successfully applied to many problems, training a GAN is a notoriously challenging task and requires a significant number of hyperparameter tuning, neural architecture engineering, and a non-trivial amount of "tricks". The success in many practical applications coupled with the lack of a measure to quantify the failure modes of GANs resulted in a plethora of proposed losses, regularization and normalization schemes, as well as neural …
Insilico Medicine（英矽智能）；National Research University Higher School of Economics（俄罗斯国立高等经济研究大学）
Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard Gaussian distribution as a prior. Previous works show that the richer family of prior distributions may help to avoid the mode collapse problem in GANs and to improve the evidence lower bound in VAEs. We propose a new family of prior distributions---Tensor Ring Induced Prior (TRIP)---that packs an exponential number of Gaussians into a high-dimensional lattice …
Generative adversarial networks (GANs) are neural networks that learn data distributions through adversarial training. In intensive studies, recent GANs have shown promising results for reproducing training images. However, in spite of noise, they reproduce images with fidelity. As an alternative, we propose a novel family of GANs called noise robust GANs (NR-GANs), which can learn a clean image generator even when training images are noisy. In particular, NR-GANs can solve this problem without having complete noise information (e.g., the noise distribution type, noise amount, or signal-noise …
Generative Adversarial Networks (GANs) are a powerful class of generative models. Despite their successes, the most appropriate choice of a GAN network architecture is still not well understood. GAN models for image synthesis have adopted a deep convolutional network architecture, which eliminates or minimizes the use of fully connected and pooling layers in favor of convolution layers in the generator and discriminator of GANs. In this paper, we demonstrate that a convolution network architecture utilizing deep fully connected layers and pooling layers can be more effective than the tradition…
Generative Adversarial Networks (GANs) became very popular for generation of realistically looking images. In this paper, we propose to use GANs to synthesize artificial financial data for research and benchmarking purposes. We test this approach on three American Express datasets, and show that properly trained GANs can replicate these datasets with high fidelity. For our experiments, we define a novel type of GAN, and suggest methods for data preprocessing that allow good training and testing performance of GANs. We also discuss methods for evaluating the quality of generated data, and their…
In this note, we point out a basic link between generative adversarial (GA) training and binary classification -- any powerful discriminator essentially computes an (f-)divergence between real and generated samples. The result, repeatedly re-derived in decision theory, has implications for GA Networks (GANs), providing an alternative perspective on training f-GANs by designing the discriminator loss function.
Generative Adversarial Networks (GANs) have shown great promise in modeling high dimensional data. The learning objective of GANs usually minimizes some measure discrepancy, \textit{e.g.}, $f$-divergence~($f$-GANs) or Integral Probability Metric~(Wasserstein GANs). With $f$-divergence as the objective function, the discriminator essentially estimates the density ratio, and the estimated ratio proves useful in further improving the sample quality of the generator. However, how to leverage the information contained in the discriminator of Wasserstein GANs (WGAN) is less explored. In this paper, …
In recent years, unsupervised/weakly-supervised conditional generative adversarial networks (GANs) have achieved many successes on the task of modeling and generating data. However, one of their weaknesses lies in their poor ability to separate, or disentangle, the different factors that characterize the representation encoded in their latent space. To address this issue, we propose a novel structure for unsupervised conditional GANs powered by a novel Information Compensation Connection (IC-Connection). The proposed IC-Connection enables GANs to compensate for information loss incurred during…
We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, resolving the longstanding problem that no provably convergent algorithm exists for general GANs. We then propose a principled procedure to reduce our novel prox methods to simple sampling routines, leading to practically efficient algorithms. Finally, we provide experimental evidenc…
University of Technology Sydney（悉尼科技大学）；The University of Sydney（悉尼大学）；Southern University of Science and Technology（南方科技大学）；University of Birmingham（伯明翰大学）
Generative adversarial networks (GAN) have been effective for learning generative models for real-world data. However, existing GANs (GAN and its variants) tend to suffer from training problems such as instability and mode collapse. In this paper, we propose a novel GAN framework called evolutionary generative adversarial networks (E-GAN) for stable GAN training and improved generative performance. Unlike existing GANs, which employ a pre-defined adversarial objective function alternately training a generator and a discriminator, we utilize different adversarial training objectives as mutation…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；Massachusetts Institute of Technology（麻省理工学院）；University of California Santa Barbara（加州大学圣巴巴拉分校）
We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable $m$-step stochastic numerical integrators. We introduce different formulations and training methods for learning models of stochastic dynamics based on observation of trajectory samples. We develop approaches using discriminators based on Maximum Mean Discrepancy (MMD), training protocols using conditional and marginal distributions, and methods for learning…
As the success of Generative Adversarial Networks (GANs) on natural images quickly propels them into various real-life applications across different domains, it becomes more and more important to clearly understand their limitations. Specifically, understanding GANs' capability across the full spectrum of spatial frequencies, i.e. beyond the low-frequency dominant spectrum of natural images, is critical for assessing the reliability of GAN generated data in any detail-sensitive application (e.g. denoising, filling and super-resolution in medical and satellite images). In this paper, we show th…
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Calico Life Sciences（加利科生命科学）
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our framework, samples are generated by sampling components from component generators and feeding these components to a composition function which combines them into a "composed sample". This compositional training approach improves the modularity, extensibility and interpretability of Generative Adversarial Networks (GANs) - providing a principled way to incrementally c…
Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when learning the generator. We propose a novel algorithm that repeats the density ratio estimation and f-divergence minimization. Our algorithm offers a new perspective toward the understanding of GANs and is able to make use of multiple viewpoints obtained in the research of density ratio estimation, e.g. what divergence is stable and relative density ratio is usefu…
College of Engineering, Cornell University（康奈尔大学工程学院）
This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming ta…
Generative Adversarial Networks (GANs) have become a widely popular framework for generative modelling of high-dimensional datasets. However their training is well-known to be difficult. This work presents a rigorous statistical analysis of GANs providing straight-forward explanations for common training pathologies such as vanishing gradients. Furthermore, it proposes a new training objective, Kernel GANs, and demonstrates its practical effectiveness on large-scale real-world data sets. A key element in the analysis is the distinction between training with respect to the (unknown) data distri…
Generative Adversarial Networks (GANs) have achieved remarkable results in the task of generating realistic natural images. In most successful applications, GAN models share two common aspects: solving a challenging saddle point optimization problem, interpreted as an adversarial game between a generator and a discriminator functions; and parameterizing the generator and the discriminator as deep convolutional neural networks. The goal of this paper is to disentangle the contribution of these two factors to the success of GANs. In particular, we introduce Generative Latent Optimization (GLO), …
We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which…
