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The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…

Generative adversarial network (GAN) has become one of the most important neural network models for classical unsupervised machine learning. A variety of discriminator loss functions have been developed to train GAN's discriminators and…

We propose discriminative adversarial networks (DAN) for semi-supervised learning and loss function learning. Our DAN approach builds upon generative adversarial networks (GANs) and conditional GANs but includes the key differentiator of…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

This paper studies generative adversarial networks (GANs) from the perspective of statistical inference. A GAN is a popular machine learning method in which the parameters of two neural networks, a generator and a discriminator, are…

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the…

Generative adversarial networks are the state of the art approach towards learned synthetic image generation. Although early successes were mostly unsupervised, bit by bit, this trend has been superseded by approaches based on labelled…

We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein…

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to…

We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every…

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…

The aim of this paper is to prove the exponential convergence, local and global, of Adam algorithm under precise conditions on the parameters, when the objective function lacks differentiability. More precisely, we require Lipschitz…

We introduce the notion of conditional Lipschitz shadowing, which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain…

Generating images from natural language is one of the primary applications of recent conditional generative models. Besides testing our ability to model conditional, highly dimensional distributions, text to image synthesis has many…

Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…

Generative adversarial networks (GANs) are unsupervised learning methods for training a generator distribution to produce samples that approximate those drawn from a target distribution. Many such methods can be formulated as minimization…

Generative adversarial networks (GANs) are so complex that the existing learning theories do not provide a satisfactory explanation for why GANs have great success in practice. The same situation also remains largely open for deep neural…

The relaxation function is the cornerstone to perform calculations in weakly driven processes. Properties that such a function should obey are already established, but the difficulty in its calculation is still an issue to be overcome. In…

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several…