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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…

Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…

Conditional Generative Adversarial Networks are known to be difficult to train, especially when the conditions are continuous and high-dimensional. To partially alleviate this difficulty, we propose a simple generator regularization term on…

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…

We deconstruct the performance of GANs into three components: 1. Formulation: we propose a perturbation view of the population target of GANs. Building on this interpretation, we show that GANs can be viewed as a generalization of the…

Generative Adversarial Networks (GANs) have become a very popular tool for implicitly learning high-dimensional probability distributions. Several improvements have been made to the original GAN formulation to address some of its…

We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle…

Image inpainting is a restoration method that reconstructs missing image parts. However, a carefully selected mask of known pixels that yield a high quality inpainting can also act as a sparse image representation. This challenging spatial…

Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…

Training generative adversarial networks (GANs) on high quality (HQ) images involves important computing resources. This requirement represents a bottleneck for the development of applications of GANs. We propose a transfer learning…

We propose to improve unconditional Generative Adversarial Networks (GAN) by training the self-supervised learning with the adversarial process. In particular, we apply self-supervised learning via the geometric transformation on input…

This paper presents a novel method for accelerating path planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of the free…

This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…

While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent works have shown that they suffer from lack of diversity or mode collapse. The theoretical work…

In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally…

Generative adversarial networks are a class of generative algorithms that have been widely used to produce state-of-the-art samples. In this paper, we investigate GAN to perform anomaly detection on time series dataset. In order to achieve…

Suffering from the extreme training data imbalance between seen and unseen classes, most of existing state-of-the-art approaches fail to achieve satisfactory results for the challenging generalized zero-shot learning task. To circumvent the…

We study the inverse optimal control problem in social sciences: we aim at learning a user's true cost function from the observed temporal behavior. In contrast to traditional phenomenological works that aim to learn a generative model to…

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…

Learning generative models is challenging for a network edge node with limited data and computing power. Since tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from the cloud or…